TM 663 Operations Planning September 12, 2011 Paula Jensen

TM 663 Operations Planning September 12, 2011 Paula Jensen
2nd Session: Chapter 2: Inventory Control From EOQ to ROP

Agenda Chapter 2: Inventory Control From EOQ to ROP

Tentative Schedule Chapters Assigned 8/29/2011 0,1 9/5/2011 Holiday
8/29/ ,1 9/5/2011 Holiday 9/12/ 9/19/ , 3 9/26/ , 5 10/3/2011 6, 7 10/10/2011 Holiday 10/17/2011 Exam 1 10/24/ ,9 10/31/2011 9,10 11/7/ , 12 11/14/ , 14 Chapters Assigned 11/21/2011 Exam 2 11/28/ p: 1-3 12/5/ p:1-4, 17 p1 12/13/2011 Final 18, 19 Not covered We may rearrange a bit. We could skip chapter 11 &12 and do 18 &19

Inventory Control There is a trade-off between set-ups and inventory.
There is a trade-off between customer service and inventory There is a trade-off between variability and inventory

The EOQ Model To a pessimist, the glass is half empty.
to an optimist, it is half full. – Anonymous

EOQ History Introduced in 1913 by Ford W. Harris, “How Many Parts to Make at Once” Interest on capital tied up in wages, material and overhead sets a maximum limit to the quantity of parts which can be profitably manufactured at one time; “set-up” costs on the job fix the minimum. Experience has shown one manager a way to determine the economical size of lots. Early application of mathematical modeling to Scientific Management

MedEquip Example Small manufacturer of medical diagnostic equipment.
Purchases standard steel “racks” into which components are mounted. Metal working shop can produce (and sell) racks more cheaply if they are produced in batches due to wasted time setting up shop. MedEquip doesn’t want to tie up too much precious capital in inventory. Question: how many racks should MedEquip order at once?

EOQ Modeling Assumptions
1. Production is instantaneous – there is no capacity constraint and the entire lot is produced simultaneously. 2. Delivery is immediate – there is no time lag between production and availability to satisfy demand. 3. Demand is deterministic – there is no uncertainty about the quantity or timing of demand. 4. Demand is constant over time – in fact, it can be represented as a straight line, so that if annual demand is 365 units this translates into a daily demand of one unit. 5. A production run incurs a fixed setup cost – regardless of the size of the lot or the status of the factory, the setup cost is constant. 6. Products can be analyzed singly – either there is only a single product or conditions exist that ensure separability of products.

Notation D demand rate (units per year) c unit production cost, not counting setup or inventory costs (dollars per unit) A fixed or setup cost to place an order (dollars) h holding cost (dollars per year); if the holding cost is consists entirely of interest on money tied up in inventory, then h = ic where i is an annual interest rate. Q the unknown size of the order or lot size decision variable

Inventory vs Time in EOQ Model
Q/D 2Q/D 3Q/D 4Q/D Time

Costs Holding Cost: Setup Costs: A per lot, so
Production Cost: c per unit Cost Function:

MedEquip Example Costs
D = 1000 racks per year c = $250 A = $500 (estimated from supplier’s pricing) h = (0.1)($250) + $10 = $35 per unit per year

Costs in EOQ Model

Economic Order Quantity
EOQ Square Root Formula MedEquip Solution

EOQ Modeling Assumptions
1. Production is instantaneous – there is no capacity constraint and the entire lot is produced simultaneously. 2. Delivery is immediate – there is no time lag between production and availability to satisfy demand. 3. Demand is deterministic – there is no uncertainty about the quantity or timing of demand. 4. Demand is constant over time – in fact, it can be represented as a straight line, so that if annual demand is 365 units this translates into a daily demand of one unit. 5. A production run incurs a fixed setup cost – regardless of the size of the lot or the status of the factory, the setup cost is constant. 6. Products can be analyzed singly – either there is only a single product or conditions exist that ensure separability of products. relax via EPL model

Notation – EPL Model D demand rate (units per year) P production rate (units per year), where P>D c unit production cost, not counting setup or inventory costs (dollars per unit) A fixed or setup cost to place an order (dollars) h holding cost (dollars per year); if the holding cost is consists entirely of interest on money tied up in inventory, then h = ic where i is an annual interest rate. Q the unknown size of the production lot size decision variable

Inventory vs Time in EPL Model
Production run of Q takes Q/P time units (P-D)(Q/P) -D P-D (P-D)(Q/P)/2 Inventory Time

Solution to EPL Model Annual Cost Function:
Solution (by taking derivative and setting equal to zero): setup holding production tends to EOQ as P otherwise larger than EOQ because replenishment takes longer

The Key Insight of EOQ Order Frequency: Inventory Investment:
There is a tradeoff between lot size and inventory Order Frequency: Inventory Investment:

EOQ Tradeoff Curve

Sensitivity of EOQ Model to Quantity
Optimal Unit Cost: Optimal Annual Cost: Multiply Y* by D and simplify, We neglect unit cost, c, since it does not affect Q*

Sensitivity of EOQ Model to Quantity (cont.)
Annual Cost from Using Q': Ratio: Example: If Q' = 2Q*, then the ratio of the actual to optimal cost is (1/2)[2 + (1/2)] = 1.25

Sensitivity of EOQ Model to Order Interval
Order Interval: Let T represent time (in years) between orders (production runs) Optimal Order Interval:

Sensitivity of EOQ Model to Order Interval (cont.)
Ratio of Actual to Optimal Costs: If we use T' instead of T* Powers-of-Two Order Intervals: The optimal order interval, T* must lie within a multiplicative factor of 2 of a “power-of-two.” Hence, the maximum error from using the best power-of-two is

The “Root-Two” Interval
divide by less than 2 to get to 2m multiply by less than 2 to get to 2m+1

Medequip Example Optimum: Q*=169, so T*=Q*/D =169/1000 years = 62 days
Round to Nearest Power-of-Two: 62 is between 32 and 64, but since 322=45.25, it is “closest” to 64. So, round to T’=64 days or Q’= T’D=(64/365)1000=175. Only 0.07% error because we were lucky and happened to be close to a power-of-two. But we can’t do worse than 6%.

Powers-of-Two Order Intervals
Order Interval Week

EOQ Takeaways Batching causes inventory (i.e., larger lot sizes translate into more stock). Under specific modeling assumptions the lot size that optimally balances holding and setup costs is given by the square root formula: Total cost is relatively insensitive to lot size (so rounding for other reasons, like coordinating shipping, may be attractive).

The Wagner-Whitin Model
Change is not made without inconvenience, even from worse to better. – Robert Hooker

EOQ Assumptions 1. Instantaneous production. 2. Immediate delivery. 3. Deterministic demand. 4. Constant demand. 5. Known fixed setup costs. 6. Single product or separable products. WW model relaxes this one

Dynamic Lot Sizing Notation
t a period (e.g., day, week, month); we will consider t = 1, … ,T, where T represents the planning horizon. Dt demand in period t (in units) ct unit production cost (in dollars per unit), not counting setup or inventory costs in period t At fixed or setup cost (in dollars) to place an order in period t ht holding cost (in dollars) to carry a unit of inventory from period t to period t +1 Qt the unknown size of the order or lot size in period t decision variables

Wagner-Whitin Example
Data Lot-for-Lot Solution

Wagner-Whitin Example (cont.)
Fixed Order Quantity Solution

Wagner-Whitin Property
Under an optimal lot-sizing policy either the inventory carried to period t+1 from a previous period will be zero or the production quantity in period t+1 will be zero.

Basic Idea of Wagner-Whitin Algorithm
By WW Property I, either Qt=0 or Qt=D1+…+Dk for some k. If jk* = last period of production in a k period problem then we will produce exactly Dk+…DT in period jk*. We can then consider periods 1, … , jk*-1 as if they are an independent jk*-1 period problem.

Wagner-Whitin Example
Step 1: Obviously, just satisfy D1 (note we are neglecting production cost, since it is fixed). Step 2: Two choices, either j2* = 1 or j2* = 2.

Step3: Three choices, j3* = 1, 2, 3.

Step 4: Four choices, j4* = 1, 2, 3, 4.

Planning Horizon Property
If jt*=t, then the last period in which production occurs in an optimal t+1 period policy must be in the set t, t+1,…t+1. In the Example: We produce in period 4 for period 4 of a 4 period problem. We would never produce in period 3 for period 5 in a 5 period problem.

Step 5: Only two choices, j5* = 4, 5. Step 6: Three choices, j6* = 4, 5, 6. And so on.

Wagner-Whitin Example Solution
Produce in period 1 for 1, 2, 3 ( = 80 units) Produce in period 4 for 4, 5, 6, 7 ( = 130 units) Produce in period 8 for 8, 9, 10 ( = 90 units

Wagner-Whitin Example Solution (cont.)
Optimal Policy: Produce in period 8 for 8, 9, 10 ( = 90 units) Produce in period 4 for 4, 5, 6, 7 ( = 130 units) Produce in period 1 for 1, 2, 3 ( = 80 units) Note: we produce in 7 for an 8 period problem, but this never comes into play in optimal solution.

Problems with Wagner-Whitin
1. Fixed setup costs. 2. Deterministic demand and production (no uncertainty) 3. Never produce when there is inventory (WW Property I). safety stock (don't let inventory fall to zero) random yields (can't produce for exact no. periods)

Statistical Reorder Point Models
When your pills get down to four, Order more. – Anonymous, from Hadley &Whitin

EOQ Assumptions EPL model relaxes this one 1. Instantaneous production. 2. Immediate delivery. 3. Deterministic demand. 4. Constant demand. 5. Known fixed setup costs. 6. Single product or separable products. lags can be added to EOQ or other models newsvendor and (Q,r) relax this one WW model relaxes this one can use constraint approach Chapter 17 extends (Q,r) to multiple product cases

Modeling Philosophies for Handling Uncertainty
1. Use deterministic model – adjust solution - EOQ to compute order quantity, then add safety stock - deterministic scheduling algorithm, then add safety lead time 2. Use stochastic model - news vendor model - base stock and (Q,r) models - variance constrained investment models

The Newsvendor Approach
Assumptions: 1. single period 2. random demand with known distribution 3. linear overage/shortage costs 4. minimum expected cost criterion Examples: newspapers or other items with rapid obsolescence Christmas trees or other seasonal items capacity for short-life products

Newsvendor Model Notation

Newsvendor Model Cost Function: Note: for any given
day, we will be either over or short, not both. But in expectation, overage and shortage can both be positive.

Newsvendor Model (cont.)
Optimal Solution: taking derivative of Y(Q) with respect to Q, setting equal to zero, and solving yields: Notes: Critical Ratio is probability stock covers demand 1 G(x) Q*

Newsvendor Example – T Shirts
Scenario: Demand for T-shirts is exponential with mean 1000 (i.e., G(x) = P(X  x) = 1- e-x/1000). (Note - this is an odd demand distribution; Poisson or Normal would probably be better modeling choices.) Cost of shirts is $10. Selling price is $15. Unsold shirts can be sold off at $8. Model Parameters: cs = 15 – 10 = $5 co = 10 – 8 = $2

Newsvendor Example – T Shirts (cont.)
Solution: Sensitivity: If co = $10 (i.e., shirts must be discarded) then

Newsvendor Model with Normal Demand
Suppose demand is normally distributed with mean  and standard deviation . Then the critical ratio formula reduces to: (z) z Note: Q* increases in both  and  if z is positive (i.e., if ratio is greater than 0.5).

Multiple Period Problems
Difficulty: Technically, Newsvendor model is for a single period. Extensions: But Newsvendor model can be applied to multiple period situations, provided: demand during each period is iid, distributed according to G(x) there is no setup cost associated with placing an order stockouts are either lost or backordered Key: make sure co and cs appropriately represent overage and shortage cost.

Example Scenario: Problem: how should they set order amounts?
GAP orders a particular clothing item every Friday mean weekly demand is 100, std dev is 25 wholesale cost is $10, retail is $25 holding cost has been set at $0.5 per week (to reflect obsolescence, damage, etc.) Problem: how should they set order amounts?

Example (cont.) Newsvendor Parameters: Solution: c0 = $0.5 cs = $15
Every Friday, they should order-up-to 146, that is, if there are x on hand, then order 146-x.

Newsvendor Takeaways Inventory is a hedge against demand uncertainty.
Amount of protection depends on “overage” and “shortage” costs, as well as distribution of demand. If shortage cost exceeds overage cost, optimal order quantity generally increases in both the mean and standard deviation of demand.

The (Q,r) Approach Assumptions: Decision Variables:
1. Continuous review of inventory. 2. Demands occur one at a time. 3. Unfilled demand is backordered. 4. Replenishment lead times are fixed and known. Decision Variables: Reorder Point: r – affects likelihood of stockout (safety stock). Order Quantity: Q – affects order frequency (cycle inventory).

Inventory vs Time in (Q,r) Model

Base Stock Model Assumptions
1. There is no fixed cost associated with placing an order. 2. There is no constraint on the number of orders that can be placed per year. That is, we can replenish one at a time (Q=1).

Base Stock Notation l = delivery lead time
Q = 1, order quantity (fixed at one) r = reorder point R = r +1, base stock level l = delivery lead time q = mean demand during l  = std dev of demand during l p(x) = Prob{demand during lead time l equals x} G(x) = Prob{demand during lead time l is less than x} h = unit holding cost b = unit backorder cost S(R) = average fill rate (service level) B(R) = average backorder level I(R) = average on-hand inventory level

Inventory Balance Equations
inventory position = on-hand inventory - backorders + orders Under Base Stock Policy inventory position = R

Inventory Profile for Base Stock System (R=5)

Service Level (Fill Rate)
Let: X = (random) demand during lead time l so E[X] = . Consider a specific replenishment order. Since inventory position is always R, the only way this item can stock out is if X  R. Expected Service Level:

Backorder Level Note: At any point in time, number of orders equals number demands during last l time units (X) so from our previous balance equation: R = on-hand inventory - backorders + orders on-hand inventory - backorders = R - X Note: on-hand inventory and backorders are never positive at the same time, so if X=x, then Expected Backorder Level: simpler version for spreadsheet computing

Inventory Level Observe: Result: on-hand inventory - backorders = R-X
E[X] =  from data E[backorders] = B(R) from previous slide Result: I(R) = R -  + B(R)

Base Stock Example q = 10 units (per month) Assume Poisson demand, so
l = one month q = 10 units (per month) Assume Poisson demand, so Note: Poisson demand is a good choice when no variability data is available.

Base Stock Example Calculations

Base Stock Example Results
Service Level: For fill rate of 90%, we must set R-1= r =14, so R=15 and safety stock s = r- = 4. Resulting service is 91.7%. Backorder Level: B(R) = B(15) = 0.103 Inventory Level: I(R) = R -  + B(R) = = 5.103

“Optimal” Base Stock Levels
Objective Function: Y(R) = hI(R) + bB(R) = h(R-+B(R)) + bB(R) = h(R- ) + (h+b)B(R) Solution: if we assume G is continuous, we can use calculus to get holding plus backorder cost Implication: set base stock level so fill rate is b/(h+b). Note: R* increases in b and decreases in h.

Base Stock Normal Approximation
If G is normal(,), then where (z)=b/(h+b). So R* =  + z  Note: R* increases in  and also increases in  provided z>0.

“Optimal” Base Stock Example
Data: Approximate Poisson with mean 10 by normal with mean 10 units/month and standard deviation 10 = 3.16 units/month. Set h=$15, b=$25. Calculations: since (0.32) = 0.625, z=0.32 and hence R* =  + z = (3.16) =  11 Observation: from previous table fill rate is G(10) = 0.583, so maybe backorder cost is too low.

Inventory Pooling Situation: Specialized Inventory:
n different parts with lead time demand normal(, ) z=2 for all parts (i.e., fill rate is around 97.5%) Specialized Inventory: base stock level for each item =  + 2  total safety stock = 2n  Pooled Inventory: suppose parts are substitutes for one another lead time demand is normal (n ,n ) base stock level (for same service) = n +2 n  ratio of safety stock to specialized safety stock = 1/ n cycle stock safety stock

Effect of Pooling on Safety Stock
Conclusion: cycle stock is not affected by pooling, but safety stock falls dramatically. So, for systems with high safety stock, pooling (through product design, late customization, etc.) can be an attractive strategy.

Pooling Example PC’s consist of 6 components (CPU, HD, CD ROM, RAM, removable storage device, keyboard) 3 choices of each component: 36 = 729 different PC’s Each component costs $150 ($900 material cost per PC) Demand for all models is Poisson distributed with mean 100 per year Replenishment lead time is 3 months (0.25 years) Use base stock policy with fill rate of 99%

Pooling Example - Stock PC’s
Base Stock Level for Each PC:  = 100  0.25 = 25, so using Poisson formulas, G(R-1)  R = 38 units On-Hand Inventory for Each PC: I(R) = R -  + B(R) = = units Total On-Hand Inventory :  729  $900 = $8,538,358

Pooling Example - Stock Components
729 models of PC 3 types of each comp. Necessary Service for Each Component: S = (0.99)1/6 = Base Stock Level for Components: = (100  729/3)0.25 = 6075, so G(R-1)  R = 6306 On-Hand Inventory Level for Each Component: I(R) = R -  + B(R) = = units Total On-Hand Inventory :  18  $150 = $623,798 93% reduction!

Base Stock Insights Reorder points control prob of stockouts by establishing safety stock. To achieve a given fill rate, the required base stock level (and hence safety stock) is an increasing function of mean and (provided backorder cost exceeds shortage cost) std dev of demand during replenishment lead time. The “optimal” fill rate is an increasing in the backorder cost and a decreasing in the holding cost. We can use either a service constraint or a backorder cost to determine the appropriate base stock level. Base stock levels in multi-stage production systems are very similar to kanban systems and therefore the above insights apply. Base stock model allows us to quantify benefits of inventory pooling.

The Single Product (Q,r) Model
Motivation: Either 1. Fixed cost associated with replenishment orders and cost per backorder. 2. Constraint on number of replenishment orders per year and service constraint. Objective: Under (1) As in EOQ, this makes batch production attractive.

Summary of (Q,r) Model Assumptions
One-at-a-time demands. Demand is uncertain, but stationary over time and distribution is known. Continuous review of inventory level. Fixed replenishment lead time. Constant replenishment batch sizes. Stockouts are backordered.

(Q,r) Notation

(Q,r) Notation (cont.) Decision Variables: Performance Measures:

Inventory and Inventory Position for Q=4, r=4
uniformly distributed between r+1=5 and r+Q=8

Costs in (Q,r) Model Fixed Setup Cost: AF(Q)
Stockout Cost: kD(1-S(Q,r)), where k is cost per stockout Backorder Cost: bB(Q,r) Inventory Carrying Costs: cI(Q,r)

Fixed Setup Cost in (Q,r) Model
Observation: since the number of orders per year is D/Q,

Stockout Cost in (Q,r) Model
Key Observation: inventory position is uniformly distributed between r+1 and r+Q. So, service in (Q,r) model is weighted sum of service in base stock model. Result: Note: this form is easier to use in spreadsheets because it does not involve a sum.

Service Level Approximations
Type I (base stock): Type II: Note: computes number of stockouts per cycle, underestimates S(Q,r) Note: neglects B(r,Q) term, underestimates S(Q,r)

Backorder Costs in (Q,r) Model
Key Observation: B(Q,r) can also be computed by averaging base stock backorder level function over the range [r+1,r+Q]. Result: Notes: 1. B(Q,r) B(r) is a base stock approximation for backorder level. 2. If we can compute B(x) (base stock backorder level function), then we can compute stockout and backorder costs in (Q,r) model.

Inventory Costs in (Q,r) Model
Approximate Analysis: on average inventory declines from Q+s to s+1 so Exact Analysis: this neglects backorders, which add to average inventory since on-hand inventory can never go below zero. The corrected version turns out to be

Inventory vs Time in (Q,r) Model
Expected Inventory Actual Inventory Exact I(Q,r) = Approx I(Q,r) + B(Q,r) s+Q Inventory r Approx I(Q,r) s+1=r-+1 Time

Expected Inventory Level for Q=4, r=4, q=2

(Q,r) Model with Backorder Cost
Objective Function: Approximation: B(Q,r) makes optimization complicated because it depends on both Q and r. To simplify, approximate with base stock backorder formula, B(r):

Results of Approximate Optimization
Assumptions: Q,r can be treated as continuous variables G(x) is a continuous cdf Results: Note: this is just the EOQ formula Note: this is just the base stock formula if G is normal(,), where (z)=b/(h+b)

(Q,r) Example D = 14 units per year c = $150 per unit
Stocking Repair Parts: D = 14 units per year c = $150 per unit h = 0.1 × = $25 per unit l = 45 days q = (14 × 45)/365 = units during replenishment lead time A = $10 b = $40 Demand during lead time is Poisson

Values for Poisson(q) Distribution
95

Calculations for Example

Performance Measures for Example

Observations on Example
Orders placed at rate of 3.5 per year Fill rate fairly high (90.4%) Very few outstanding backorders (0.049 on average) Average on-hand inventory just below 3 (2.823)

Varying the Example Change: suppose we order twice as often so F=7 per year, then Q=2 and: which may be too low, so increase r from 2 to 3: This is better. For this policy (Q=2, r=4) we can compute B(2,3)=0.026, I(Q,r)=2.80. Conclusion: this has higher service and lower inventory than the original policy (Q=4, r=2). But the cost of achieving this is an extra 3.5 replenishment orders per year.

(Q,r) Model with Stockout Cost
Objective Function: Approximation: Assume we can still use EOQ to compute Q* but replace S(Q,r) by Type II approximation and B(Q,r) by base stock approximation:

Results of Approximate Optimization
Assumptions: Q,r can be treated as continuous variables G(x) is a continuous cdf Results: Note: this is just the EOQ formula Note: another version of base stock formula (only z is different) if G is normal(,), where (z)=kD/(kD+hQ)

Backorder vs. Stockout Model
Backorder Model when real concern is about stockout time because B(Q,r) is proportional to time orders wait for backorders useful in multi-level systems Stockout Model when concern is about fill rate better approximation of lost sales situations (e.g., retail) Note: We can use either model to generate frontier of solutions Keep track of all performance measures regardless of model B-model will work best for backorders, S-model for stockouts

Lead Time Variability Problem: replenishment lead times may be variable, which increases variability of lead time demand. Notation: L = replenishment lead time (days), a random variable l = E[L] = expected replenishment lead time (days) L = std dev of replenishment lead time (days) Dt = demand on day t, a random variable, assumed independent and identically distributed d = E[Dt] = expected daily demand D = std dev of daily demand (units)

Including Lead Time Variability in Formulas
Standard Deviation of Lead Time Demand: Modified Base Stock Formula (Poisson demand case): if demand is Poisson Inflation term due to lead time variability Note:  can be used in any base stock or (Q,r) formula as before. In general, it will inflate safety stock.

Single Product (Q,r) Insights
Basic Insights: Safety stock provides a buffer against stockouts. Cycle stock is an alternative to setups/orders. Other Insights: 1. Increasing D tends to increase optimal order quantity Q. 2. Increasing q tends to increase the optimal reorder point. (Note: either increasing D or l increases q.) 3. Increasing the variability of the demand process tends to increase the optimal reorder point (provided z > 0). 4. Increasing the holding cost tends to decrease the optimal order quantity and reorder point.

3rd Session: Chapter 2: Inventory Control From EOQ to ROP continued Chapter 3:The MRP Crusade

Material Requirements Planning (MRP)
Unlike many other approaches and techniques, material requirements planning “works” which is its best recommendation. – Joseph Orlicky, 1974

History Begun around 1960 as computerized approach to purchasing and production scheduling. Joseph Orlicky, Oliver Wight, and others. APICS launched “MRP Crusade” in 1972 to promote MRP.

Key Insight Independent Demand – finished products
Dependent Demand – components It makes no sense to independently forecast dependent demands.

Assumptions 1. Known deterministic demands. 2. Fixed, known production leadtimes. 3. Infinite capacity. Idea is to “back out” demand for components by using leadtimes and bills of material.

MRP Procedure 1. Netting: net requirements against projected inventory 2. Lot Sizing: planned order quantities 3. Time Phasing: planned orders backed out by leadtime 4. BOM Explosion: gross requirements for components

Inputs Master Production Schedule (MPS): due dates and quantities for all top level items Bills of Material (BOM): for all parent items Inventory Status: (on hand plus scheduled receipts) for all items Planned Leadtimes: for all items

Example - Stool Indented BOM Graphical BOM Stool Base (1) Legs (4)
Bolts (2) Seat (1) Stool Level 0 Base (1) Seat (1) Level 1 Legs (4) Bolts (4) Bolts (2) Level 2 Note: bolts are treated at lowest level in which they occur for MRP calcs. Actually, they might be left off BOM altogether in practice.

Example

Example (cont.) BOM explosion

Terminology Level Code: lowest level on any BOM on which part is found
Planning Horizon: should be longer than longest cumulative leadtime for any product Time Bucket: units planning horizon is divided into Lot-for-Lot: batch sizes equal demands (other lot sizing techniques, e.g., EOQ or Wagner-Whitin can be used) Pegging: identify gross requirements with next level in BOM (single pegging) or customer order (full pegging) that generated it. Single usually used because full is difficult due to lot-sizing, yield loss, safety stocks, etc.

More Terminology Firm Planned Orders (FPO’s): planned order that the MRP system does not automatically change when conditions change – can stabilize system Service Parts: parts used in service and maintenance – must be included in gross requirements Order Launching: process of releasing orders to shop or vendors – may include inflation factor to compensate for shrinkage Exception Codes: codes to identify possible data inaccuracy (e.g., dates beyond planning horizon, exceptionally large or small order quantities, invalid part numbers, etc.) or system diagnostics (e.g., orders open past due, component delays, etc.)

Lot Sizing in MRP Lot-for-lot – “chase” demand
Fixed order quantity method – constant lot sizes EOQ – using average demand Fixed order period method – use constant lot intervals Part period balancing – try to make setup/ordering cost equal to holding cost Wagner-Whitin – “optimal” method

Lot Sizing Example Wagner-Whitin: $560 Lot-for-Lot: $1000
Note: WW is “optimal” given this objective.

Lot Sizing Example (cont.)
Fixed Order Quantity (using EOQ):

Lot Sizing Example (cont.)
Fixed Order Period (FOP): 3 periods

Nervousness Note: we are using FOP lot-sizing rule.

Nervousness Example (cont.)
* Past Due Note: Small reduction in requirements caused large change in orders and made schedule infeasible.

Reducing Nervousness Reduce Causes of Plan Changes:
Stabilize MPS (e.g., frozen zones and time fences) Reduce unplanned demands by incorporating spare parts forecasts into gross requirements Use discipline in following MRP plan for releases Control changes in safety stocks or leadtimes Alter Lot-Sizing Procedures: Fixed order quantities at top level Lot for lot at intermediate levels Fixed order intervals at bottom level Use Firm Planned Orders: Planned orders that do not automatically change when conditions change Managerial action required to change a FPO

Handling Change New order in MPS Order completed late Scrap loss
Causes of Change: New order in MPS Order completed late Scrap loss Engineering changes in BOM Responses to Change: Regenerative MRP: completely re-do MRP calculations starting with MPS and exploding through BOMs. Net Change MRP: store material requirements plan and alter only those parts affected by change (continuously on-line or batched daily). Comparison: Regenerative fixes errors. Net change responds faster but must be regenerated periodically.

Rescheduling Top Down Planning: use MRP system with changes (e.g., altered MPS or scheduled receipts) to recompute plan can lead to infeasibilities (exception codes) Orlicky suggested using minimum leadtimes bottom line is that MPS may be infeasible Bottom Up Replanning: use pegging and firm planned orders to guide rescheduling process pegging allows tracing of release to sources in MPS FPO’s allow fixing of releases necessary for firm customer orders compressed leadtimes (expediting) are often used to justify using FPO’s to override system leadtimes

Safety Stocks and Safety Leadtimes
generate net requirements to ensure min level of inventory at all times used as hedge against quantity uncertainties (e.g., yield loss) Safety Leadtimes: inflate production leadtimes in part record used as hedge against time uncertainty (e.g., delivery delays)

Safety Stock Example Note: safety stock level is 20.

Safety Stock vs. Safety Leadtime

Safety Stock vs. Safety Leadtime (cont.)

Manufacturing Resource Planning (MRP II)
Sometime called MRP, in contrast with mrp (“little” mrp); more recent implementations are called ERP (Enterprise Resource Planning). Extended MRP into: Master Production Scheduling (MPS) Rough Cut Capacity Planning (RCCP) Capacity Requirements Planning (CRP) Production Activity Control (PAC)

MRP II Planning Hierarchy
Demand Forecast Resource Planning Aggregate Production Planning Rough-cut Capacity Planning Master Production Scheduling Bills of Material Material Requirements Planning Inventory Status Job Pool Capacity Requirements Planning Job Release Routing Data Job Dispatching

Master Production Scheduling (MPS)
MPS drives MRP Should be accurate in near term (firm orders) May be inaccurate in long term (forecasts) Software supports forecasting order entry netting against inventory Frequently establishes a “frozen zone” in MPS

Rough Cut Capacity Planning (RCCP)
Quick check on capacity of key resources Use Bill of Resource (BOR) for each item in MPS Generates usage of resources by exploding MPS against BOR (offset by leadtimes) Infeasibilities addressed by altering MPS or adding capacity (e.g., overtime)

Capacity Requirements Planning (CRP)
Uses routing data (work centers and times) for all items Explodes orders against routing information Generates usage profile of all work centers Identifies overload conditions More detailed than RCCP No provision for fixing problems Leadtimes remain fixed despite queueing

Production Activity Control (PAC)
Sometimes called “shop floor control” Provides routing/standard time information Sets planned start times Can be used for prioritizing/expediting Can perform input-output control (compare planned with actual throughput) Modern term is MES (Manufacturing Execution System), which represents functions between Planning and Control.

Enterprise Resources Planning
SCM BPR MRP MRP II ERP Goal: link information across entire enterprise: manufacturing distribution accounting financial personnel IT

“Integrated” ERP Approach
Advantages: integrated functionality consistent user interfaces integrated database single vendor and contract unified architecture unified product support Disadvantages: incompatibility with existing systems long and expensive implementation incompatibility with existing management practices loss of flexibility to use tactical point systems long product development and implementation cycles long payback period lack of technological innovation

Other Planning Tools Manufacturing Execution Systems (MES):
automated implementation of shop floor control data tracking (WIP, yield, quality, etc.) merging with ERP? Advanced Planning Systems (APS): algorithms for performing specific functions finite capacity scheduling, forecasting, available to promise, demand management, warehouse management, distribution, etc. partnerships between developers and ERP vendors

Conclusions Insight: distinction between independent and dependent demands Advantages: General approach Supports planning hierarchy (MRP II, ERP) Problems: Assumptions – especially infinite capacity Cultural factors – e.g., data accuracy, training, etc. Focus – authority delegated to computer

Chapter 4: From the JIT Revolution to Lean Manufacturing Chapter 5: What Went Wrong?

Agenda Airplanes Factory Physics
Chapter 4: From the JIT Revolution to Lean Chapter 5: What Went Wrong (New Assignment Chapter 4 Study Questions: 4,5,6,7 Chapter 5 Study Questions: 2,3,4,6 )

Just In Time (JIT) I tip my hat to the new constitution
Take a bow for the new revolution Smile and grin at the change all around Pick up my guitar and play Just like yesterday Then I get on my knees and pray WE DON'T GET FOOLED AGAIN! –The Who

Origins of JIT Japanese firms, particularly Toyota, in 1970's and 1980's Taiichi Ohno and Shigeo Shingo Geographical and cultural roots Japanese objectives “catch up with America” (within 3 years of 1945) small lots of many models Japanese motivation Japanese domestic production in 1949 – 25,622 trucks, 1,008 cars American to Japanese productivity ratio – 9:1 Era of “slow growth” in 1970's

Toyota Production System
Pillars: 1. just-in-time, and 2. autonomation, or automation with a human touch Practices: setup reduction (SMED) worker training vendor relations quality control foolproofing (baka-yoke) many others

Supermarket Stimulus Customers get only what they need
Stock replenished quickly But, who holds inventory?

Auto-Activated Loom Stimulus
Automatically detect problems and shut down Foolproofing Automation with a human touch

Zero Inventories Metaphorical Writing: – Shingo 1990 – Ohno 1988
The Toyota production wrings water out of towels that are already dry. There is nothing more important than planting “trees of will”. – Shingo 1990 5W = 1H – Ohno 1988 Platonic Ideal: Zero Inventories connotes a level of perfection not ever attainable in a production process. However, the concept of a high level of excellence is important because it stimulates a quest for constant improvement through imaginative attention to both the overall task and to the minute details. – Hall 1983

The Seven Zeros Zero Defects: To avoid delays due to defects. (Quality at the source) Zero (Excess) Lot Size: To avoid “waiting inventory” delays. (Usually stated as a lot size of one.) Zero Setups: To minimize setup delay and facilitate small lot sizes. Zero Breakdowns: To avoid stopping tightly coupled line. Zero (Excess) Handling: To promote flow of parts. Zero Lead Time: To ensure rapid replenishment of parts (very close to the core of the zero inventories objective). Zero Surging: Necessary in system without WIP buffers.

The Environment as a Control
Constraints or Controls? machine setup times vendor deliveries quality levels (scrap, rework) production schedule (e.g. customer due dates) product designs Impact: the manufacturing system can be made much easier to manage by improving the environment.

Implementing JIT Production Smoothing:
relatively constant volumes relatively constant product mix Mixed Model Production (heijunka): 10,000 per month (20 working days) 500 per day (2 shifts) 250 per shift (480 minutes) 1 unit every 1.92 minutes

Implementing JIT (cont.)
Production Sequence: Mix of 50% A, 25% B, 25% C in daily production of 500 units 0.5  500 = units of A 0.25  500 = 125 units of B 0.25  500 = 125 units of C A – B – A – C – A – B – A – C – A – B – A – C – A – B – A – C …

Inherent Inflexibility of JIT
Sources of Inflexibility: Stable volume Stable mix Precise sequence Rapid (instant?) replenishment Measures to Promote Flexibility: Capacity buffers Setup reduction Cross training Plant layout

Capacity Buffers Problems: Buffer Capacity:
JIT is intrinsically rigid (volume, mix, sequence) No explicit link between production and customers How to deal with quota shortfalls Buffer Capacity: Protection against quota shortfalls Regular flow allows matching against customer demands Two shifting: 4 – 8 – 4 – 8 Contrast with WIP buffers found in MRP systems

Setup Reduction Motivation: Small lot sequences not feasible with large setups. Internal vs. External Setups: External – performed while machine is still running Internal – performed while machine is down Approach: 1. Separate the internal setup from the external setup 2. Convert as much as possible of the internal setup to the external setup 3. Eliminate the adjustment process 4. Abolish the setup itself (e.g., uniform product design, combined production, parallel machines)

Cross Training Adds flexibility to inherently inflexible system
Allows capacity to float to smooth flow Reduces boredom Fosters appreciation for overall picture Increase potential for idea generation

Workforce Agility Cross-Trained Workers: Shared Tasks:
float where needed appreciate line-wide perspective provide more heads per problem area Shared Tasks: can be done by adjacent stations reduces variability in tasks, and hence line stoppages/quality problems

Plant Layout Promote flow with little WIP
Facilitate workers staffing multiple machines U-shaped cells Maximum visibility Minimum walking Flexible in number of workers Facilitates monitoring of work entering and leaving cell Workers can conveniently cooperate to smooth flow and address problems

Layout for JIT Cellular Layout: Advanced Material Handling:
Proximity for flow control, material handling, floating labor, etc. May require duplication of machinery (decreased utilization?) logical cells? Advanced Material Handling: Avoid large transfer batches Close coordination of physically separate operations Inbound Stock Outbound Stock

Focused Factories Pareto Analysis: Dedicated Lines:
Small percentage of sku’s represent large percentage of volume Large percentage of sku’s represent little volume but much complexity Dedicated Lines: for families of high runners few setups little complexity Job Shop Environment: for low runners many setups poorer performance, but only on smaller portion of business Saw Lathe Mill Drill Saw Mill Drill Paint Stores Assembly Warehouse Grind Mill Drill Paint Weld Grind Lathe Drill Saw Grind Paint Stores Lathe Assembly Warehouse Mill Drill

Total Quality Management
Origins: Americans (Shewhart, Deming, Juran, Feigenbaum) Fertility of Japan: Japanese abhorrence for wasting scarce resources The Japanese innate resistance to specialists (including QA) Integrality to JIT: JIT requires high quality to work JIT promotes high quality identification of problems facilitates rapid detection of problems pressure to improve quality

Total Quality Management (cont.)
Techniques: Process Control (SPC) Easy-to-See Quality Insistence on Compliance (quality first, output second) Line Stop Correcting One's Own Errors (no rework loops) 100 Percent Check (not statistical sampling) Continual Improvement Housekeeping Small Lots Vendor Certification Total Preventive Maintenance

Kanban Definition: A “kanban” is a sign-board or card in Japanese and is the name of the flow control system developed by Toyota. Role: Kanban is a tool for realizing just-in-time. For this tool to work fairly well, the production process must be managed to flow as much as possible. This is really the basic condition. Other important conditions are leveling production as much as possible and always working in accordance with standard work methods. – Ohno 1988 Push vs. Pull: Kanban is a “pull system” Push systems schedule releases Pull systems authorize releases

One-Card Kanban Outbound stockpoint Outbound stockpoint Production
Completed parts with cards enter outbound stockpoint. Production cards When stock is removed, place production card in hold box. Production card authorizes start of work.

Two-Card Kanban Inbound stockpoint Outbound stockpoint
Move stock to inbound stock point. Move card authorizes pickup of parts. When stock is removed, place production card in hold box. Remove move card and place in hold box. Production cards Move cards Production card authorizes start of work.

MRP versus Kanban MRP … Kanban … … Kanban Signals Full Containers
Lover Level Inven-tory … Assem-bly Kanban Lover Level Inven-tory … Assem-bly … Kanban Signals Full Containers

Motorola won the 1988 Malcolm Baldridge Quality Award
Goodbye JIT, Hello Lean In 1990 lean appeared in The Machine That Changed the World (Womack, Jones, Roos) Lean is a neater package than JIT; it focuses on flow, the value stream, and elimination of waste. Lean became the rage. Lean appears to be more successful than JIT in achieving results. SixSigma appeared in at Motorola as a method of creating radically better products 4.5 PPM Motorola won the 1988 Malcolm Baldridge Quality Award ABB, GE, Allied Signal, and Kodak have big successes

The Lessons of JIT/Lean
The production environment itself is a control Operational details matter strategically Controlling WIP is important Speed and flexibility are important assets Quality can come first Continual improvement is a condition for survival

Key Insights of TQM/SixSigma
Quality and Logistics must be improved together “If you don’t have time to do it right, when will you find time to do it over.” Variability must be identified and reduced Determine the root cause Eliminate the root cause

What Went Wrong? Look ma, the emperor has no clothes!
– Hans Christian Andersen Our task is not to fix the blame for the past, but to fix the course for the future. – John F. Kennedy

American Manufacturing Trouble in 1980s
Slowdown in productivity growth Severe decline in market share in various markets Widespread perception of inferior quality Persistently large trade deficit

Causes Cultural factors Governmental policies Poor product design
Marketing mistakes Counterproductive financial strategies Poor operations management

Management Tools Quantitative Methods Material Requirements Planning
inventory scheduling plant layout facility location Material Requirements Planning Just-in-Time

Trouble with Quantitative Methods
Cultural Factors: The frontier ethic – best and brightest shun OM Faith in the scientific method – emphasis on mathematical precision Combined Effect: Top management out of OM loop Sophisticated techniques for narrower and narrower problems

EOQ Unrealistic Assumptions: Ill Effects: fixed, known setup cost
constant, deterministic demand instantaneous delivery single product or no product interactions Ill Effects: Inefficiency in lot-sizing Wasted effort in trying to fit model Myopic perspective about lot-sizing Missed importance of setup reduction Missed value of splitting move lots

Scheduling 2 & 3 machine min makespan problem (Johnson 1954)
Virtually no applications Mathematically challenging Hundreds of follow-on papers At this time, it appears that one research paper (that by Johnson) set a wave of research in motion that devoured scores of person-years of research time on an intractable problem of little practical consequence. – Dudek Panwalkar, Smith, 1992

OM Trends Engineering Courses: became virtually math courses
Management Courses: anecdotal case studies Calls for Changes: Strategic importance of operational details OM is technical We need a science of manufacturing

Trouble with MRP MRP Successes: But …
Number of MRP systems in America grew from a handful in the early 1960's, to 150 in 1971 APICS MRP Crusade in 1972 spurred number of MRP systems in the U.S. as high as 8000 In 1984, 16 companies sold $400 million in MRP software In 1989, $1.2 billion worth of MRP software was sold to American industry, constituting just under one-third of the entire American market for computer services By late 1990’s, ERP was a $10 billion industry (ERP consulting even bigger); SAP was world’s fourth largest software company But …

Surveys of MRP Users 1980 Survey of Over 1,100 Firms:
much less than 10% of U.S. and European companies recoup MRP investment within two years 1982 Survey of 679 APICS Members: 9.5% regarded their companies as being Class A users 60% reported their firms as being Class C or Class D users This from an APICS survey of materials managers 1986 Survey of 33 S. Carolina MRP Users: Similar responses to 1982 survey Average eventual investment in hardware, software, personnel, and training for an MRP system was $795,000 with a standard deviation of $1,191,000

APICS Explanations 1. Lack of top management commitment, 2. Lack of education of those who use the system, 3. An unrealistic master production schedule, 4. Inaccurate data, including bills of material and inventory records.

The Fundamental Flaw of MRP
… an MRP system is capacity-insensitive, and properly so, as its function is to determine what materials and components will be needed and when, in order to execute a given master production schedule. There can be only one correct answer to that, and it cannot therefore vary depending on what capacity does or does not exist. – Orlicky 1975 But, lead times do depend on loading when capacity is finite Incentive to inflate leadtimes Result is increased congestion, increased WIP, decreased customer service

Historical Interpretation of MRP
MRP is the quintessential American production control system When Scientific Management (developed here) met the computer (developed here), MRP was the result Unfortunately, the computer that Scientific Management met was a computer of the 1960's Insufficient RAM to process parts simultaneously Fixed leadtimes allow transaction based system

MRP Patches MRP II provides planning hierarchy and data management features CRP is the sin of MRP repeated over and over Approaches like closed-loop MRP either: wait for WIP explosion to modify releases, or fail to consider PAC in plan ERP extended MRP to supply chains but did not by itself change underlying paradigm Can MES save MRP? wide variety of commercial approaches to MES interface between planning and execution still critical

Trouble With JIT $64,000 Question: Is JIT a system, and, if so, is it transportable? Answers: “Unquestionably” and “Yes” –Schonberger, Hall, Monden “Maybe not” and “To a limited extent” –Hayes Conjecture: JIT is a system of beliefs, but a collection of methods

Romantic versus Pragmatic JIT
Romantic JIT: An aesthetic ideal Simplicity in the extreme Almost trivial to implement Phrased in stirring rhetoric Pragmatic JIT: setup time reduction (SMED) plant layout (e.g., U-shaped cells) quality-control preventive maintenance design for manufacturability many others

Mortals Emulating Genius
Persistence: Toyota took 25 years to reduce setups from 2-3 hours to 3 minutes. Environmental Factors: Harder to address than direct procedures. Some people imagine that Toyota has put on a smart new set of clothes, the kanban system, so they go out and purchase the same outfit and try it on. They quickly discover that they are much too fat to wear it. – Shingo Prioritization: Systems view is first thing to get lost. Deliberate obfuscation? If the U.S. had understood what Toyota was doing, it would have been no good for us. – Ohno

A Matter of Perspective
Policies conflict Romantic JIT bans the t-word (Schonberger) Japanese originators creatively balanced objectives subtly, implicitly pursued policies across functions context-specific procedures Dangers of lack of perspective management by slogan inventory is the root of all evil water and rocks analogy effort wasted on chubchiks (e.g., unnecessary setup reduction) failure to coordinate efforts (e.g., cells running large batches of parts)

3rd Edition Updates were not in the slides in August
Trends in Manufacturing 6s an improvement methodology w/ training program Lean philosophy promotes the right incentives IT (SCM and ERP) provide data to make decisions MISSING A SCIENTIFIC FRAMEWORK relationships of between cycle time, production rate, utilization, inventory, WIP, capacity, variability in demand, variability in manufacturing process

Business Process Re-engineering
Systems Analysis applied to Management “the fundamental rethinking and radical redesign of business practices to achieve dramatic improvements in critical, contemporary measures of performance, such as cost, quality, service, and speed. Most resign schemes included eliminating jobs, so it was associated with downsizing Revolutionary aspect paved the way for ERP, which required restructuring manufacturing processes to fit software.

Lean Manufacturing Uses value stream mapping (VSM): a variation of process flow mapping. It has problems: No exact definition of “value-added” Value-added time is so short is does not offer a reasonable target for a cycle time VSM does not provide a means of diagnosing causes of long cycle times VSM collects capacity and demand data, but does not compute utilization No feasibility check for a “future state”.

Six Sigma (6s) Emphasizes the experimental aspect of the scientific method Define Measure Analyze Improve Control Story about 6s students ignoring Factory Physics training

Where from Here? Problems with Traditional Approaches: Reality:
OM (quantitative methods) has stressed math over realism MRP is fundamentally flawed, in the basics, not the details JIT is a collection of methods and slogans, not a system Reality: manufacturing is large scale, complex, and varied continual improvement is essential no “technological silver bullet” can save us

Where from Here? A Science of Manufacturing... What Can We Hope For?
Better Education basics intuition synthesis Better Tools descriptive models prescriptive models integrated framework A Science of Manufacturing...

ENGM 663 Paula Jensen Chapter 6: A Science of Manufacturing Chapter 7: Basic Factory Dynamics

Agenda Factory Physics
Chapter 6: A Science of Manufacturing (From 2nd Ed) Chapter 7: Basic Factory Dynamics (New Assignment Chapter 6: Problem 1 Chapter 7: Problems 5, 8, 10) Test 1 Study Guide

Objectives, Measures, and Controls
I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but have scarcely, in your thoughts, advanced to the stage of Science, whatever the matter may be. – Lord Kelvin

Why a Science of Manufacturing?
Confusion in Industry: too many “revolutions” management by buzzword sales glitz over substance Confusion in Academia: high-powered methodology applied to non-problems huge variation in what is taught Example of Other Fields: Civil Engineering–statics, dynamics Electrical Engineering – electricity and magnetism Many others

Automobile Design Requirements: Can we do it? Answer:
Mass of car of 1000 kg Acceleration of 2.7 meters per second squared (zero to 60 in seconds) Engine with no more than 200 Newtons of force Can we do it? Answer: No way! F = ma 200 Nt  (1000 kg) (2.7 m/s2) = 2,700 Nt.

? Factory Design Requirements: Can we do it? Answer:
3000 units per day, with a lead time of not greater than 10 days, and with a service level (percent of jobs that finish on time) of at least 90%. Can we do it? Answer: ? Who knows?

Factory Tradeoff Curves

Goals of a Science of Manufacturing
Tools: descriptive models prescriptive models solution techniques Terminology: rationalize buzzwords recognize commonalities across environments Perspective: basics intuition synthesis

The Nature of Science Purpose: Steps:
The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypothesis or axioms. --- Albert Einstein Steps: 1. Observation. 2. Classification. 3. Theoretical Conjecture. 4. Experimental verification/refutation. 5. Repeat.

Systems Analysis Definition: Systems analysis is a structured approach to problem-solving that involves 1. Identification of objectives (what you want to accomplish), measures (for comparing alternatives), and controls (what you can change). 2. Generation of specific alternatives. 3. Modeling (some form of abstraction from reality to facilitate comparison of alternatives). 4. Optimization (at least to the extent of ranking alternatives and choosing “best” one). 5. Iteration (going back through the process as new facets arise).

System Analysis Paradigm
REAL WORLD OPERATIONS ANALYSIS ANALOG WORLD Conjecture Objectives Verify constraints Identify Alternatives Choose Measures of Effectiveness Specify Parameters and Controls Model Interactions Verify & Validate Model SYSTEMS DESIGN Compare Alternatives Choose Policies Ask “What If” Questions Compare Controls Optimize Control Levels Sensitivity Analysis Implement Policies Train Users Fine Tune System IMPLEMENTATION EVALUATION Evaluate System Performance Look For Oversights Identify Future Opportunities Validate Model Predictions Question Assumptions Identify Other Controls

General Measures and Objectives
Fundamental Objective: elementary starting point source of agreement example - make money over the long-term Hierarchy of Objectives: more basic objectives that support fundamental objective closer to improvement policies Tradeoffs:objectives conflict we need models

Hierarchical Objectives
High Profitability Low Costs High Sales Low Unit Costs Quality Product High Customer Service High Throughput High Utilization Low Inventory Fast Response Many products Less Variability Short Cycle Times Low Utilization High Inventory More Variability

Corporate Measures and Objectives
Fundamental Objective: Maximize the wealth and well-being of the stakeholders over the long term. Financial Performance Measures: 1. Net-profit. 2. Return on investment. Components: 1. Revenue. 2. Expenses. 3. Assets.

Plant Measures and Objectives
Throughput: product that is high quality and is sold. Costs: Operating budget of plant. Assets: Capital equipment and WIP. Objectives: Maximize profit. Minimize unit costs. Tradeoffs: we would like (but can’t always have) Throughput Cost Assets

Systems Analysis Tools
Process Mapping: identify main sequence of activities highlight bottlenecks clarify critical connections across business systems Workshops: structured interaction between various parties many methods: Nominal Group Technique, Delphi, etc. roles of moderator and provocateur are critical

Systems Analysis Tools (cont.)
Conjecture and Refutation: promotes group ownership of ideas places critical thinking in a constructive mode everyday use of the scientific method Modeling: always done with specific purpose value of model is its usefulness modeling is an iterative process

The Need for Process Mapping
Example: North American Switch Manufacturer week leadtimes in spite of dramatically reduced factory cycle times: 10% Sales 15% Order Entry 15% Order Coding 20% Engineering 10% Order Coding 15% Scheduling 5% Premanufacturing and Manufacturing 10% Delivery and Prep Conclusion: Lead time reduction must address entire value delivery system.

Process Mapping Activities
Purpose: understand current system by identifying main sequence of activities highlighting bottlenecks clarifying critical connections across business system Types of Maps: Assembly Flowchart: diagram of activities to assembly product. Process Flowchart: diagram of how pieces of system interrelate in an organization. Relationship Map: diagram of specific steps to accomplish a task, without indication of functions or subsystems. Cross-Functional Process Map: diagram of specific steps to accomplish a task organized by function or subsystem responsible for the step.

Sample Assembly Flowchart
CELL 1 START PANASERT 1050 ROBOT 1100 ROBOT 1150 ROBOT 1200 CIM FLEX 1250 ROBOT 1300 ROBOT 1350 ROBOT 1375 ROBOT 1380 SOLDER STATION 1000 DECODER SINGULATION ROBOT 1500 RECEIVER SINGULATION ROBOT 1750 LASER TRIM 1775 CELL 2 EOL TEST 1550 LEGEND UNIX CELL CONTROLLER TEST BAY

Process Flowchart for Order Entry
Receive Customer Order Form Generate Standard Layout Plan Customer Approval? No Yes Review Plan/Lists Generate Parts Lists Approval? No Yes Enter Parts Lists into System End of Bucket? No Yes Generate Cutting Orders

Sample Relationship Map
Operating departments make independent decision Production Control - controls work flow Customers Warehouse Production control Salesmen Order Processing Production Scheduling Design Fabricating Finishing Shipping Salesman controls the order processing and design flow

Sample Cross-Functional Process Map
Field Offices Customer needs observed Field support needs reviewed Field support planned Market opportunity defined New product evaluated Price and distribution options reviewed Price point set Roll-out planned Marketing New product concept floated New product prototype developed Engineering Final product engineered Process feasibility review and cost estimating Tooling and capacity planned Production readiness planned Manufacturing Production TIME

Conclusions Science of Manufacturing: Systems Approach: Modeling:
important for practice provides a structure for OM education Systems Approach: one of the most powerful engineering tools a key management skill as well (e.g., re-engineering) Modeling: part, but not all, of systems analysis key to a science of manufacturing more descriptive models are needed

Basic Factory Dynamics
Physics should be explained as simply as possible, but no simpler. – Albert Einstein

HAL Case Large Panel Line: produces unpopulated printed circuit boards
Line runs 24 hr/day (but 19.5 hrs of productive time) Recent Performance: throughput = 1,400 panels per day (71.8 panels/hr) WIP = 47,600 panels CT = 34 days (663 hr at 19.5 hr/day) customer service = 75% on-time delivery Is HAL lean? What data do we need to decide?

HAL - Large Panel Line Processes
Lamination (Cores): press copper and prepreg into core blanks Machining: trim cores to size Internal Circuitize: etch circuitry into copper of cores Optical Test and Repair (Internal): scan panels optically for defects Lamination (Composites): press cores into multiple layer boards External Circuitize: etch circuitry into copper on outside of composites Optical Test and Repair (External): scan composites optically for defects Drilling: holes to provide connections between layers Copper Plate: deposits copper in holes to establish connections Procoat: apply plastic coating to protect boards Sizing: cut panels into boards End of Line Test: final electrical test

HAL Case - Science? External Benchmarking Internal Benchmarking
but other plants may not be comparable Internal Benchmarking capacity data: what is utilization? but this ignores WIP effects Need relationships between WIP, TH, CT, service!

Definitions Workstations: a collection of one or more identical machines. Parts: a component, sub-assembly, or an assembly that moves through the workstations. End Items: parts sold directly to customers; relationship to constituent parts defined in bill of material. Consumables: bits, chemicals, gasses, etc., used in process but do not become part of the product that is sold. Routing: sequence of workstations needed to make a part. Order: request from customer. Job: transfer quantity on the line.

Definitions (cont.) Throughput (TH): for a line, throughput is the average quantity of good (non-defective) parts produced per unit time. Work in Process (WIP): inventory between the start and endpoints of a product routing. Raw Material Inventory (RMI): material stocked at beginning of routing. Crib and Finished Goods Inventory (FGI): crib inventory is material held in a stockpoint at the end of a routing; FGI is material held in inventory prior to shipping to the customer. Cycle Time (CT): time between release of the job at the beginning of the routing until it reaches an inventory point at the end of the routing.

Factory Physics® Definition: A manufacturing system is a goal-oriented network of processes through which parts flow. Structure: Plant is made up of routings (lines), which in turn are made up of processes. Focus: Factory Physics® is concerned with the network and flows at the routing (line) level.

Parameters Descriptors of a Line: 1) Bottleneck Rate (rb): Rate (parts/unit time or jobs/unit time) of the process center having the highest long-term utilization. 2) Raw Process Time (T0): Sum of the long-term average process times of each station in the line. 3) Congestion Coefficient (): A unitless measure of congestion. Zero variability case, a = 0. “Practical worst case,” a = 1. “Worst possible case,” a = W0. Note: we won’t use  quantitatively, but point it out to recognize that lines with same rb and T0 can behave very differently.

Parameters (cont.) Relationship: Critical WIP (W0): WIP level in which a line having no congestion would achieve maximum throughput (i.e., rb) with minimum cycle time (i.e., T0). W0 = rb T0

The Penny Fab Characteristics: Parameters:
Four identical tools in series. Each takes 2 hours per piece (penny). No variability. CONWIP job releases. Parameters: rb = T0 = W0 = a = 0.5 pennies/hour 8 hours 0.5  8 = 4 pennies 0 (no variability, best case conditions)

The Penny Fab

The Penny Fab (WIP=1) Time = 0 hours

Penny Fab Performance

TH vs. WIP: Best Case rb 1/T0 W0

CT vs. WIP: Best Case 1/rb T0 W0

Best Case Performance Best Case Law: The minimum cycle time (CTbest) for a given WIP level, w, is given by The maximum throughput (THbest) for a given WIP level, w is given by,

Best Case Performance (cont.)
Example: For Penny Fab, rb = 0.5 and T0 = 8, so W0 = 0.5  8 = 4, which are exactly the curves we plotted.

A Manufacturing Law Little's Law: The fundamental relation between WIP, CT, and TH over the long-term is: Insights: Fundamental relationship Simple units transformation Definition of cycle time (CT = WIP/TH)

Penny Fab Two 2 hr 5 hr 3 hr 10 hr

Penny Fab Two 0.5 0.4 0.6 0.67 0.4 p/hr 20 hr 8 pennies
rb = ____________ T0 = ____________ W0 = ____________

Penny Fab Two Simulation (Time=0)
2 2 hr 5 hr 3 hr 10 hr

7 4 2 hr 5 hr 3 hr 10 hr

7 6 9 2 hr 5 hr 3 hr 10 hr

7 8 9 2 hr 5 hr 3 hr 10 hr

17 12 8 9 2 hr 5 hr 3 hr 10 hr

17 12 10 9 2 hr 5 hr 3 hr 10 hr

17 19 12 10 14 2 hr 5 hr 3 hr 10 hr

17 19 12 12 14 2 hr 5 hr 3 hr 10 hr

17 19 17 22 14 14 2 hr 5 hr 3 hr 10 hr

17 19 17 22 16 19 24 2 hr 5 hr 3 hr 10 hr

17 19 17 22 19 24 2 hr 5 hr 3 hr 10 hr

27 19 22 22 20 19 24 2 hr 5 hr 3 hr 10 hr

27 29 22 22 20 24 24 22 2 hr 5 hr 3 hr 10 hr

27 Note: job will arrive at bottleneck just in time to prevent starvation. 29 22 22 22 24 24 22 2 hr 5 hr 3 hr 10 hr

27 29 27 32 25 24 24 24 2 hr 5 hr 3 hr Note: job will arrive at bottleneck just in time to prevent starvation. 10 hr

27 29 27 32 25 29 34 27 2 hr 5 hr 3 hr And so on…. Bottleneck will just stay busy; all others will starve periodically 10 hr

Worst Case Observation: The Best Case yields the minimum cycle time and maximum throughput for each WIP level. Question: What conditions would cause the maximum cycle time and minimum throughput? Experiment: set average process times same as Best Case (so rb and T0 unchanged) follow a marked job through system imagine marked job experiences maximum queueing

Worst Case Penny Fab Time = 0 hours

Worst Case Penny Fab Time = 32 hours Note: CT = 32 hours = 4 8 = wT0
TH = 4/32 = 1/8 = 1/T0

TH vs. WIP: Worst Case Best Case rb Worst Case 1/T0 W0

CT vs. WIP: Worst Case Worst Case Best Case T0 W0

Worst Case Performance
Worst Case Law: The worst case cycle time for a given WIP level, w, is given by, CTworst = w T0 The worst case throughput for a given WIP level, w, is given by, THworst = 1 / T0 Randomness? None - perfectly predictable, but bad!

Practical Worst Case Observation: There is a BIG GAP between the Best Case and Worst Case performance. Question: Can we find an intermediate case that: divides “good” and “bad” lines, and is computable? Experiment: consider a line with a given rb and T0 and: single machine stations balanced lines variability such that all WIP configurations (states) are equally likely

PWC Example – 3 jobs, 4 stations
clumped up states spread out states

Practical Worst Case Let w = jobs in system, N = no. stations in line, and t = process time at all stations: CT(single) = (1 + (w-1)/N) t CT(line) = N [1 + (w-1)/N] t = Nt + (w-1)t = T0 + (w-1)/rb TH = WIP/CT = [w/(w+W0-1)]rb From Little’s Law

Practical Worst Case Performance
Practical Worst Case Definition: The practical worst case (PWC) cycle time for a given WIP level, w, is given by, The PWC throughput for a given WIP level, w, is given by, where W0 is the critical WIP.

TH vs. WIP: Practical Worst Case
Best Case rb PWC Good (lean) Bad (fat) Worst Case 1/T0 W0

CT vs. WIP: Practical Worst Case
PWC Bad (fat) Best Case Good (lean) T0 W0

Penny Fab Two Performance
Note: process times in PF2 have var equal to PWC. But… unlike PWC, it has unbalanced line and multi machine stations. Best Case rb Penny Fab 2 Practical Worst Case 1/T0 Worst Case W0

Penny Fab Two Performance (cont.)
Worst Case Practical Worst Case Penny Fab 2 1/rb T0 Best Case W0

Back to the HAL Case - Capacity Data

HAL Case - Situation Critical WIP: rbT0 = 114  33.9 = 3,869
Actual Values: CT = 34 days = 663 hours (at 19.5 hr/day) WIP = 47,600 panels TH = 71.8 panels/hour Conclusions: Throughput is 63% of capacity WIP is 12.3 times critical WIP CT is 24.1 times raw process time

HAL Case - Analysis Conclusion: actual system is much worse than PWC!
TH Resulting from PWC with WIP = 47,600? Much higher than actual TH! WIP Required for PWC to Achieve TH = 0.63rb? Much lower than actual WIP! Conclusion: actual system is much worse than PWC!

HAL Internal Benchmarking Outcome
“Lean" Region “Fat" Region

Labor Constrained Systems
Motivation: performance of some systems are limited by labor or a combination of labor and equipment. Full Flexibility with Workers Tied to Jobs: WIP limited by number of workers (n) capacity of line is n/T0 Best case achieves capacity and has workers in “zones” ample capacity case also achieves full capacity with “pick and run” policy

Labor Constrained Systems (cont.)
Full Flexibility with Workers Not Tied to Jobs: TH depends on WIP levels THCW(n)  TH(w)  THCW(w) need policy to direct workers to jobs (focus on downstream is effective) Agile Workforce Systems bucket brigades kanban with shared tasks worksharing with overlapping zones many others

Factory Dynamics Takeaways
Performance Measures: throughput WIP cycle time service Range of Cases: best case practical worst case worst case Diagnostics: simple assessment based on rb, T0, actual WIP,actual TH evaluate relative to practical worst case

TM 663 Operations Planning October 24, 2011 Paula Jensen
Chapter 8: Variability Basics Chapter 9: The Corrupting Influence of Variability

Agenda Paula’s Idea Factory Physics Chapter 8: Variability Basics
Chapter 9: The Corrupting Influence of Variability (New Assignment To be assigned later Chapter 8: Problem Chapter 9: Problems)

Variability Basics God does not play dice with the universe.
– Albert Einstein Stop telling God what to do. – Niels Bohr

Variability Makes a Difference!
Little’s Law: TH = WIP/CT, so same throughput can be obtained with large WIP, long CT or small WIP, short CT. The difference? Penny Fab One: achieves full TH (0.5 j/hr) at WIP=W0=4 jobs if it behaves like Best Case, but requires WIP=27 jobs to achieve 95% of capacity if it behaves like the Practical Worst Case. Why? Variability! Variability!

Tortise and Hare Example
Two machines: subject to same workload: 69 jobs/day (2.875 jobs/hr) subject to unpredictable outages (availability = 75%) Hare X19: long, but infrequent outages Tortoise 2000: short, but more frequent outages Performance: Hare X19 is substantially worse on all measures than Tortoise Why? Variability!

Variability Views Variability: Randomness:
Any departure from uniformity Random versus controllable variation Randomness: Essential reality? Artifact of incomplete knowledge? Management implications: robustness is key

Probabilistic Intuition
Uses of Intuition: driving a car throwing a ball mastering the stock market First Moment Effects: Throughput increases with machine speed Throughput increases with availability Inventory increases with lot size Our intuition is good for first moments g

Probabilistic Intuition (cont.)
Second Moment Effects: Which is more variable – processing times of parts or batches? Which are more disruptive – long, infrequent failures or short frequent ones? Our intuition is less secure for second moments Misinterpretation – e.g., regression to the mean

Variability Definition: Variability is anything that causes the system to depart from regular, predictable behavior. Sources of Variability: setups • workpace variation machine failures • differential skill levels materials shortages • engineering change orders yield loss • customer orders rework • product differentiation operator unavailability • material handling

Measuring Process Variability
Note: we often use the “squared coefficient of variation” (SCV), ce2

Variability Classes in Factory Physics®
Low variability (LV) Moderate variability (MV) High variability (HV) Effective Process Times: actual process times are generally LV effective process times include setups, failure outages, etc. HV, LV, and MV are all possible in effective process times Relation to Performance Cases: For balanced systems MV – Practical Worst Case LV – between Best Case and Practical Worst Case HV – between Practical Worst Case and Worst Case ce 0.75 1.33

Measuring Process Variability – Example
Question: can we measure ce this way? Answer: No! Won’t consider “rare” events properly.

Natural Variability Definition: variability without explicitly analyzed cause Sources: operator pace material fluctuations product type (if not explicitly considered) product quality Observation: natural process variability is usually in the LV category.

Down Time – Mean Effects
Definitions:

Down Time – Mean Effects (cont.)
Availability: Fraction of time machine is up Effective Processing Time and Rate:

Totoise and Hare - Availability
Hare X19: t0 = 15 min 0 = 3.35 min c0 = 0 /t0 = 3.35/15 = 0.05 mf = 12.4 hrs (744 min) mr = hrs (248 min) cr = 1.0 Availability: Tortoise: t0 = 15 min 0 = 3.35 min c0 = 0 /t0 = 3.35/15 = 0.05 mf = 1.9 hrs (114 min) mr = hrs (38 min) cr = 1.0 A = A = No difference between machines in terms of availability.

Down Time – Variability Effects
Effective Variability: Conclusions: Failures inflate mean, variance, and CV of effective process time Mean (te) increases proportionally with 1/A SCV (ce2) increases proportionally with mr SCV (ce2) increases proportionally in cr2 For constant availability (A), long infrequent outages increase SCV more than short frequent ones Variability depends on repair times in addition to availability

Tortoise and Hare - Variability
Hare X19: te = ce2 = Tortoise 2000 te = ce2 = Hare X19 is much more variable than Tortoise 2000!

Setups – Mean and Variability Effects
Analysis:

Setups – Mean and Variability Effects (cont.)
Observations: Setups increase mean and variance of processing times. Variability reduction is one benefit of flexible machines. However, the interaction is complex.

Setup – Example Fast, inflexible machine – 2 hr setup every 10 jobs
Data: Fast, inflexible machine – 2 hr setup every 10 jobs Slower, flexible machine – no setups Traditional Analysis? No difference!

Setup – Example (cont.) Factory Physics® Approach: Compare mean and variance Fast, inflexible machine – 2 hr setup every 10 jobs

Setup – Example (cont.) Conclusion:
Slower, flexible machine – no setups Conclusion: Flexibility can reduce variability.

Setup – Example (cont.) New Machine: Consider a third machine same as previous machine with setups, but with shorter, more frequent setups Analysis: Conclusion: Shorter, more frequent setups induce less variability.

Other Process Variability Inflators
Sources: operator unavailability recycle batching material unavailability et cetera, et cetera, et cetera Effects: inflate te inflate ce Consequences: Effective process variability can be LV, MV,or HV.

Illustrating Flow Variability
Low variability arrivals t smooth! High variability arrivals t bursty!

Measuring Flow Variability

Propagation of Variability
ce2(i) Single Machine Station: where u is the station utilization given by u = rate Multi-Machine Station: where m is the number of (identical) machines and ca2(i) cd2(i) = ca2(i+1) i i+1 departure var depends on arrival var and process var

Propagation of Variability – High Utilization Station
HV LV HV LV LV HV Conclusion: flow variability out of a high utilization station is determined primarily by process variability at that station.

Propagation of Variability – Low Utilization Station
HV LV HV LV LV HV Conclusion: flow variability out of a low utilization station is determined primarily by flow variability into that station.

Variability Interactions
Importance of Queueing: manufacturing plants are queueing networks queueing and waiting time comprise majority of cycle time System Characteristics: Arrival process Service process Number of servers Maximum queue size (blocking) Service discipline (FCFS, LCFS, EDD, SPT, etc.) Balking Routing Many more

Kendall's Classification
A/B/C A: arrival process B: service process C: number of machines M: exponential (Markovian) distribution G: completely general distribution D: constant (deterministic) distribution. B A C Queue Server

Queueing Parameters ra = the rate of arrivals in customers (jobs) per unit time (ta = 1/ra = the average time between arrivals). ca = the CV of inter-arrival times. m = the number of machines. re = the rate of the station in jobs per unit time = m/te. ce = the CV of effective process times. u = utilization of station = ra/re. Note: a station can be described with 5 parameters.

Queueing Measures Measures: Relationships:
CTq = the expected waiting time spent in queue. CT = the expected time spent at the process center, i.e., queue time plus process time. WIP = the average WIP level (in jobs) at the station. WIPq = the expected WIP (in jobs) in queue. Relationships: CT = CTq + te WIP = ra  CT WIPq = ra  CTq Result: If we know CTq, we can compute WIP, WIPq, CT.

The G/G/1 Queue Formula: Observations:
Useful model of single machine workstations Separate terms for variability, utilization, process time. CTq (and other measures) increase with ca2 and ce2 Flow variability, process variability, or both can combine to inflate queue time. Variability causes congestion!

The G/G/m Queue Formula: Observations:
Useful model of multi-machine workstations Extremely general. Fast and accurate. Easily implemented in a spreadsheet (or packages like MPX).

VUT Spreadsheet basic data failures setups yield measures

Effects of Blocking VUT Equation:
characterizes stations with infinite space for queueing useful for seeing what will happen to WIP, CT without restrictions But real world systems often constrain WIP: physical constraints (e.g., space or spoilage) logical constraints (e.g., kanbans) Blocking Models: estimate WIP and TH for given set of rates, buffer sizes much more complex than non-blocking (open) models, often require simulation to evaluate realistic systems

The M/M/1/b Queue Model of Station 2 Note: there is room
for b=B+2 jobs in system, B in the buffer and one at each station. Infinite raw materials B buffer spaces Model of Station 2 Goes to u/(1-u) as b Always less than WIP(M/M/1) Goes to ra as b Always less than TH(M/M/1) Little’s law Note: u>1 is possible; formulas valid for u1

Blocking Example M/M/1/b system has less WIP and less TH
than M/M/1 system 18% less TH 90% less WIP

Seeking Out Variability
General Strategies: look for long queues (Little's law) look for blocking focus on high utilization resources consider both flow and process variability ask “why” five times Specific Targets: equipment failures setups rework operator pacing anything that prevents regular arrivals and process times

Variability Pooling Basic Idea: the CV of a sum of independent random variables decreases with the number of random variables. Example (Time to process a batch of parts):

Safety Stock Pooling Example
PC’s consist of 6 components (CPU, HD, CD ROM, RAM, removable storage device, keyboard) 3 choices of each component: 36 = 729 different PC’s Each component costs $150 ($900 material cost per PC) Demand for all models is normally distributed with mean 100 per year, standard deviation 10 per year Replenishment lead time is 3 months, so average demand during LT is  = 25 for computers and  = 25(729/3) = 6075 for components Use base stock policy with fill rate of 99%

Pooling Example - Stock PC’s
cycle stock Base Stock Level for Each PC: R =  + zs = ( 25) = 37 On-Hand Inventory for Each PC: I(R) = R -  + B(R)  R -  = zs = = 12 units Total (Approximate) On-Hand Inventory : 12 729  $900 = $7,873,200 safety stock

Pooling Example - Stock Components
Necessary Service for Each Component: S = (0.99)1/6 = zs = 2.93 Base Stock Level for Each Component: R =  + zs = ( 6075) = 6303 On-Hand Inventory Level for Each Component: I(R) = R -  + B(R)  R -  = zs = = 228 units Total Safety Stock: 228  18  $150 = $615,600 cycle stock safety stock 92% reduction!

Basic Variability Takeaways
Variability Measures: CV of effective process times CV of interarrival times Components of Process Variability failures setups many others - deflate capacity and inflate variability long infrequent disruptions worse than short frequent ones Consequences of Variability: variability causes congestion (i.e., WIP/CT inflation) variability propagates variability and utilization interact pooled variability less destructive than individual variability

The Corrupting Influence of Variability
When luck is on your side, you can do without brains. – Giordano Bruno,burned at the stake in 1600 The more you know the luckier you get. – “J.R. Ewing” of Dallas

Performance of a Serial Line
Measures: Throughput Inventory (RMI, WIP, FGI) Cycle Time Lead Time Customer Service Quality Evaluation: Comparison to “perfect” values (e.g., rb, T0) Relative weights consistent with business strategy? Links to Business Strategy: Would inventory reduction result in significant cost savings? Would CT (or LT) reduction result in significant competitive advantage? Would TH increase help generate significantly more revenue? Would improved customer service generate business over the long run? Remember – standards change over time!

Capacity Laws Capacity Law: In steady state, all plants will release work at an average rate that is strictly less than average capacity. Utilization Law: If a station increases utilization without making any other change, average WIP and cycle time will increase in a highly nonlinear fashion. Notes: Cannot run at full capacity (including overtime, etc.) Failure to recognize this leads to “fire fighting”

Cycle Time vs. Utilization

What Really Happens: System with Insufficient Capacity

What Really Happens: Two Cases with Releases at 100% of Capacity

What Really Happens: Two Cases with Releases at 82% of Capacity

Overtime Vicious Cycle
Release work at plant capacity. Variability causes WIP to increase. Jobs are late, customers complain,… Authorize one-time use of overtime. WIP falls, cycle times go down, backlog is reduced. Breathe sigh of relief. Go to Step 1!

Mechanics of Overtime Vicious Cycle

Influence of Variability
Variability Law: Increasing variability always degrades the performance of a production system. Examples: process time variability pushes best case toward worst case higher demand variability requires more safety stock for same level of customer service higher cycle time variability requires longer lead time quotes to attain same level of on-time delivery

Variability Buffering
Buffering Law: Systems with variability must be buffered by some combination of: 1. inventory 2. capacity 3. time. Interpretation: If you cannot pay to reduce variability, you will pay in terms of high WIP, under-utilized capacity, or reduced customer service (i.e., lost sales, long lead times, and/or late deliveries).

Variability Buffering Examples
Ballpoint Pens: can’t buffer with time (who will backorder a cheap pen?) can’t buffer with capacity (too expensive, and slow) must buffer with inventory Ambulance Service: can’t buffer with inventory (stock of emergency services?) can’t buffer with time (violates strategic objectives) must buffer with capacity Organ Transplants: can’t buffer with WIP (perishable) can’t buffer with capacity (ethically anyway) must buffer with time

Simulation Studies TH Constrained System (push)
1 2 3 4 ra, ca B(1)= te(1), ce(1) B(2)= te(2), ce(2) B(3)= te(3), ce(3) B(4)= te(4), ce(4) WIP Constrained System (pull) Infinite raw materials 1 2 3 4 te(1), ce(1) B(2) te(2), ce(2) B(3) te(3), ce(3) B(4) te(4), ce(4)

Variability in Push Systems
Notes: ra = 0.8, ca = ce(i) in all cases. B(i) = , i = 1-4 in all cases. Observations: TH is set by release rate in a push system. Increasing capacity (rb) reduces need for WIP buffering. Reducing process variability reduces WIP, CT, and CT variability for a given throughput level.

Variability in Pull Systems
Notes: Station 1 pulls in job whenever it becomes empty. B(i) = 0, i = 1, 2, 4 in all cases, except case 6, which has B(2) = 1.

Variability in Pull Systems (cont.)
Observations: Capping WIP without reducing variability reduces TH. WIP cap limits effect of process variability on WIP/CT. Reducing process variability increases TH, given same buffers. Adding buffer space at bottleneck increases TH. Magnitude of impact of adding buffers depends on variability. Buffering less helpful at non-bottlenecks. Reducing process variability reduces CT variability. Conclusion: consequences of variability are different in push and pull systems, but in either case the buffering law implies that you will pay for variability somehow.

Example – Discrete Parts Flowline
process buffer process buffer process Inventory Buffers: raw materials, WIP between processes, FGI Capacity Buffers: overtime, equipment capacity, staffing Time Buffers: frozen zone, time fences, lead time quotes Variability Reduction: smaller WIP & FGI , shorter cycle times

Example – Batch Chemical Process
reactor column reactor column reactor column tank tank Inventory Buffers: raw materials, WIP in tanks, finished goods Capacity Buffers: idle time at reactors Time Buffers: lead times in supply chain Variability Reduction: WIP is tightly constrained, so target is primarily throughput improvement, and maybe FGI reduction.

Example – Moving Assembly Line
in-line buffer fabrication lines final assembly line Inventory Buffers: components, in-line buffers Capacity Buffers: overtime, rework loops, warranty repairs Time Buffers: lead time quotes Variability Reduction: initially directed at WIP reduction, but later to achieve better use of capacity (e.g., more throughput)

Buffer Flexibility Buffer Flexibility Corollary: Flexibility reduces the amount of variability buffering required in a production system. Examples: Flexible Capacity: cross-trained workers Flexible Inventory: generic stock (e.g., assemble to order) Flexible Time: variable lead time quotes

Variability from Batching
VUT Equation: CT depends on process variability and flow variability Batching: affects flow variability affects waiting inventory Conclusion: batching is an important determinant of performance

Process Batch Versus Move Batch
Dedicated Assembly Line: What should the batch size be? Process Batch: Related to length of setup. The longer the setup the larger the lot size required for the same capacity. Move (transfer) Batch: Why should it equal process batch? The smaller the move batch, the shorter the cycle time. The smaller the move batch, the more material handling. Lot Splitting: Move batch can be different from process batch. 1. Establish smallest economical move batch. 2. Group batches of like families together at bottleneck to avoid setups. 3. Implement using a “backlog”.

Process Batching Effects
Types of Process Batching: 1. Serial Batching: processes with sequence-dependent setups “batch size” is number of jobs between setups batching used to reduce loss of capacity from setups 2. Parallel Batching: true “batch” operations (e.g., heat treat) “batch size” is number of jobs run together batching used to increase effective rate of process

Process Batching Process Batching Law: In stations with batch operations or significant changeover times: The minimum process batch size that yields a stable system may be greater than one. As process batch size becomes large, cycle time grows proportionally with batch size. Cycle time at the station will be minimized for some process batch size, which may be greater than one. Basic Batching Tradeoff: WIP versus capacity

Serial Batching Parameters: Time to process batch: te = kt + s ts k t0
setup t0 ra,ca forming batch queue of batches te = 10(1) + 5 = 15

Process Batching Effects (cont.)
Arrival rate of batches: ra/k Utilization: u = (ra/k)(kt + s) For stability: u < 1 requires ra = 0.4/10 = 0.04 u = 0.04(10·1+5) = 0.6 minimum batch size required for stability of system...

Process Batching Effects (cont.)
Average queue time at station: Average cycle time depends on move batch size: Move batch = process batch Move batch = 1 Note: we assume arrival CV of batches is ca regardless of batch size – an approximation... Note: splitting move batches reduces wait for batch time.

Cycle Time vs. Batch Size – 5 hr setup
Optimum Batch Sizes

Cycle Time vs. Batch Size – 2.5 hr setup
Optimum Batch Sizes

Setup Time Reduction Where? Steps:
Stations where capacity is expensive Excess capacity may sometimes be cheaper Steps: 1. Externalize portions of setup 2. Reduce adjustment time (guides, clamps, etc.) 3. Technological advancements (hoists, quick-release, etc.) Caveat: Don’t count on capacity increase; more flexibility will require more setups.

Parallel Batching Parameters: Time to form batch:
Time to process batch: te = t t ra,ca k W = ((10 – 1)/2)(1/0.005) = 90 forming batch queue of batches te = 90

Parallel Batching (cont.)
Arrival of batches: ra/k Utilization: u = (ra/k)(t) For stability: u < 1 requires ra/k = 0.05/10 = 0.005 u = (0.005)(90) = 0.45 minimum batch size required for stability of system... k > 0.05(90) = 4.5

Average wait-for-batch time: Average queue plus process time at station: Total cycle time: batch size affects both wait-for-batch time and queue time

Cycle Time vs. Batch Size in a Parallel Operation
queue time due to utilization wait for batch time Optimum Batch Size B

Variable Batch Sizes Observation: Waiting for full batch in parallel batch operation may not make sense. Could just process whatever is there when operation becomes available. Example: Furnace has space for 120 wrenches Heat treat requires 1 hour Demand averages 100 wrenches/hr Induction coil can heat treat 1 wrench in 30 seconds What is difference between performance of furnace and coil?

Variable Batch Sizes (cont.)
Furnace: Ignoring queueing due to variability Process starts every hour 100 wrenches in furnace 50 wrenches waiting on average 150 total wrenches in WIP CT = WIP/TH = 150/100 = 3/2 hr = 90 min Induction Coil: Capacity same as furnace (120 wrenches/hr), but CT = 0.5 min = hr WIP = TH × CT = 100 × = 0.83 wrenches Conclusion: Dramatic reduction in WIP and CT due to small batches—independent of variability or other factors. 100 50

Move Batching Move Batching Law: Cycle times over a segment of a routing are roughly proportional to the transfer batch sizes used over that segment, provided there is no waiting for the conveyance device. Insights: Basic Batching Tradeoff: WIP vs. move frequency Queueing for conveyance device can offset CT reduction from reduced move batch size Move batching intimately related to material handling and layout decisions

Move Batching Problem: Two machines in series
First machine receives individual parts at rate ra with CV of ca(1) and puts out batches of size k. First machine has mean process time of te(1) for one part with CV of ce(1). Second machine receives batches of k and put out individual parts. How does cycle time depend on the batch size k? te(1),ce(1) k ra,ca(1) te(2),ce(2) single job batch Station 1 Station 2

Move Batching Calculations
Time at First Station: Average time before batching is: Average time forming the batch is: Average time spent at the first station is: regular VUT equation... first part waits (k-1)(1/ra), last part doesn’t wait, so average is (k-1)(1/ra)/2

Move Batching Calculations (cont.)
Output of First Station: Time between output of individual parts into the batch is ta. Time between output of batches of size k is kta. Variance of interoutput times of parts is cd2(1)ta2, where Variance of batches of size k is kcd2(1)ta2. SCV of batch arrivals to station 2 is: because cd2(1)=d2/ta2 by def of CV because departures are independent, so variances add variance divided by mean squared...

Time at Second Station: Time to process a batch of size k is kte(2). Variance of time to process a batch of size k is kce2(2)te2(2). SCV for a batch of size k is: Mean time spent in partial batch of size k is: So, average time spent at the second station is: independent process times... first part doesn’t wait, last part waits (k-1)te(2), so average is (k-1)te(2)/2 VUT equation to compute queue time of batches...

Total Cycle Time: Insight: Cycle time increases with k. Inflation term does not involve CV’s Congestion from batching is more bad control than randomness. inflation factor due to move batching

Assembly Operations Assembly Operations Law: The performance of an assembly station is degraded by increasing any of the following: Number of components being assembled. Variability of component arrivals. Lack of coordination between component arrivals. Observations: This law can be viewed as special instance of variability law. Number of components affected by product/process design. Arrival variability affected by process variability and production control. Coordination affected by scheduling and shop floor control.

Attacking Variability
Objectives reduce cycle time increase throughput improve customer service Levers reduce variability directly buffer using inventory buffer using capacity buffer using time increase buffer flexibility

Cycle Time Definition (Station Cycle Time): The average cycle time at a station is made up of the following components: cycle time = move time + queue time + setup time process time + wait-to-batch time wait-in-batch time + wait-to-match time Definition (Line Cycle Time): The average cycle time in a line is equal to the sum of the cycle times at the individual stations less any time that overlaps two or more stations. delay times typically make up 90% of CT

Reducing Queue Delay CTq = V U t Reduce Variability
failures setups uneven arrivals, etc. Reduce Utilization arrival rate (yield, rework, etc.) process rate (speed, time, availability, etc)

Reducing Batching Delay
CTbatch = delay at stations + delay between stations Reduce Process Batching Optimize batch sizes Reduce setups Stations where capacity is expensive Capacity vs. WIP/CT tradeoff Reduce Move Batching Move more frequently Layout to support material handling (e.g., cells)

Reducing Matching Delay
CTbatch = delay due to lack of synchronization Reduce Variability on high utilization fabrication lines usual variability reduction methods Improve Coordination scheduling pull mechanisms modular designs Reduce Number of Components product redesign kitting

Increasing Throughput
TH = P(bottleneck is busy)  bottleneck rate Reduce Blocking/Starving buffer with inventory (near bottleneck) reduce system “desire to queue” Increase Capacity add equipment increase operating time (e.g. spell breaks) increase reliability reduce yield loss/rework CTq = V U t Reduce Variability Reduce Utilization Note: if WIP is limited, then system degrades via TH loss rather than WIP/CT inflation

Customer Service Elements of Customer Service:
lead time fill rate (% of orders delivered on-time) quality Law (Lead Time): The manufacturing lead time for a routing that yields a given service level is an increasing function of both the mean and standard deviation of the cycle time of the routing.

Improving Customer Service
LT = CT + z CT Reduce CT Visible to Customer delayed differentiation assemble to order stock components Reduce Average CT queue time batch time match time Reduce CT Variability generally same as methods for reducing average CT: improve reliability improve maintainability reduce labor variability improve quality improve scheduling, etc.

Cycle Time and Lead Time
CT = 10 CT = 3 CT = 10 CT = 6

Diagnostics Using Factory Physics®
Situation: Two machines in series; machine 2 is bottleneck ca2 = 1 Machine 1: Machine 2: Space at machine 2 for 20 jobs of WIP Desired throughput 2.4 jobs/hr, not being met

Diagnostic Example (cont.)
Proposal: Install second machine at station 2 Expensive Very little space Analysis Tools: Analysis: Step 1: At 2.4 job/hr CTq at first station is 645 minutes, average WIP is 25.8 jobs. CTq at second station is 892 minutes, average WIP is 35.7 jobs. Space requirements at machine 2 are violated! VUT equation propogation equation Ask why five times...

Step 2: Why is CTq at machine 2 so big? Break CTq into The min term is small. The correction term is moderate (u  ) The 3.16 correction is large. Step 3: Why is the correction term so large? Look at components of correction term. ce2 = 1.04, ca2 = 5.27. Arrivals to machine are highly variable.

Step 4: Why is ca2 to machine 2 so large? Recall that ca2 to machine 2 equals cd2 from machine 1, and ce2 at machine 1 is large. Step 5: Why is ce2 at machine 1 large? Effective CV at machine 1 is affected by failures, The inflation due to failures is large. Reducing MTTR at machine 1 would substantially improve performance.

Procoat Case – Situation
Problem: Current WIP around 1500 panels Desired capacity of 3000 panels/day (19.5 hr day with breaks/lunches) Typical output of 1150 panels/day Outside vendor being used to make up slack Proposal: Expose is bottleneck, but in clean room Expansion would be expensive Suggested alternative is to add bake oven for touchups

Procoat Case – Layout IN OUT Loader Clean Coat 1 Coat 2 Unloader
Touchup D&I Inspect Unloader Bake Develop Loader Manufacturing Inspect Expose Clean Room OUT

Procoat Case – Capacity Calculations
rb = 2,879 p/day T0 = 546 min = 0.47 days W0 = rbT0 = 1,343 panels

Procoat Case – Benchmarking
TH Resulting from PWC with WIP = 1,500: Conclusion: actual system is significantly worse than PWC. Higher than actual TH Question: what to do?

Procoat Case – Factory Physics® Analysis
Bottleneck Capacity - rate: - time: Bottleneck Starving - process variability: - flow variability: (Expose) operator training, setup reduction break spelling, shift changes reduces “desire to queue” so that clean room buffer is adequate operator training coater line – field ready replacements

Procoat Case – Outcome 3300 3000 Best Case 2700 "Good" Region After
2400 Practical Worst Case 2100 1800 TH (panels/day) "Bad" Region 1500 1200 Before 900 600 300 Worst Case -300 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 WIP (panels)

Corrupting Influence Takeaways
Variance Degrades Performance: many sources of variability planned and unplanned Variability Must be Buffered: inventory capacity time Flexibility Reduces Need for Buffering: still need buffers, but smaller ones

Corrupting Influence Takeaways (cont.)
Variability and Utilization Interact: congestion effects multiply utilization effects are highly nonlinear importance of bottleneck management Batching is an Important Source of Variability: process and move batching serial and parallel batching wait-to-batch time in addition to variability effects

Assembly Operations Magnify Impact of Variability: wait-to-match time caused by lack of synchronization Variability Propagates: flow variability is as disruptive as process variability non-bottlenecks can be major problems

TM 663 Operations Planning October 31, 2011 Paula Jensen
Chapter 9: The Corrupting Influence of Variability(continued) Chapter 10:Push & Pull Production Systems

Agenda Factory Physics (New Assignment Chapter 8: Problem 6, 8
Chapter 9: Problems 1-4 Chapter 10: Problems 1, 2, 3, 5) Video

Setup Time Reduction Where? Steps:
Stations where capacity is expensive Excess capacity may sometimes be cheaper Steps: 1. Externalize portions of setup 2. Reduce adjustment time (guides, clamps, etc.) 3. Technological advancements (hoists, quick-release, etc.) Caveat: Don’t count on capacity increase; more flexibility will require more setups.

Parallel Batching Parameters: Time to form batch:
Time to process batch: te = t t ra,ca k W = ((10 – 1)/2)(1/0.005) = 90 forming batch queue of batches te = 90

Arrival of batches: ra/k Utilization: u = (ra/k)(t) For stability: u < 1 requires ra/k = 0.05/10 = 0.005 u = (0.005)(90) = 0.45 minimum batch size required for stability of system... k > 0.05(90) = 4.5

Average wait-for-batch time: Average queue plus process time at station: Total cycle time: batch size affects both wait-for-batch time and queue time

Cycle Time vs. Batch Size in a Parallel Operation
queue time due to utilization wait for batch time Optimum Batch Size B

Variable Batch Sizes Observation: Waiting for full batch in parallel batch operation may not make sense. Could just process whatever is there when operation becomes available. Example: Furnace has space for 120 wrenches Heat treat requires 1 hour Demand averages 100 wrenches/hr Induction coil can heat treat 1 wrench in 30 seconds What is difference between performance of furnace and coil?

Variable Batch Sizes (cont.)
Furnace: Ignoring queueing due to variability Process starts every hour 100 wrenches in furnace 50 wrenches waiting on average 150 total wrenches in WIP CT = WIP/TH = 150/100 = 3/2 hr = 90 min Induction Coil: Capacity same as furnace (120 wrenches/hr), but CT = 0.5 min = hr WIP = TH × CT = 100 × = 0.83 wrenches Conclusion: Dramatic reduction in WIP and CT due to small batches—independent of variability or other factors. 100 50

Move Batching Move Batching Law: Cycle times over a segment of a routing are roughly proportional to the transfer batch sizes used over that segment, provided there is no waiting for the conveyance device. Insights: Basic Batching Tradeoff: WIP vs. move frequency Queueing for conveyance device can offset CT reduction from reduced move batch size Move batching intimately related to material handling and layout decisions

Move Batching Problem: Two machines in series
First machine receives individual parts at rate ra with CV of ca(1) and puts out batches of size k. First machine has mean process time of te(1) for one part with CV of ce(1). Second machine receives batches of k and put out individual parts. How does cycle time depend on the batch size k? te(1),ce(1) k ra,ca(1) te(2),ce(2) single job batch Station 1 Station 2

Move Batching Calculations
Time at First Station: Average time before batching is: Average time forming the batch is: Average time spent at the first station is: regular VUT equation... first part waits (k-1)(1/ra), last part doesn’t wait, so average is (k-1)(1/ra)/2

Output of First Station: Time between output of individual parts into the batch is ta. Time between output of batches of size k is kta. Variance of interoutput times of parts is cd2(1)ta2, where Variance of batches of size k is kcd2(1)ta2. SCV of batch arrivals to station 2 is: because cd2(1)=d2/ta2 by def of CV because departures are independent, so variances add variance divided by mean squared...