1. OPSM 301 Spring 2012 Class 13: Inventory Management

2. Inventory “The stock of any item or resource used in an organization”
“All the money that the system has invested in purchasing things it intends to sell”
Inventory is the stock of any item or resource used in an organization. An inventory system is the set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be. By convention, manufacturing inventory generally refers to materials entities that contribute to or become part of a firm's product output.
Manufacturing inventory is typically classified into raw materials, finished products, component parts, supplies, and work in process. In services, inventory generally refers to the tangible goods to be sold and the supplies necessary to administer the service.

3. Types of Inventories Inputs - Raw Materials
Processes - Work-in-Process
Outputs - Finished Goods

4. Definition of Inventory
Inventory: the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process
Manufacturing inventory: refers to items that contribute to or become part of a firm’s product
Inventory system: the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be 3

5. The Material Flow Cycle
Cycle time
95% 5%
Input Wait for Wait to Move Wait in queue Setup Run Output
inspection be moved time for operator time time

6. Flow time T = Inventory I / Throughput R
Chapter 6
Operational Flows
Throughput R
Inventory I
Notes:
FLOW TIME T
I = R T
Flow time T = Inventory I / Throughput R

7. Why do Buffers Build? Why hold Inventory?
Chapter 6
Why do Buffers Build? Why hold Inventory?
Economies of scale
Fixed costs associated with batches
Quantity discounts
Trade Promotions
Uncertainty
Information Uncertainty
Supply/demand uncertainty
Seasonal Variability
Strategic
Flooding, availability
Cycle/Batch stock
Notes:
Safety stock
Seasonal stock
Strategic stock
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8. Why do we need Inventory?
Variability (uncertainty)
Demand
Capacity availability
Materials and lead times
Processing times
Time
Delivery lead time, production lead time
Economies of Scale
Purchasing, production

9. Functions Provided by Inventories
Purpose /Reason Type Cost
Transportation Pipeline Transportation Costs
Economies in Setups Cycle Stocks Setup/Order Costs
Seasonality in Demand Seasonal Stock Smoothing Costs
Uncertainty in Demand Safety Stock Shortage/Stock-out
Costs
Economies in Purchase Cycle Stocks Price Discounts
Inflation and/or
Price Fluctuations Speculative Stock Costs due to Price

10. Inventory Costs The following costs affect the inventory size:
Ordering Cost
Receiving and inspection
Transportation
Setup (or production change) costs
Costs for arranging specific equipment setups etc.
Holding (Carrying) Cost
Cost of money
Insurance
Taxes
Shrinkage, spoilage, obsolescence
Stock-out (Shortage) Cost
Lost sales, customers etc.
Emergency shipment costs

11. Economies of Scale: Inventory Management for a Retailer
The South Face retail shop in Vermont has observed a stable monthly demand for its line of Gore-Tex jackets on the order of 100 jackets per month. The retail shop incurs a fixed cost of $2,000 every time it places an order to the California warehouse for stock replenishment. The marginal cost of a jacket is $200, and South Face’s cost of capital is approximately 25%.
What order size would you recommend for The South Face?
retailer
warehouse

12. Parameters EOQ Model R (or D) demand rate (units per year)
C unit production cost, not counting setup or inventory costs (dollars per unit)
S 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

13. Inventory Usage Over Time
Inventory Level
Average Inventory (Q*/2)
Minimum inventory
Order quantity = Q (maximum inventory level)
Usage Rate

14. Total Annual Cost
Total Annual Cost =
Annual
Purchasing
Cost
Ordering
Holding +
Using calculus, we can take the derivative of the total cost function and set the derivative (slope) equal to zero
We can also use economic intuition

15. Find most economical order quantity: Spreadsheet for The South Face
Number of units per order/batch
Number of batches per year
Annual Setup Cost
Annual Holding cots
Total Cost Q
R/Q
SR/Q
hQ/2 50 24
48000
1250
49250
100 12
24000
2500
26500
150 8
16000
3750
19750
200 6
12000
5000
17000
250 5
9600
6250
15850
300 4
8000
7500
15500
310
7742
7750
15492
320
350 3
6857
8750
15607
400
6000
10000
450
5333
11250
16583
500 2
4800
12500
17300
550
4364
13750
18114
600
4000
15000
19000
650
3692
16250
19942
700
3429
17500
20929
750
3200
18750
21950
800
3000
20000
23000
850 1
2824
21250
24074
900
2667
22500
25167
950
2526
23750
26276
1000
2400
25000
27400
1050
2286
26250
28536
1100
2182
27500
29682

16. Accurate Response to Scale Economies: Economic Order Quantity EOQ
Total annual costs
H Q/2: Annual holding cost
S R /Q:Annual setup cost
Order Size Q
Fixed cost per order
The order quantity that minimizes total supply chain cost is:
Annual unit demand
Annual unit holding cost
J.A. Van Mieghem/Operations/Supply Chain Mgt
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

17. Optimal Economies of Scale: For a South Face retailer
R = 100 units/ month = 1200 units/year C = $ 200 / unit
r = 0.25/year S = $ 2,000 / order
Unit annual holding cost = H = 0.25/yr x $200 = $50/yr
Optimal order quantity = Q = sqrt(2 x 1200 x 2000/50) = 309.8
Number of orders per year = R/Q =3.87
Time between orders = Q/R = 0.25yr =13 weeks
Annual order cost = (R/Q)S = $/year
Average inventory I = Q/2 = 154.9
Annual holding cost = (Q/2)H = $/year
Average flow time T = I/R = 0.12 yr = 6.7 weeks
J.A. Van Mieghem/Operations/Supply Chain Mgt
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

18. An EOQ Example Q* = 2DS H Q* = 2(1,000)(10) 0.50 = 40,000 = 200 units
Determine optimal number of needles to order
D = 1,000 units
S = $10 per order
H = $.50 per unit per year
Q* =
2DS H
Q* =
2(1,000)(10)
0.50
= 40,000 = 200 units

19. Expected number of orders
An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order
H = $.50 per unit per year
= N = =
Expected number of orders
Demand
Order quantity D Q*
N = = 5 orders per year
1,000
200

20. Expected time between orders Number of working days per year
An EOQ Example
Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year
= T =
Expected time between orders
Number of working days per year N
T = = 50 days between orders
250 5

21. An EOQ Example Determine optimal number of needles to order
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
Total annual cost = Setup cost + Holding cost
TC = S H D Q 2
TC = ($10) ($.50)
1,000
200 2
TC = (5)($10) + (100)($.50) = $50 + $50 = $100

22. Learning Objectives: Batching & Economies of Scale
Increasing batch size Q of order (or production) increases average inventories (and thus flow times).
Average inventory for a batch size of Q is Q/2.
The optimal batch size minimizes supply chain costs by trading off setup cost and holding cost and is given by the EOQ formula.
To reduce batch size, one must reduce setup cost (time).
Economies of scale are manifested by the square-root relationship between QEOQ and (R, S):
If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often.
To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.
J.A. Van Mieghem/Operations/Supply Chain Mgt
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

23. Role of Leadtime L: South Face cont.
The lead time from when a South Face retailer places an order to when the order is received is two weeks. If demand is stable as before, when should the retailer place an order?
Inventory Profile:
Two key decisions in inventory management are:
How much to order?
When to order?
Inventory Q -R
Time t
J.A. Van Mieghem/Operations/Supply Chain Mgt
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

24. Continuous Review Policy: Ordering Decisions and the Re-order Point
ROP L -R
Place
order n
I(t) Q
time
Receive
order n+1
order n+2
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

25. ROP and Inventory position
ROP = L × R
But if lead time L is greater than time between orders, there will be more than one order outstanding
Inventory position = Inventory level (On-hand inventory) + On-order inventory
Copyright © 2013 Pearson Education Inc. publishing as Prentice Hall

26. Determine the economic order quantity and the reorder point
EOQ Example
Annual Demand = 1,000 units
Days per year considered in average daily demand = 250
Cost to place an order = $10
Holding cost per unit per year = $0.50
Lead time = 7 days
Cost per unit = $15
Determine the economic order quantity and the reorder point

27. Number of working days in a year
Reorder Point Example
Demand = 8,000 iPods per year
250 working day year
Lead time for orders is 3 working days
d = D
Number of working days in a year
= 8,000/250 = 32 units
ROP = d x L
= 32 units per day x 3 days = 96 units

28. Economic Order Quantity (EOQ) Model
Robust, widely used
Insensitive to errors in estimating parameters ( Rule):
40% error in one of the parameters
20% error in Q
< 2% of total cost penalty

29. An EOQ Example Management underestimated demand by 50%
D = 1,000 units Q* = 200 units
S = $10 per order N = 5 orders per year
H = $.50 per unit per year T = 50 days
1,500 units
TC = S H D Q 2
TC = ($10) ($.50) = $75 + $50 = $125
1,500
200 2
Total annual cost increases by only 25%

30. An EOQ Example Actual EOQ for new demand is 244.9 units
D = 1,000 units Q* = units
S = $10 per order
H = $.50 per unit per year
1,500 units
TC = S H D Q 2
Only 2% less than the total cost of $125 when the order quantity was 200
TC = ($10) ($.50)
1,500
244.9 2
TC = $ $61.24 = $122.48