1. Chapter 2
Inventory Management and Risk Pooling

2. Stephen C. Graves Copyright 2003
CASE: Steel Works
Background of case and intent
Overview of business
What does data tell you about Specialty?
How much inventory might you expect?
What opportunities are there for Custom?
Wrap up
Overall structure of discussion; I’ll lead thru background
Stephen C. Graves Copyright 2003
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3. Stephen C. Graves Copyright 2003
Background & Intent
Abstraction from summer consulting job
Intent is to examine a realistic, but simplified inventory context and perform a diagnosis of problem – poor service and too much inventory
Emphasis is on quick diagnosis (like a Kaizen event), using simple tools and principles, to identify high leverage points
Actual project– specialty industrial chemicals
Note – there is not much real information in case, so we’ll need to make some inferences; depending on what one assumes, analysis and rec’s might change.
Stephen C. Graves Copyright 2003
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4. Stephen C. Graves Copyright 2003
Custom Products
Rapid growth, 1/3 of total sales ($133 MM)
One customer per product
Very high margins
High service level
3 plants, co-located with R&D center
Each product produced at a single plant
Note – Steel Works started in 1980, $400 mm in sales, rapid growth, seem to compete on technological innovation and service.
two businesses; Custom and Specialty products
Steel Works started with Custom products – what are the salient characteristics of this business?
New Products developed for a single customer for a specific need
Stephen C. Graves Copyright 2003
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5. Stephen C. Graves Copyright 2003
Specialty Products
Rapid growth, 2/3 of total sales ($267 MM)
6 product families
3 plants, each producing 2 product families
130 customers, 120 products
Few big customers
Highly volatile demand
High service level
What re the characteristics of Specialty products division?
Note – products are developed in Custom for a single customer; after some negotiation, Steel Works get rights to sell to other companies, and transfers this over to Specialty to make and service
What does coefficient of variation mean? (note footnote is wrong?)
Coefficient of variation = standard deviation (s) / mean (m)
What does cv > 0.5?
Note that cv depends on time period.
e.g., month m = 20, s = 10 then cv =.5
week m = 5, s = 5 then cv = 1
day m = 1, s = 2.5 then cv = 2.5
year m = 240, s=34 then cv=0.14
Stephen C. Graves Copyright 2003
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6. Consultant Recommendation
Drop low volume products
Improve forecasts
Consolidate warehouses
Fred Chow – actual name …
What do you think of the recommendations?
Key customers buy low volume products
Improve forecasts – easier said than done, although certainly some opportunity in Custom where 1 customer per product; but you’d improve the forecast by talking with customer, not by regression
Consolidate warehouses – yes will save inventory, but will increase transportation. Not enough information in case to really assess this – and Gary had concluded that it would take some effort to get data to make this assessment
Stephen C. Graves Copyright 2003
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7. Stephen C. Graves Copyright 2003
What Does Data Tell You? m s cv
DB R10
15.5
13.2
0.85
DB R12
1008
256
0.25
DB R15
2464
494
0.20
DF R10 97
92.5
0.95
DF R12
18.5
11.4
0.62
DF R15 55 80
1.46
DF R23
35.5
45.9
1.29
What does data tell you about SW’s customers? About their demand? Use blank sheet
For Durabend R12: one customer = 97% of demand
Can we drop the small customers?
What else could you do? – impose a minimum order quantity
Can we get a forecast from customer 194?
For 7 products:ABC like: few products represent most of volume
high volume is not very volatile
low volume is very volatile
High percent of products do have high demand variability
But low percentage of volume has high demand variability
Stephen C. Graves Copyright 2003
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8. Stephen C. Graves Copyright 2003
What Does Data Tell You?
Durabend R12:
One customer accounts for 97% of demand
7 products:
High volume (2) is not very volatile
Low volume (5) is very volatile
Is this atypical?
How much inventory would you expect? Develop an approach – how is inventory replenished? What is a realistic story for how planning and operational system works?
Stephen C. Graves Copyright 2003
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9. How Much Inventory Should You Expect?
Assume base stock model with periodic review
Review period = r = ?
Lead time = L = ?
How do you imagine this planning operation works?
Note –we use sigma as a surrogate for forecast accuracy.
What is r here? What is L? How to set z?
Monthly production cycle suggests r = 1 month; lead time is time between review epoch (when schedule is set) and when production is completed and inventory available for use. I expect L is at least 1 week, and might be more.
Note that batch sizes are on the order of one month
Why would you mange this with periodic review? rather than continuous review?
Stephen C. Graves Copyright 2003
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10. Stephen C. Graves Copyright 2003m s
Cycle stock
Saf. stock
E[I]
Act. Inv.
DB R10
15.5
13.2 8 26 34 72
DB R12
1008
256
504
510
1014
740
DB R15
2464
494
1232
990
2222
1875
DF R10 97
92.5 49
185
234
604
DF R12
18.5
11.4 9 23 32 55
DF R15 80 28
160
188
388
DF R23
35.5
45.9 18 92
110
190 S
1848
1986
3834
3824
Assumes r=1 month; L = 1 week = ¼ month;
z = 2/sqrt(5/4) = 1.8; (so safety stock = z * sqrt(5/4) * sigma = 2 sigma)
service level = coverage probability = 97% for z = 1.8
Note L is a guess – case doesn’t tell us. But need explain how to think about L in this context.
Assumes end of month is good estimate of actual inventory
Why is actual service so bad? Not enough ss for A items, too much for C items
Where do you have the most leverage? -- A items
What’s the benefit of more accurate forecasts? More frequent production?
Are normal assumptions OK here? Might look at maximum lead time demand?
Note : base stock = r*mu + safety stock; might compare to maximum monthly demand ; note that DF R15 and DF R23 are very lumpy, so might set base stock equal to maximum monthly demand
Might calculate base stock for some items, e.g., for DB R10, B = 15.5* = 45
Assumes r = 1; L=0.25; and z = 1.8
Cycle stock = r m/ Safety stock = z s r+L
Stephen C. Graves Copyright 2003
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11. What Are the Opportunities at Custom?
Combine production and inventory for common items, e. g. DF R23
Produce monthly: reduce setups by half and pool safety stocks
Produce twice a month: same number of setups but cut cycle stock and review period in half
Work through a small example to show benefits
Why would you not want to combine production?
Also, could get similar benefits by combining warehouses.
Consider DF 23; suppose specialty has mean 36, variance of 2025 (45* 45)
Assume custom has same demand moments.
When we treat separate, each has SS proportional to sigma ( 45) * sqrt (r+L). Suppose r+L = 1 month.
When we combine, SS proportional to sqrt ( ) = 45 * sqrt(2). Savings is 30% reduction in SS.
Also, when we combine, we would produce together. For instance, if we produce each once a month, then we could produce combined once a month and eliminate half of set ups. Or we could produce twice a month (same number of setups), but reduce cycle stock in half. But then this would also reduce SS, as r goes from (say) 4 weeks to 2 weeks.
So by pooling, we might reduce both cycle stock and SS by (approximately) half, keeping the same number of setups.
Stephen C. Graves Copyright 2003
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12. Stephen C. Graves Copyright 2003
Wrap Up
Realistic diagnostic exercise
In real life: not as clean, more data and more considerations
Yet simple models and principles can provide valuable guidance
My next session --- Instron case– think about how do you want to run the operation? What are the main tactics and operating polices to use?
Stephen C. Graves Copyright 2003
All Rights Reserved

13. 2.1 Introduction Why Is Inventory Important?
Distribution and inventory (logistics) costs are quite substantial
Total U.S. Manufacturing Inventories ($m):
: $m ,773
: $m 1,000,774
: $m 1,324,108
Inventory-Sales Ratio (U.S. Manufacturers):
: 1.56
: 1.25

14. Why Is Inventory Important?
GM’s production and distribution network
20,000 supplier plants
133 parts plants
31 assembly plants
11,000 dealers
Freight transportation costs: $4.1 billion (60% for material shipments)
GM inventory valued at $7.4 billion (70%WIP; Rest Finished Vehicles)
Decision tool to reduce:
combined corporate cost of inventory and transportation.
26% annual cost reduction by adjusting:
Shipment sizes (inventory policy)
Routes (transportation strategy)

15. Why Is Inventory Required?
Uncertainty in customer demand
Shorter product lifecycles
More competing products
Uncertainty in supplies
Quality/Quantity/Costs/Delivery Times
Delivery lead times
Incentives for larger shipments

16. Holding the right amount at the right time is difficult!
Dell Computer’s was sharply off in its forecast of demand, resulting in inventory write-downs
1993 stock plunge
Liz Claiborne’s higher-than-anticipated excess inventories
1993 unexpected earnings decline,
IBM’s ineffective inventory management
1994 shortages in the ThinkPad line
Cisco’s declining sales
2001 $ 2.25B excess inventory charge

17. Inventory Management-Demand Forecasts
Uncertain demand makes demand forecast critical for inventory related decisions:
What to order?
When to order?
How much is the optimal order quantity?
Approach includes a set of techniques
INVENTORY POLICY!!

18. Supply Chain Factors in Inventory Policy
Estimation of customer demand
Replenishment lead time
The number of different products being considered
The length of the planning horizon
Costs
Order cost:
Product cost
Transportation cost
Inventory holding cost, or inventory carrying cost:
State taxes, property taxes, and insurance on inventories
Maintenance costs
Obsolescence cost
Opportunity costs
Service level requirements

19. 2.2 Single Stage Inventory Control
Single supply chain stage
Variety of techniques
Economic Lot Size Model
Demand Uncertainty
Single Period Models
Initial Inventory
Multiple Order Opportunities
Continuous Review Policy
Variable Lead Times
Periodic Review Policy
Service Level Optimization

20. 2.2.1. Economic Lot Size Model
FIGURE 2-3: Inventory level as a function of time

21. Assumptions D items per day: Constant demand rate
Q items per order: Order quantities are fixed, i.e., each time the warehouse places an order, it is for Q items.
K, fixed setup cost, incurred every time the warehouse places an order.
h, inventory carrying cost accrued per unit held in inventory per day that the unit is held (also known as, holding cost)
Lead time = 0
(the time that elapses between the placement of an order and its receipt)
Initial inventory = 0
Planning horizon is long (infinite).

22. Deriving EOQ Total cost at every cycle:
Average inventory holding cost in a cycle: Q/2
Cycle time T =Q/D
Average total cost per unit time:

23. EOQ: Costs
FIGURE 2-4: Economic lot size model: total cost per unit time

24. Sensitivity Analysis
Total inventory cost relatively insensitive to order quantities
Actual order quantity: Q
Q is a multiple b of the optimal order quantity Q*.
For a given b, the quantity ordered is Q = bQ* b .5 .8 .9 1
1.1
1.2
1.5 2
Increase in cost
25%
2.5%
0.5%
.4%
1.6%
8.9%

25. 2.2.2. Demand Uncertainty The forecast is always wrong
It is difficult to match supply and demand
The longer the forecast horizon, the worse the forecast
It is even more difficult if one needs to predict customer demand for a long period of time
Aggregate forecasts are more accurate.
More difficult to predict customer demand for individual SKUs
Much easier to predict demand across all SKUs within one product family

26. 2.2.3. Single Period Models Short lifecycle products
One ordering opportunity only
Order quantity to be decided before demand occurs
Order Quantity > Demand => Dispose excess inventory
Order Quantity < Demand => Lose sales/profits

27. Single Period Models Using historical data
identify a variety of demand scenarios
determine probability each of these scenarios will occur
Given a specific inventory policy
determine the profit associated with a particular scenario
given a specific order quantity
weight each scenario’s profit by the likelihood that it will occur
determine the average, or expected, profit for a particular ordering quantity.
Order the quantity that maximizes the average profit.

28. Single Period Model Example
FIGURE 2-5: Probabilistic forecast

29. Additional Information
Fixed production cost: $100,000
Variable production cost per unit: $80.
During the summer season, selling price: $125 per unit.
Salvage value: Any swimsuit not sold during the summer season is sold to a discount store for $20.

30. Two Scenarios
Manufacturer produces 10,000 units while demand ends at 12,000 swimsuits
Profit
= 125(10,000) - 80(10,000) - 100,000
= $350,000
Manufacturer produces 10,000 units while demand ends at 8,000 swimsuits
= 125(8,000) + 20(2,000) - 80(10,000) - 100,000
= $140,000

31. Probability of Profitability Scenarios with Production = 10,000 Units
Probability of demand being 8000 units = 11%
Probability of profit of $140,000 = 11%
Probability of demand being units = 27%
Probability of profit of $140,000 = 27%
Total profit = Weighted average of profit scenarios

32. Order Quantity that Maximizes Expected Profit
FIGURE 2-6: Average profit as a function of production quantity

33. Relationship Between Optimal Quantity and Average Demand
Compare marginal profit of selling an additional unit and marginal cost of not selling an additional unit
Marginal profit/unit =
Selling Price - Variable Ordering (or, Production) Cost
Marginal cost/unit =
Variable Ordering (or, Production) Cost - Salvage Value
If Marginal Profit > Marginal Cost => Optimal Quantity > Average Demand
If Marginal Profit < Marginal Cost => Optimal Quantity < Average Demand

34. For the Swimsuit Example
Average demand = 13,000 units.
Optimal production quantity = 12,000 units.
Marginal profit = $45
Marginal cost = $60.
Thus, Marginal Cost > Marginal Profit
=> optimal production quantity < average demand.

35. Risk-Reward Tradeoffs
Optimal production quantity maximizes average profit is about 12,000
Producing 9,000 units or producing 16,000 units will lead to about the same average profit of $294,000.
If we had to choose between producing 9,000 units and 16,000 units, which one should we choose?

36. Risk-Reward Tradeoffs
FIGURE 2-7: A frequency histogram of profit

37. Risk-Reward Tradeoffs
Production Quantity = 9000 units
Profit is:
either $200,000 with probability of about 11 %
or $305,000 with probability of about 89 %
Production quantity = 16,000 units.
Distribution of profit is not symmetrical.
Losses of $220,000 about 11% of the time
Profits of at least $410,000 about 50% of the time
With the same average profit, increasing the production quantity:
Increases the possible risk
Increases the possible reward

38. Observations
The optimal order quantity is not necessarily equal to forecast, or average, demand.
As the order quantity increases, average profit typically increases until the production quantity reaches a certain value, after which the average profit starts decreasing.
Risk/Reward trade-off: As we increase the production quantity, both risk and reward increases.

39. 2.2.4. What If the Manufacturer Has an Initial Inventory?
Trade-off between:
Using on-hand inventory to meet demand and avoid paying fixed production cost: need sufficient inventory stock
Paying the fixed cost of production and not have as much inventory

40. Initial Inventory Solution
FIGURE 2-8: Profit and the impact of initial inventory

41. Manufacturer Initial Inventory = 5,000
If nothing is produced, average profit =
225,000 (from the figure) + 5,000 x 80 = 625,000
If the manufacturer decides to produce
Production should increase inventory from 5,000 units to 12,000 units.
Average profit =
371,000 (from the figure) + 5,000 • 80 = 771,000

42. Manufacturer Initial Inventory = 10,000
No need to produce anything
average profit > profit achieved if we produce to increase inventory to 12,000 units
If we produce, the most we can make on average is a profit of $375,000.
Same average profit with initial inventory of 8,500 units and not producing anything.
If initial inventory < 8,500 units => produce to raise the inventory level to 12,000 units.
If initial inventory is at least 8,500 units, we should not produce anything
(s, S) policy or (min, max) policy

43. 2.2.5. Multiple Order Opportunities
REASONS
To balance annual inventory holding costs and annual fixed order costs.
To satisfy demand occurring during lead time.
To protect against uncertainty in demand.
TWO POLICIES
Continuous review policy
inventory is reviewed continuously
an order is placed when the inventory reaches a particular level or reorder point.
inventory can be continuously reviewed (computerized inventory systems are used)
Periodic review policy
inventory is reviewed at regular intervals
appropriate quantity is ordered after each review.
it is impossible or inconvenient to frequently review inventory and place orders if necessary.

44. 2.2.6. Continuous Review Policy
Daily demand is random and follows a normal distribution.
Every time the distributor places an order from the manufacturer, the distributor pays a fixed cost, K, plus an amount proportional to the quantity ordered.
Inventory holding cost is charged per item per unit time.
Inventory level is continuously reviewed, and if an order is placed, the order arrives after the appropriate lead time.
If a customer order arrives when there is no inventory on hand to fill the order (i.e., when the distributor is stocked out), the order is lost.
The distributor specifies a required service level.

45. Continuous Review Policy
AVG = Average daily demand faced by the distributor
STD = Standard deviation of daily demand faced by the distributor
L = Replenishment lead time from the supplier to the
distributor in days
h = Cost of holding one unit of the product for one day at the distributor
α = service level. This implies that the probability of stocking out is 1 - α

46. Continuous Review Policy
(Q,R) policy – whenever inventory level falls to a reorder level R, place an order for Q units
What is the value of R?

47. Continuous Review Policy
Average demand during lead time: L x AVG
Safety stock:
Reorder Level, R:
Order Quantity, Q:

48. Service Level & Safety Factor, z
90%
91%
92%
93%
94%
95%
96%
97%
98%
99%
99.9% z
1.29
1.34
1.41
1.48
1.56
1.65
1.75
1.88
2.05
2.33
3.08
z is chosen from statistical tables to ensure
that the probability of stockouts during lead time is exactly 1 - α

49. Inventory Level Over Time
FIGURE 2-9: Inventory level as a function of time in a (Q,R) policy
Inventory level before receiving an order =
Inventory level after receiving an order =
Average Inventory =

50. Continuous Review Policy Example
A distributor of TV sets that orders from a manufacturer and sells to retailers
Fixed ordering cost = $4,500
Cost of a TV set to the distributor = $250
Annual inventory holding cost = 18% of product cost
Replenishment lead time = 2 weeks
Expected service level = 97%

51. Continuous Review Policy Example
Month
Sept
Oct
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug
Sales
200
152
100
221
287
176
151
198
246
309 98
156
Average monthly demand =
Standard deviation of monthly demand = 66.53
Average weekly demand = Average Monthly Demand/4.3
Standard deviation of weekly demand = Monthly standard deviation/√4.3

52. Continuous Review Policy Example
Parameter
Average weekly demand
Standard deviation of weekly demand
Average demand during lead time
Safety stock
Reorder point
Value
44.58
32.08
89.16
86.20
176
Weekly holding cost =
Optimal order quantity =
Average inventory level = 679/ = 426

53. 2.2.7. Variable Lead Times Average lead time, AVGL
Standard deviation, STDL.
Reorder Level, R:
Amount of safety stock=
Order Quantity =

54. 2.2.8. Periodic Review Policy
Inventory level is reviewed periodically at regular intervals
An appropriate quantity is ordered after each review
Two Cases:
Short Intervals (e.g. Daily)
Define two inventory levels s and S
During each inventory review, if the inventory position falls below s, order enough to raise the inventory position to S.
(s, S) policy
Longer Intervals (e.g. Weekly or Monthly)
May make sense to always order after an inventory level review.
Determine a target inventory level, the base-stock level
During each review period, the inventory position is reviewed
Order enough to raise the inventory position to the base-stock level.
Base-stock level policy

55. (s,S) policy
Calculate the Q and R values as if this were a continuous review model
Set s equal to R
Set S equal to R+Q.

56. Base-Stock Level Policy
Determine a target inventory level, the base-stock level
Each review period, review the inventory position is reviewed and order enough to raise the inventory position to the base-stock level
Assume:
r = length of the review period
L = lead time
AVG = average daily demand
STD = standard deviation of this daily demand.

57. Base-Stock Level Policy
Average demand during an interval of r + L days=
Safety Stock=

58. Base-Stock Level Policy
FIGURE 2-10: Inventory level as a function of time in a periodic review policy

59. Base-Stock Level Policy Example
Assume:
distributor places an order for TVs every 3 weeks
Lead time is 2 weeks
Base-stock level needs to cover 5 weeks
Average demand = x 5 = 222.9
Safety stock =
Base-stock level = = 359
Average inventory level =
Distributor keeps 5 (= /44.58) weeks of supply.

60. 2.2.9. Service Level Optimization
Optimal inventory policy assumes a specific service level target.
What is the appropriate level of service?
May be determined by the downstream customer
Retailer may require the supplier, to maintain a specific service level
Supplier will use that target to manage its own inventory
Facility may have the flexibility to choose the appropriate level of service

61. Service Level Optimization
FIGURE 2-11: Service level inventory versus inventory level as a function of lead time

62. Trade-Offs Everything else being equal:
the higher the service level, the higher the inventory level.
for the same inventory level, the longer the lead time to the facility, the lower the level of service provided by the facility.
the lower the inventory level, the higher the impact of a unit of inventory on service level and hence on expected profit

63. Retail Strategy
Given a target service level across all products determine service level for each SKU so as to maximize expected profit.
Everything else being equal, service level will be higher for products with:
high profit margin
high volume
low variability
short lead time

64. Profit Optimization and Service Level
FIGURE 2-12: Service level optimization by SKU

65. Profit Optimization and Service Level
Target inventory level = 95% across all products.
Service level > 99% for many products with high profit margin, high volume and low variability.
Service level < 95% for products with low profit margin, low volume and high variability.

66. 2.3 Risk Pooling
Demand variability is reduced if one aggregates demand across locations.
More likely that high demand from one customer will be offset by low demand from another.
Reduction in variability allows a decrease in safety stock and therefore reduces average inventory.

67. Demand Variation
Standard deviation measures how much demand tends to vary around the average
Gives an absolute measure of the variability
Coefficient of variation is the ratio of standard deviation to average demand
Gives a relative measure of the variability, relative to the average demand

68. Acme Risk Pooling Case
Electronic equipment manufacturer and distributor
2 warehouses for distribution in New York and New Jersey (partitioning the northeast market into two regions)
Customers (that is, retailers) receiving items from warehouses (each retailer is assigned a warehouse)
Warehouses receive material from Chicago
Current rule: 97 % service level
Each warehouse operate to satisfy 97 % of demand (3 % probability of stock-out)

69. New Idea
Replace the 2 warehouses with a single warehouse (located some suitable place) and try to implement the same service level 97 %
Delivery lead times may increase
But may decrease total inventory investment considerably.

70. Historical Data PRODUCT A PRODUCT B Week 1 2 3 4 5 6 7 8 Massachusetts33 45 37 38 55 30 18 58
New Jersey 46 35 41 40 26 48
Total 79 80 78 81 36
113
PRODUCT B

71. Summary of Historical Data
Statistics
Product
Average Demand
Standard Deviation of Demand
Coefficient of Variation
Massachusetts A
39.3
13.2
0.34 B
1.125
1.36
1.21
New Jersey
38.6
12.0
0.31
1.25
1.58
1.26
Total
77.9
20.71
0.27
2.375
1.9
0.81

72. Inventory Levels Product Average Demand During Lead Time Safety Stock
Reorder Point Q
Massachusetts A
39.3
25.08 65
132 B
1.125
2.58 4 25
New Jersey
38.6
22.8 62 31
1.25 3 5 24
Total
77.9
39.35
118
186
2.375
3.61 6 33

73. Savings in Inventory Average inventory for Product A:
At NJ warehouse is about 88 units
At MA warehouse is about 91 units
In the centralized warehouse is about 132 units
Average inventory reduced by about 36 percent
Average inventory for Product B:
At NJ warehouse is about 15 units
At MA warehouse is about 14 units
In the centralized warehouse is about 20 units
Average inventory reduced by about 43 percent

74. Critical Points
The higher the coefficient of variation, the greater the benefit from risk pooling
The higher the variability, the higher the safety stocks kept by the warehouses. The variability of the demand aggregated by the single warehouse is lower
The benefits from risk pooling depend on the behavior of the demand from one market relative to demand from another
risk pooling benefits are higher in situations where demands observed at warehouses are negatively correlated
Reallocation of items from one market to another easily accomplished in centralized systems. Not possible to do in decentralized systems where they serve different markets

75. 2.4 Centralized vs. Decentralized Systems
Safety stock: lower with centralization
Service level: higher service level for the same inventory investment with centralization
Overhead costs: higher in decentralized system
Customer lead time: response times lower in the decentralized system
Transportation costs: not clear. Consider outbound and inbound costs.

76. 2.5 Managing Inventory in the Supply Chain
Inventory decisions are given by a single decision maker whose objective is to minimize the system-wide cost
The decision maker has access to inventory information at each of the retailers and at the warehouse
Echelons and echelon inventory
Echelon inventory at any stage or level of the system equals the inventory on hand at the echelon, plus all downstream inventory (downstream means closer to the customer)

77. Echelon Inventory
FIGURE 2-13: A serial supply chain

78. Reorder Point with Echelon Inventory
Le = echelon lead time,
lead time between the retailer and the distributor plus the lead time between the distributor and its supplier, the wholesaler.
AVG = average demand at the retailer
STD = standard deviation of demand at the retailer
Reorder point

79. 4-Stage Supply Chain Example
Average weekly demand faced by the retailer is 45
Standard deviation of demand is 32
At each stage, management is attempting to maintain a service level of 97% (z=1.88)
Lead time between each of the stages, and between the manufacturer and its suppliers is 1 week

80. Costs and Order QuantitiesK D H Q
retailer
250 45
1.2
137
distributor
200 .9
141
wholesaler
205 .8
152
manufacturer
500 .7
255

81. Reorder Points at Each Stage
For the retailer, R=1* *32*√1 = 105
For the distributor, R=2* *32*√2 = 175
For the wholesaler, R=3* *32*√3 = 239
For the manufacturer, R=4* *32*√4 = 300

82. More than One Facility at Each Stage
Follow the same approach
Echelon inventory at the warehouse is the inventory at the warehouse, plus all of the inventory in transit to and in stock at each of the retailers.
Similarly, the echelon inventory position at the warehouse is the echelon inventory at the warehouse, plus those items ordered by the warehouse that have not yet arrived minus all items that are backordered.

83. Warehouse Echelon Inventory
FIGURE 2-14: The warehouse echelon inventory

84. 2.6 Practical Issues Periodic inventory review.
Tight management of usage rates, lead times, and safety stock.
Reduce safety stock levels.
Introduce or enhance cycle counting practice.
ABC approach.
Shift more inventory or inventory ownership to suppliers.
Quantitative approaches.
FOCUS: not reducing costs but reducing inventory levels.
Significant effort in industry to increase inventory turnover

85. Inventory Turnover Ratios for Different Manufacturers
Industry
Upper quartile
Median
Lower quartile
Electronic components and accessories
8.1
4.9
3.3
Electronic computers
22.7
7.0
2.7
Household audio and video equipment
6.3
3.9
2.5
Paper Mills
11.7
8.0
5.5
Industrial chemicals
14.1
6.4
4.2
Bakery products
39.7
23.0
12.6
Books: Publishing and printing
7.2
2.8
1.5

86. 2.7 Forecasting RULES OF FORECASTING The forecast is always wrong.
The longer the forecast horizon, the worse the forecast.
Aggregate forecasts are more accurate.

87. Utility of Forecasting
Part of the available tools for a manager
Despite difficulties with forecasts, it can be used for a variety of decisions
Number of techniques allow prudent use of forecasts as needed

88. Techniques Judgment Methods Market research/survey Time Series Trends
Sales-force composite
Experts panel
Delphi method
Market research/survey
Time Series
Moving Averages
Exponential Smoothing
Trends
Regression
Holt’s method
Seasonal patterns – Seasonal decomposition
Trend + Seasonality – Winter’s Method
Causal Methods

89. The Most Appropriate Technique(s)
Purpose of the forecast
How will the forecast be used?
Dynamics of system for which forecast will be made
How accurate is the past history in predicting the future?

90. SUMMARY Matching supply with demand a major challenge
Forecast demand is always wrong
Longer the forecast horizon, less accurate the forecast
Aggregate demand more accurate than disaggregated demand
Need the most appropriate technique
Need the most appropriate inventory policy