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Chapter 3 Inventory Chapter 3 Inventory Management and Risk Management and Risk
PoolingPooling
Chapter 3 Inventory Chapter 3 Inventory Management and Risk Management and Risk
PoolingPooling
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Outline of the Outline of the contentscontents
Introduction to Inventory Management
The Effect of Demand Uncertainty(s,S) PolicyPeriodic Review PolicySupply ContractsRisk Pooling
Centralized vs. Decentralized Systems
Practical Issues in Inventory Management
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InventoryInventory
Where do we hold inventory? Suppliers and manufacturers Warehouses and distribution centers Retailers
Types of Inventory Raw materials WIP Finished goods
Why do we hold inventory? Economies of scale Uncertainty in supply and demand Lead Time, Capacity limitations
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InventoryInventoryInventoryInventory
Managing inventory in complex supply chains is typically difficult, and may have a significant impact on the customer service level and supply chain system-wide cost.
Inventory in three typesRaw material inventory (where?)Work-in-process inventory (where?)Finished product inventory (where?)
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Why hold Inventory?Why hold Inventory?
Unexpected changes in customer demand. The short life cycle of an increasing number of products. Thus,
historical data may not be available or may be quite limited. The presence of many competing products in the marketplace.
(Discussed in Chapters 5 and 9)
The presence in many situations of a significant uncertaintyuncertainty in the quantity and quality of the supply, supplier costs, and delivery times.A need to hold inventory due to delivery lead times – even if there is no uncertainty in supply or demand.Economies of scale offered by transportation companies that encourage firms to transport large quantities of items, and therefore hold large inventories.
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Managing inventory – examplesManaging inventory – examples
By effectively managing inventory:Xerox eliminated $700 million inventory from
its supply chain.Wal-Mart became the largest retail company
utilizing efficient inventory management.GM has reduced parts inventory and
transportation costs by 26% annually .
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Managing inventory – examplesManaging inventory – examples
By not managing inventory successfullyIn 1993, Dell’s stock plunged after the company
predicted a loss. (sharply off in its forecast of demand)In 1994, “IBM continues to struggle with shortages in
their ThinkPad line” (WSJ, Oct 7, 1994)In 1993, “Liz Claiborne said its unexpected earning
decline is the consequence of higher than anticipated excess inventory” (WSJ, July 15, 1993)
In 2001, Cisco took a $2.25B excess inventory charge due to declining scales.
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Two important issues in inventory Two important issues in inventory managementmanagement
Demand forecastingForecast demand is a critical element in
determining order quantity.What is the relationship between forecast
demand and the optimal order quantity?Should the order quantity “=“ or “>” or “<“ the
forecast demand?…..
Order quantity calculation
A single warehouse inventory A single warehouse inventory exampleexample
A single warehouse inventory A single warehouse inventory exampleexample
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Key factors affecting inventory Key factors affecting inventory policy?policy?
Customer demandKnown in advance or may be random (forecasting tools
can be used).
Replenishment lead timeMay be known at the time we place the order or may be
uncertain.
The number of different productsHigh-mix and low volume?
The length of the planning horizon
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Key factors affecting inventory Key factors affecting inventory policy?policy?
Costs (order cost and inventory holding cost)Order cost: the cost of the product and the transportation
costInventory holding cost
State taxes, property taxes, and insurance on inventoriesMaintenance costsObsolescence cost (an item will lose some of its value
because of changes in the market.)Opportunities costs (the return on investment that one
would receive had money been invested in something else (e.g. stock market) instead of inventory.
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Key factors affecting inventory Key factors affecting inventory policy?policy?
Service level requirementsIt is not possible to meat customer orders 100
percent of the time. Managements need to specify an acceptable level of service
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3.2.1 The Economic Lot Size model3.2.1 The Economic Lot Size model
Economic lot size model is used to trade-off the costs between ordering and storage.Assumptions (for a single item and has a unlimited quantity of the product) Demand is constant at a rate of D items per day. Order quantities are fixed at Q items per order. A fixed cost (setup cost) K, incurred every time the warehouse
places an order. An inventory carrying cost, h, also referred to as a holding cost, is
accrued per unit held in inventory per day that the unit is held. The lead time, the time that elapses between the placement of an
order and its receipt, is zero Initial inventory is zero. The planning horizon is long (infinite).
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3.2.1 The Economic Lot Size model3.2.1 The Economic Lot Size model
GoalFind the optimal order policy that minimizes annual
purchasing and carrying costs while meeting all demand.
Realistic system?A known fixed demand over a long horizon is clear
unrealistic.This model will help us to develop inventory policies
that are effective for more complex realistic systems.
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3.2.1 The Economic Lot Size model3.2.1 The Economic Lot Size model
Time
Inventory
OrderSize
Notes:• No Stockouts• Order when no inventory• Order Size determines policy
Avg. Inven
Saw-toothed inventory pattern
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3.2.1 The Economic Lot Size model3.2.1 The Economic Lot Size model
Total costsPurchase Cost is ConstantHolding Cost: (Avg. Inven) × (Holding Cost)Ordering (Setup Cost):
Number of Orders × Order Cost
Goal: Find the order Quantity that minimizes these costs.
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3.2.1 The Economic Lot Size model3.2.1 The Economic Lot Size model
Total inventory cost in a cycle of length T
Average total cost per unit of time
EOQ model:
2
hTQK
2
hQ
Q
KD
h
KDQ 2*
A fixed cost (setup cost)
An inventory holding cost Q/2: average inventoryLevel.
Q=TD -> T=Q/D
Setup cost/unit Holding/unit
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3.2.1 The Economic Lot Size model3.2.1 The Economic Lot Size model
2
hQ
Q
KD
Total Cost
Order Cost
Holding Cost
h
KDQ 2*
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Economic Lot Size model : Important Economic Lot Size model : Important ObservationsObservations
Tradeoff between set-up costs and holding costs when determining order quantity. In fact, we order so that these costs are equal per unit time
Total Cost is not particularly sensitive to the optimal order quantity
See page. 48.
Q = bQ*
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The Effect of Demand UncertaintyThe Effect of Demand Uncertainty
Most companies treat the world as if it were predictable:Production and inventory planning are based on forecasts of
demand made far in advance of the selling seasonCompanies are aware of demand uncertainty when they
create a forecast, but they design their planning process as if the forecast truly represents reality
Recent technological advances have increased the level of demand uncertainty:Short product life cycles Increasing product variety
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Demand ForecastsDemand Forecasts
The three principles of all forecasting techniques:
Forecasting is always wrongThe longer the forecast horizon the worst is the
forecast Aggregate forecasts are more accurate
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Swimsuit productionSwimsuit production
(Read the case on page 49)
Fashion items have short life cycles, high variety of competitors
Swimsuit New designs are completedOne production opportunityBased on past sales, knowledge of the industry, and
economic conditions, the marketing department has a probabilistic forecast
The forecast averages about 13,000, but there is a chance that demand will be greater or less than this.
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Probabilistic forecastProbabilistic forecast
Demand Scenarios
0%
5%
10%
15%
20%
25%
30%
8000 10000 12000 14000 16000 18000
Sales
Pro
bab
ilit
y
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DataData
Production cost per unit (C): $80
Selling price per unit (S): $125
Salvage value per unit (V): $20
Fixed production cost (F): $100,000
Q is production quantity, D demand
Profit = Revenue - Variable Cost - Fixed Cost + Salvage
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Example scenariosExample scenarios
Scenario One:Suppose you make 12,000 swimsuits and
demand ends up being 13,000 swimsuits.Profit = 125(12,000) - 80(12,000) - 100,000 =
$440,000
Scenario Two:Suppose you make 12,000 swimsuits and
demand ends up being 11,000 swimsuits.Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000)
= $ 335,000
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What to make?What to make?
Find order quantity that maximizes weighted average profit.
Question: Will this quantity be less than, equal to, or greater than average demand?
See Excel Spreadsheet for Chapter 3
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What to Make?What to Make?
Average demand is 13,100
Look at marginal cost vs. marginal profitif extra swimsuit sold, profit is 125-80 = 45if not sold, cost is 80-20 = 60
So we will make less than average demand
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Expected ProfitExpected Profit
Expected Profit
$0
$50,000
$100,000
$150,000
$200,000
$250,000
$300,000
$350,000
$400,000
8000 12000 16000 20000Order Quantity
Pro
fit
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Expected ProfitExpected Profit
Expected Profit
$0
$100,000
$200,000
$300,000
$400,000
8000 12000 16000 20000
Order Quantity
Pro
fit
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Important ObservationsImportant Observations
Tradeoff between ordering enough to meet demand and ordering too much
Several quantities have the same average profit
Average profit does not tell the whole story
Question: 9000 and 16000 units lead to about the same average profit, so which do we prefer?
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Probability of OutcomesProbability of Outcomes
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Cost
Pro
bab
ilit
y
Q=9000
Q=16000
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Key Points from this case studyKey Points from this case study
The optimal order quantity is not necessarily equal to average forecast demand
The optimal quantity depends on the relationship between marginal profit and marginal cost
As order quantity increases, average profit first increases and then decreases
As production quantity increases, risk increases. In other words, the probability of large gains and of large losses increases
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The effect of Initial InventoryThe effect of Initial Inventory
Suppose that one of the swimsuit designs is a model produced last year.Some inventory is left from last yearAssume the same demand pattern as beforeIf only old inventory is sold, no setup cost
From Figure 3-6, the profit can be obtained:225000+5000×80=625,000
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Initial Inventory and ProfitInitial Inventory and Profit
0
100000
200000
300000
400000
500000
Production Quantity
Prof
itFix production costs
225000
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QuestionsQuestions
If there are 7000 units remaining, what should the company do?
What should they do if there are 10,000 remaining?
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Initial Inventory and ProfitInitial Inventory and Profit
0
100000
200000
300000
400000
500000
Production Quantity
Pro
fit
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(s, S)(s, S) Policies Policies
For some starting inventory levels, it is better to not start production
If we start, we always produce to the same level
Thus, we use an (s,S) policy. If the inventory level is below s, we produce up to S.
s is the reorder point, and S is the order-up-to level
The difference between the two levels is driven by the fixed costs associated with ordering, transportation, or manufacturing
Swimsuit case: s = 8,500 and S = 12,000
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Supply contractsSupply contracts
In as supply contract, the buyer and supplier may agree on:Pricing and volume discountsMaximum and minimum purchase quantitiesDelivery lead timesProduct or material qualityProduct return policies
Refer to the Excel spreadsheet (supply contract).
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Swimsuit example againSwimsuit example again
(Read the case of example 3-2 on page 53)
Sequential supply chain: each party determines its own course of action
independent of the other parties.For the earlier example, the retailer assumes all of the
risk, of having more inventory than sales, while the manufacturer takes no risk.
Larger the order is, better it is for the manufacturer but it has a reverse impact to the retailer.
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Buy-back contractsBuy-back contracts
In a buy-back contract, the seller agrees to buy back unsold goods from the buyer for some agreed-upon price.
Study example 3-3 on page 54 and explain how does it work?
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Revenue-sharing contractsRevenue-sharing contracts
For the swimsuit example, if the manufacturer is willing to give discounts, the retailer will have an incentive to order more.
Study example 3-4 and explain how does it works.
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Quantity-flexibility contractsQuantity-flexibility contracts
The supplier provides full unsold items as long as the number of returns is no larger than a certain quantity.
How is it different from buy-back contracts?
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Sales rebate contractsSales rebate contracts
Sales rebate (discounts) contacts provide a direct incentive to the retailer to increase sales by means of a rebate paid by the supplier for any item sold above a certain quantity.
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Global optimizationGlobal optimization
What is the best strategy for the entire supply chain?The difficulty with global optimization is that it requires the firm to surrender decision-making power to an unbiased decision maker.See example 3-5 on page 56Its main drawback is that it does not provide a mechanism to allocate supply chain profit between the partners.See example 3-6 on page 57
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Multiple reorder opportunitiesMultiple reorder opportunities
Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The distributor periodically places orders to replenish its inventory
Continuous review policy and periodic review policy
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The Multi-Period Inventory ModelThe Multi-Period Inventory Model
Normally distributed random demand
Fixed order cost plus a cost proportional to amount ordered.
Inventory cost is charged per item per unit time
If an order arrives and there is no inventory, the order is lost
The distributor has a required service level. This is expressed as the the likelihood that the distributor will not stock out during lead time.
Intuitively, what will a good policy look like?
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Continuous review policyContinuous review policy
Known parametersAVG = average daily demand faced by the distributorSTD = Standard deviation of daily demand faced by the
distributorL = Replenishment lead time from the supplier to the
distributor in daysh = Cost of holding one unit of the product for one day
at the distributor = service level
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Continuous review policyContinuous review policy
Inventory position: The actual inventory at the warehouse plus items
ordered by the distributor that have not yet arrived minus items that are backordered.
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The (s,S) PolicyThe (s,S) Policy
(s, S) Policy: Whenever the inventory position drops below a certain level, s, we order to raise the inventory position to level S.
The reorder point is a function of:The Lead TimeAverage demandDemand variabilityService level
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A View of (s, S) PolicyA View of (s, S) Policy
Time
Inve
ntor
y L
evel
S
s
0
LeadTime
Inventory Position
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AnalysisAnalysis
The reorder point has two components:To account for average demand during lead time:
L AVG
To account for deviations from average (we call this safety stock)
z STD L
where z is chosen from statistical tables to ensure that the probability of stockouts during leadtime is (1-).
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AnalysisAnalysis
Reorder level (s)L AVG + z STD L
It needs to satisfy
Probability {Demand during lead time L AVG + z STD L} = (1-)
Refer to Table 3-2 on page 59 for z values.
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AnalysisAnalysis
Use EOQ model
Q =
S = Q + s
Average inventory level = (S + s)
=
h
AVGK 2
LSTDzQ
2
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Reminder:Reminder: The Normal DistributionThe Normal Distribution
0 10 20 30 40 50 60
Average = 30
Standard Deviation = 5
Standard Deviation = 10
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The distributor holds inventory to:The distributor holds inventory to:
Satisfy demand during lead time
Protect against demand uncertainty
Balance fixed costs and holding costs
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Distributor of the TV setsDistributor of the TV sets
The distributor has historically observed weekly demand of:
AVG = 44.6 STD = 32.1Replenishment lead time is 2 weeks, and desired service
level SL = 97%
Average demand during lead time is:44.6 2 = 89.2
Safety Stock is:1.88 32.1 2 = 85.3
Reorder point is thus 175, or about 3.9 weeks of supply at warehouse and in the pipeline
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Distributor of the TV setsDistributor of the TV sets
In addition to previous costs, a fixed cost K is paid every time an order is placed.
We have seen that this motivates an (s,S) policy, where reorder point and order quantity are different.
The reorder point will be the same as the previous model, in order to meet the service requirement: s = LTAVG + z AVG L
What about the order up to level?
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Distributor of the TV setsDistributor of the TV sets
We have used the EOQ model to balance fixed, variable costs: Q=(2 K AVG)/h
If there was no variability in demand, we would order Q when inventory level was at L AVG. Why?
There is variability, so we need safety stock:
z STD L
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Distributor of the TV setsDistributor of the TV sets
Consider the previous example, but with the following additional info:fixed cost of $4500 when an order is placed$250 product costholding cost 18% of product
Weekly holding cost:h = (.18 250) / 52 = 0.87
Order quantityQ=(2 4500 44.6 / 0.87 = 679
Order-up-to level:s + Q = 175 + 679 = 855
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Periodic review policyPeriodic review policy
Base-stock levelEach review period, the inventory position is
reviewed and the warehouse orders enough to raise the inventory position to the base-stock level.
Assume that orders are placed every r period of time.
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Periodic review policyPeriodic review policy
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Periodic review policyPeriodic review policy
Average demand during an interval of r + L(r + L) AVG
Safety stockz STD (r + L)
Expected level of inventory after receiving an order
r AVG + z STD (r + L)
Example 3-8 on page 63
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Market Two
Risk PoolingRisk Pooling
Consider these two systems:
Supplier
Warehouse One
Warehouse Two
Market One
Supplier Warehouse
Market One
Market Two
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Risk Pooling Risk Pooling
For the same service level, which system will require more inventory? Why?
For the same total inventory level, which system will have better service? Why?
What are the factors that affect these answers?
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Risk Pooling ExampleRisk Pooling Example
Compare the two systems: (Read the case on page. 64-66)two productsmaintain 97% service level$60 order cost$.27 weekly holding cost$1.05 transportation cost per unit in decentralized
system, $1.10 in centralized system1 week lead time
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Risk Pooling ExampleRisk Pooling Example
Week 1 2 3 4 5 6 7 8Prod A/W1 33 45 37 38 55 30 18 58Prod A/W2 46 35 41 40 26 48 18 55Prod B/W1 0 2 3 0 0 1 3 0Prod B/W2 2 4 0 0 3 1 0 0
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Risk Pooling ExampleRisk Pooling Example
Warehouse Product AVG STD CVMarket 1 A 39.3 13.2 0.34Market 2 A 38.6 12 0.31Market 1 B 1.125 1.36 1.21Market 2 B 1.25 1.58 1.26
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Risk Pooling ExampleRisk Pooling Example
Warehouse Product AVG STD CV s S Avg.Inven.
%Dec.
W 1 A 39.3 13.2 0.34 65 158 91W2 A 38.6 12 0.31 62 154 88W 1 B 1.125 1.36 1.21 4 26 15W2 B 1.25 1.58 1.26 5 27 15
Central A 77.9 20.7 0.27 118 226 132 26%Central B 2.375 1.9 0.81 6 37 20 33%
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Risk Pooling:Risk Pooling:Important ObservationsImportant Observations
Centralizing inventory control reduces both safety stock and average inventory level for the same service level.
This works best for High coefficient of variation, which reduces required
safety stock.Negatively correlated demand. Why?
What other kinds of risk pooling will we see?
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Risk Pooling: Risk Pooling: Types of Risk PoolingTypes of Risk Pooling
Risk Pooling Across Markets
Risk Pooling Across Products
Risk Pooling Across TimeDaily order up to quantity is:
LTAVG + z AVG L
10 1211 13 14 15
Demands
Orders
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To Centralize or not to CentralizeTo Centralize or not to Centralize
Safety stockSafety stock decreases as a firm moves from a
decentralized to a centralized system.Depend on CV and correlation
Service levelGiven the same total safety stock, the service level
provided by the centralized system is higher.
OverheadTypically, these costs are much greater in a
decentralized system.
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To Centralize or not to CentralizeTo Centralize or not to Centralize
Lead timeThe response time for a decentralized system is
much shorter.
Transportation CostsOutbound costs are higher for the centralized
system.Inbound costs are higher for the decentralized
system.
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Centralized Decision
Supplier
Warehouse
Retailers
Centralized SystemsCentralized Systems
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Centralized Distribution SystemsCentralized Distribution Systems
Question: How much inventory should management keep at each location?
A good strategy:The retailer raises inventory to level s each period
The supplier raises the sum of inventory in the retailer and supplier warehouses and in transit to S
If there is not enough inventory in the warehouse to meet all demands from retailers, it is allocated so that the service level at each of the retailers will be equal.
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Practical issuesPractical issues
Periodic inventory review policy
Tight management of usage rates, lead times and safety stock
Reduced safety stock levels
Introduce or enhance cycle counting practice
ABC approach
Shift more inventory, or inventory ownership, to suppliers
Quantitative approaches – inventory turnover rate
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Practical issues
Practical issuesPractical issues
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ForecastingForecasting
Three rules of forecastingThe forecast is always wrong.The longer the forecast horizon, the worse the
forecast.Aggregate forecasts are more accurate.
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ForecastingForecasting
Categories (See section 3.7)Judgment methodsMarket research methodsTime-series methodsCausal methods
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SummarySummary
Matching supply and demand in the supply chain is a critical challenge.Unfortunately, the existence the three
forecasting rules.
Globally optimal inventory policies, in which the best possible policy for the entire supply chain is implemented, are the best course of action.Well-designed supply contracts frequently make this global optimization possible.