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全球化趨勢下一般企業經常面對的問題. 高度需求變動 訂貨前置時間長 不可靠的供應程序 大量的儲存單位 (SKUs). 案例. 三*工業的問題 …( 前置時間 ) 手機的產品壽命週期: 20000 0 元 ( 產品壽週期需求變異 ) Ipad 對電子書的衝擊 … ( 競爭需求變異 ) 新機推出後一個月 — IPhone 跌 2 千; hTC 跌 5 千;三星跌 3 千 … 智慧型手機可能帶來衝擊 … 電子書 遊戲機 隨身聽 衛星導航 …. Why Is Inventory Important? 1.

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  • 高度需求變動
  • 訂貨前置時間長
  • 不可靠的供應程序
  • 大量的儲存單位(SKUs)
  • 三*工業的問題…(前置時間)
  • 手機的產品壽命週期:200000元 (產品壽週期需求變異)
  • Ipad 對電子書的衝擊… (競爭需求變異)
  • 新機推出後一個月—IPhone跌2千;hTC跌5千;三星跌3千…
  • 智慧型手機可能帶來衝擊…
    • 電子書
    • 遊戲機
    • 隨身聽
    • 衛星導航…
why is inventory important 1
Why Is Inventory Important?1

Distribution and inventory (logistics) costs are quitesubstantial

Total U.S. Manufacturing Inventories ($m):

  • 1992-01-31: $m 808,773
  • 1996-08-31: $m 1,000,774
  • 2006-05-31: $m 1,324,108

Inventory-Sales Ratio (U.S. Manufacturers):

  • 1992-01-01: 1.56
  • 2006-05-01: 1.25
why is inventory important 2
Why Is Inventory Important?2
  • 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)
  • Where do we hold inventory?
    • Suppliers and manufacturers
    • warehouses and distribution centers
    • retailers
  • Types of Inventory
    • WIP (work in process)
    • raw materials
    • finished goods
the reasons of holding inventory
The reasons of holding inventory
  • Unexpected changes in customer demand
    • The short life cycle of an increasing number of products.
    • The presence of manycompeting products in the marketplace.
  • Uncertainty in the quantity and quality of the supply, supplier costs and delivery times.
  • Delivery Lead Time, Capacity limitations
  • Economies of scale (transportation cost)
  • 小米3上市,對智慧型手機市場的衝擊…
  • 3DS上市對掌上型遊戲機市場的衝擊…
goals reduce cost improve service example 1
Goals: Reduce Cost, Improve Service― Example1
  • By effectively managing inventory:
    • Wal-Mart became the largest retail company utilizing efficient inventory management
    • GM has reduced parts inventory and transportation costs by 26% annually
goals reduce cost improve service example 2
Goals: Reduce Cost, Improve Service ― Example2
  • By not managing inventory successfully
    • In 1994, “IBM continues to struggle with shortages in their ThinkPad line” (WSJ, Oct 7, 1994)
    • In 1993, “Dell Computers predicts a loss; Stock plunges. Dell acknowledged that the company was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993)
inventory management vs demand forecasts
Inventory Managementvs. 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
supply chain factors in inventory policy 1
Supply Chain Factors in Inventory Policy1
  • Estimation of customer demand
  • Replenishment lead time
  • The number of different products being considered
  • The length of the planning horizon
  • Service level requirements
supply chain factors in inventory policy 2
Supply Chain Factors in Inventory Policy2
  • Costs
    • Order cost(or setup 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
2 2 single stage inventory control
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
  • Book Store Mug Sales
    • Demand is constant, at 20 units a week
    • Fixed order cost of $12.00, no lead time
    • Holding cost of 25%of inventory value annually
    • Mugs cost $1.00, sell for $5.00
  • Question
    • How many, when to order?
2 2 1 economic lot size model eoq ford w harris 1915
2.2.1 Economic Lot Size Model (EOQ)(Ford W. Harris, 1915)


• No Stockouts

• Order when no inventory

• Order Size determines policy




Avg. Inven


Cycle Time =T

  • D items per day: Constantdemand 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 costaccrued 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).
deriving eoq
Deriving EOQ
  • Total cost at every cycle:
  • Cycle timeT =Q/D
  • Average total cost per unit time:
eoq total cost
EOQ:Total Cost

Total Cost

Holding Cost

Order Cost

eoq optimal order quantity
EOQ: Optimal Order Quantity
  • So for our problem (Mug sales), the optimal quantity is 316
eoq important observations
EOQ: Important Observations
  • Trade-off between set-up costs and holdingcosts 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
sensitivity analysis
Sensitivity Analysis

Total inventory cost relatively insensitive to order quantities

Actual order quantity: Q

Q is a multiple bof the optimal order quantity Q*.

For a given b, the quantity ordered is Q = bQ*

2 2 2 the effect of demand uncertainty
2.2.2 The Effect of Demand Uncertainty
  • Most companies treat the world as if it were predictable:
    • Production and inventory planning are based on forecastsof demand made far in advance of the selling season
    • Companies are aware of demand uncertainty when they create a forecast, but they design their planningprocess as if the forecast truly represents reality
  • Recent technological advances have increased the level of demand uncertainty:
    • Short product life cycles
    • Increasing product variety
  • iPhone 5S 與 iPhone 5C的銷售量(參考iPhone 4??)
  • New hTC one 的銷售量…(參考蝴蝶機…???)
t hree principles of all forecasting techniques
Three principles of all forecasting techniques
  • 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
2 2 3 single period models
2.2.3. Single Period Models

Short lifecycle products(例如,ipad…)

  • One ordering opportunity only
  • Order quantity to be decided before demand occurs
    • Order Quantity > Demand => Dispose excess inventory
    • Order Quantity < Demand => Lose sales/profits
single period models
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.
swimsuit production
Swimsuit production

Example – Swimsuit production

  • Fashion items have short life cycles, high variety of competitors (智慧型手機?)
  • Swimsuit production
    • New designs are completed
    • One production opportunity
    • Based 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.
demand scenarios
Demand Scenarios

Example – Swimsuit production








Example – Swimsuit production

  • 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
two scenarios
Two Scenarios

Example – Swimsuit production

  • Scenario One:
    • Suppose you make 10,000 swimsuits and demand ends up being 12,000 swimsuits.
    • Profit = 125(10,000) - 80(10,000) - 100,000 = $350,000
  • Scenario Two:
    • Suppose you make 10,000 swimsuits and demand ends up being 8,000 swimsuits.
    • Profit = 125(8,000) - 80(10,000) - 100,000 + 20(2,000) = $ 140,000
probability of profitability scenarios with production 10 000 units
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 12000 units = 28%
    • Probability of profit of $350,000 = 28%
  • Total profit = Weighted average of profit scenarios
expected profit of production quantity q 1
Expected profit of production quantity Q1
  • Di=the ith demand
  • Pi=the profit of production quantity Q at demand Di
expected profit of production quantity q 2
Expected profit of production quantity Q2
  • f(Pi)=the probability of profit P at demand DiWhen production quantity=Q
  • Expect Profit of Q: E(P)
swimsuit production solution
Swimsuit production Solution

Example – Swimsuit production

  • Find order quantity that maximizes weighted average profit.
  • Question: Will this quantity be less than, equal to, or greater thanaverage demand?
order quantity that maximizes expected profit
Order Quantity that Maximizes Expected Profit

FIGURE 2-6: Average profit as a function of production quantity

relationship between optimal quantity and average demand
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
for the swimsuit example
For the Swimsuit Example
  • Average demand = 13,000 units.
  • Optimal production quantity = 12,000 units.
  • Marginal profit =125-80= $45
  • Marginal cost = 80-20=$60.
  • Thus, Marginal Cost > Marginal Profit

=> optimal production quantity < average demand.

risk reward trade offs
Risk-Reward Trade-offs
  • Optimal production quantity maximizes average profit is about 12,000($371000)
  • 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?
swimsuit production expected profit
Swimsuit production Expected Profit

Example – Swimsuit production


risk reward tradeoffs 1
Risk-Reward Tradeoffs1







FIGURE 2-7: A frequency histogram of profit

risk reward tradeoffs 2
Risk-Reward Tradeoffs2
  • 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
key insights from this model
Key Insights from this Model

Example – Swimsuit production

  • The optimal order quantity is not necessarily equal to average forecast demand
  • The optimal quantity depends on the relationship betweenmarginal 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
2 2 4 what if the manufacturer has an initial inventory
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
initial inventory solution
Initial Inventory Solution

Example – Swimsuit production


FIGURE 2-8: Profit and the impact of initial inventory

manufacturer initial inventory 5 000
Manufacturer Initial Inventory = 5,000

Example – Swimsuit production

  • If nothing is produced, average profit =

225,000 (from the figure) + 5,000 x 80 = 625,000 (125 5000=625000)

  • 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

trade off between produced and not produced
Trade-off between Produced and not Produced

Example – Swimsuit production

Let X is the trade-off point

manufacturer initial inventory 10 000
Manufacturer Initial Inventory = 10,000

Example – Swimsuit production

  • 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 $371,000.
    • Same average profit with initial inventory of 8,245units and not producing anything.
    • If initial inventory < 8,245 units => produce to raise the inventory level to 12,000 units.
    • If initial inventory is at least 8,245 units, we should not produce anything

(s, S) policy or (min, max) policy

s s policies
(s, S) 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
2 2 5 multiple order opportunities 1
2.2.5. Multiple Order Opportunities1


  • To balanceannual inventory holding costs and annual fixed order costs.
  • To satisfy demand occurringduringlead time.
  • To protect againstuncertainty in demand.
2 2 5 multiple order opportunities 2
2.2.5. Multiple Order Opportunities2
  • Continuous review policy(持續檢視政策)
    • 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(週期檢視政策)
    • inventory is reviewed atregular intervals
    • appropriate quantity is ordered after each review.
    • it is impossible or inconvenient to frequently review inventoryand place orders if necessary.
2 2 6 continuous review policy assumptions
2.2.6. Continuous Review Policy ― Assumptions
  • 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.(不考慮缺貨)
  • The distributor specifies a required service level.
the q r policy
The (Q,R) Policy
  • (Q,R ) Policy: Whenever the inventory position drops below a certain level, R, we order to raise the inventory position to level Q.
  • The reorder point (R) is a function of:
    • The Lead Time
    • Average demand
    • Demand variability
    • Service level
  • AVG = average daily demand
  • STD = standard deviation of daily demand
  • L = replenishment lead time in days
  • h = holding cost of one unit for one day
  • K = fixed cost (setup cost)
  • α= service level. This implies that the probability of stocking outis1 - α
  • Also, the Inventory Positionat any time is the actual inventory plus items already ordered, but not yet delivered.
analysis 1
  • The reorder point - (R) has two components:
    • 1. To account for average demand during leadtime:
    • 2. To account for deviations from average (we call this safety stock)

where z is chosen from statistical tables to ensure that the probability of stock-outs during leadtime is100%-SL.

analysis 2
  • reorder point - (R):
  • The total order-up-to level is (S)(倉庫容量):
  • The average inventory level is:
service level safety factor z
Service Level & Safety Factor, z

z is chosen from statistical tables to ensure

that the probability of stock-outs during lead time is exactly 1 - α

inventory level over time
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 =

continuous review policy example 1
Continuous Review Policy Example1
  • 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%(z=1.9)
continuous review policy example 2
Continuous Review Policy Example2

Average monthly demand = 191.17

Standard deviation of monthly demand = 66.53

Average weekly demand = Average Monthly Demand/4.3 =44.58

Standard deviation of weekly demand = Monthly standard deviation/√4.3=32.08

continuous review policy example 3
Continuous Review Policy Example3

Weekly holding cost =

Optimal order quantity =

Average inventory level = 679/2 + 86.20 = 426

2 2 7 1
  • 在許多情況下,運送至倉庫的運輸前置時間被假設是固定的,而且是預先知道,實則不然。在許多實際情況下,運送至倉庫的前置時間,必須假設為常態機率分配,平均前置時間以AVGL表示及標準差以STDL表示。在此情況下,再訂購點R的計算如下:
2 2 7 2
  • 其中AVG ×AVGL表示平均前置時間內的平均需求,而
  • 為平均前置時間內的平均需求標準差。
  • 因此,應維持之安全存貨為:
2 2 7 3
  • 如前述,訂購量上限為安全存貨加上Q和前置時間內平均需求的最大值,也就是:

Order Quantity =

2 2 8 periodic review policy 1
2.2.8. Periodic Review Policy1
  • 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
s s policy
(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.
a view of s s policy


Inventory Position





Inventory Level




A View of (s, S) Policy
2 2 8 periodic review policy 2
2.2.8. Periodic Review Policy2
  • Two Cases:
    • 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
base stock level policy 1
Base-Stock Level Policy1
  • 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.

base stock level policy 2
Base-Stock Level Policy2
  • Each review echelon, inventory position is raised to the base-stock level.
  • The base-stock level includes three components:
    • Average demand during (r +L) days (the time until the next order arrives
    • Safety stock during that time
    • Amount on hand at order time (A)
base stock level policy 3
Base-Stock Level Policy3
  • 安全存量為
  • 基本存貨水準

(base-stock level)

  • 而進貨的前一刻,前置時間內的需求已耗用,只剩安全存量
  • 因此平均存貨水準等於:


base stock level policy 4
Base-Stock Level Policy 4

FIGURE 2-10: Inventory level as a function of time in a periodic review policy

base stock level policy example
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 = 44.58 x 5 = 222.9
  • Safety stock =
  • Base-stock level = 223 + 136 = 359
  • Average inventory level =
  • Distributor keeps 5 (= 203.17/44.58) weeks of supply.
2 2 9 service level optimization
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
service level optimization
Service Level Optimization

FIGURE 2-11: Service level inventory versus inventory level as a function of lead time

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
retail strategy
Retail (多樣化產品)Strategy
  • Given a target service levelacross 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
profit optimization and service level 1
Profit Optimization and Service Level1

FIGURE 2-12: Service level optimization by SKU

profit optimization and service level 2
Profit Optimization and Service Level2
  • 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.
risk pooling question 1

Market One

Warehouse One


Warehouse Two

Market Two

Market One



Market Two

Risk Pooling ― Question1
  • Consider these two systems:
risk pooling question 2
Risk Pooling ― Question2
  • For the same service level, which system will require moreinventory? Why?
  • For the same total inventory level, which system will have better service? Why?
  • What are the factors that affect these answers?
  • 北半球冬季的泳衣銷售為淡季 But … 南半球為夏季…
2 3 risk pooling
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.
  • 零件自製 vs. 委外給專業製造商
demand variation
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


變異係數 =


acme risk pooling case
Acme Risk Pooling Case
  • Electronic equipment manufacturer and distributor
  • 2 warehouses for distribution in Massachusetts 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(z=1.9)
  • Each warehouse operate to satisfy 97 % of demand (3 % probability of stock-out)
  • Lead time for delivery is about one week
new idea
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.
  • h = holding cost of one unitforone week=0.27
  • k = fixed cost (setup cost) =60
savings in inventory
Savings in Inventory
  • Average inventory for Product A:
    • At NJ warehouse is about 88 units (ss+Q/2=22.8+131/2=88)
    • At MA warehouse is about 91 units
    • In the centralized warehouse is about 132 units
    • Average inventory reduced by about 26 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 31 percent
critical points 1
Critical Points1
  • 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
critical points 2
Critical Points2
  • 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
2 4 centralized versus decentralized systems the trade offs
2.4 Centralized versus Decentralized Systems ― The Trade-offs
  • 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.
2 5 managing inventory in the supply chain 1
2.5 Managing Inventory in the Supply Chain1
  • 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
managing inventory in the supply chain 2
Managing inventory in the supply chain2
  • Echelon inventory (階層存貨)
    • Theinventory on hand at the echelon, plusall downstream inventory (downstream means closer to the customer)
  • Echelon inventory position(階層存貨狀態)
    • The echelon inventory at the echelon, plusthose items ordered by the echelon that have not yet arrived minusall items that are backordered.
echelon inventory
Echelon Inventory

FIGURE 2-13: A serial supply chain

reorder point with echelon inventory distributor
Reorder Point with Echelon Inventory (distributor)
  • 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 deviationof demand at the retailer
  • Reorder point
4 stage supply chain example
4-Stage Supply Chain Example
  • Average weekly demand faced by the retailer is 45
  • Standard deviationof 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
reorder points at each stage
Reorder Points at Each Stage
  • For the retailer, R=1*45+1.88*32*√1 = 105
  • For the distributor, R=2*45+1.88*32*√2 = 175
  • For the wholesaler, R=3*45+1.88*32*√3 = 239
  • For the manufacturer, R=4*45+1.88*32*√4 = 300
  • At each echelon, when the echelon inventory position falls below the reorder point for that echelon, the appropriate Q is ordered.
more than one facility at each stage
More than One Facility at Each Stage
  • Follow the same approach (two stage)
  • Echelon inventory at the warehouse is the inventory at thewarehouse, plus all of the inventory intransitto and in stockat 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.
warehouse echelon inventory
Warehouse Echelon Inventory

FIGURE 2-14: The warehouse echelon inventory

reorder point with echelon inventory
Reorder Point with Echelon Inventory

The reorder point of warehouseis


Le=echelon lead time, defined as the lead time between the retailers and the warehouseplusthe lead time between the warehouse and its supplier

AVG=average demandacross all retailers

STD=standard deviation of demand across all retailers

2 6 practical issues 1
2.6 Practical Issues1
  • Periodic inventory review.
    • To identify slow-moving and obsolete products and allows management to continuously reduce inventory levels.
  • Tight management of usage rates, lead times, and safety stock.
  • Reduce safety stock levels.
  • Introduce or enhance cycle counting practice.
    • Replaces the annual physical inventory count
    • Part of inventory is counted every day, and each item is counted several times per year.
2 6 practical issues 2
2.6 Practical Issues2
  • ABC approach.
    • Class A: a high-frequency periodic review policy(e.g., a weekly review)
    • Class C: the firm eitherkeeps no inventory of expensive Class C productsor keeps a high inventory of inexpensive Class C products.
  • Shift more inventory or inventory ownership to suppliers.
  • Quantitative approaches.

FOCUS: not reducing costsbut reducing inventory levels. (JIT)

Significant effort in industry to increase inventory turnover

inventory turnover ratio
Inventory Turnover Ratio
  • Inventory turnover ratio = annual sales/avg. inventory level
  • Increase in inventory turnover leads to
    • Decrease in average inventory levels
    • Higher level of liquidity
    • Smaller risk of obsolescence
    • Reduced investment in inventory
    • Increases the risk of lost sales
factors that drive reduction in inventory
Factors that Drive Reduction in Inventory
  • Top management emphasis on inventory reduction (19%)
  • Reduce the Number of SKUs in the warehouse (10%)
  • Improved forecasting (7%)
  • Use of sophisticated inventory management software (6%)
  • Coordination among supply chain members (6%)
  • Others
2 7 forecasting
2.7 Forecasting
  • General Overview:
    • Judgment methods
    • Market research methods
    • Time-series methods
    • Causal methods
judgment methods 1
Judgment Methods1
  • Assemble the opinion of experts
  • Sales-force composite combines salespeople’s estimates
    • 優點
      • 銷售員直接與顧客接觸,較能知道顧客對於未來的考量與計畫。
    • 缺點
      • 銷售員無法區分顧客想做與實際會做的事。
      • 銷售員易過度受到最近經驗的影響。
judgment methods 2
Judgment Methods2
  • Panels of experts – internal, external, both
  • Delphi method
    • Each member surveyed
    • Opinions are compiled
    • Each member is given the opportunity to change his opinion
market research methods
Market Research Methods
  • Particularly valuable for developing forecasts of newly introduced products
  • Market testing
    • Focus groups assembled.
      • Responses tested.
      • Extrapolations to rest of market made.
  • Market surveys
    • Data gathered from potential customers
    • Interviews, phone-surveys, written surveys, etc.
time series methods
Time Series Methods
  • Past data is used to estimate future data
  • Examples include
    • Moving averages – average of some previous demand points.
    • Exponential Smoothing – more recent points receive more weight
    • Methods for data with trends:
      • Regression analysis – fits line to data
      • Holt’s method – combines exponential smoothing concepts with the ability to follow a trend
    • Methods for data with seasonality
      • Seasonal decomposition methods (seasonal patterns removed)
      • Winter’s method: advanced approach based on exponential smoothing
    • Complex methods (not clear that these work better)
  • 趨勢 - 資料中漸進而長期的移動
  • 季節變動 - 資料中短期而規則性的變動
  • 循環 - 在一年以上的時間內,呈波狀的變動
  • 不規則的變動 - 由於不尋常的情況所產生的
  • 隨機變動 - 偶然發生








  • 天真預測法(naive forecasts)
  • 移動平均法(moving average method)
  • 加權移動平均法(weighted moving average method)
  • 指數平滑化法(exponential smoothing method)

嗯, 請給我一分鐘想想.... 上週我們已銷售250個輪胎.... 所以下週我們將要銷售....

  • 倘若前一期的需求為極端值…
  • 與本期較近之期間的需求,其參考價值應較高…?
exponential smoothing
指數平滑法(Exponential Smoothing)

Ft = Ft-1 + (Dt-1 - Ft-1)

=Dt-1 +(1- )Ft-1







  • 目的
    • 在反應真實變動與平滑隨機變動之利益間取得平衡。
  • 選擇情境
    • 平均值傾向穩定時,使用較低的α值。
    • 平均值容易受變動影響時,使用較大的α值。
  • 天真預測法
  • 三期移動平均
  • 權重為0.50(最近)0.3與0.2的加權平均法
  • 平滑常數為0.40的指數平滑法(以第一期之實際值作為第二期之預測值)
  • 天真預測法
    • 64
  • 三期移動平均
    • MA3=(55+58+64)/3=59
  • WA=(0.564)+(0.3 58)+(0.2 55)
  • 雙指數平滑法(double exponential smoothing method)
  • 迴歸分析法(regression analysis)
    • 又稱最小平方法(least square method)
  • FITt+1 = Ft+1 + Tt
  • Ft+1 = FITt + α (At – FITt)
  • Tt = Tt-1 + β[(FITt – FITt-1)– Tt-1)]
  • =Tt-1 + β(Ft – FITt-1)
  • 其中
      • Ft+1=第t+1期之不含趨勢預測
      • Tt=第t期之趨勢預測值
      • FITt=第t期之含趨勢預測值
      • α=平均平滑常數
      • β=趨勢平滑常數
      • α 與β皆介於0與1之間。


0 1 2 3 4 5 t


Yt = a + b t


5 (2499)


























y = 143.5 + 6.3t

  • 若一時間數列明顯含有季節性因素,必須先計算各季之季節指數,再利用該各季節指數來對資料進行去除季節性,然後才可用一預測方法對去除季節性之資料,做正常之分析與預測。最後計算出預測值必須再乘以季節指數,使之變為含季節性之預測值。
















  • 季節指數(簡單平均)It


Suppose the projected demand for year 3 is 1320 units.





TM 12.3b

causal methods
Causal Methods
  • Forecasts are generated based on data other than the data being predicted
  • Examples include:
    • Inflation rates
    • GNP
    • Unemployment rates
    • Weather
    • Sales of other products
multiple techniques
多元技術(multiple techniques)的使用
  • 複合預測法(combination forecasts)
    • 使用不同的預測方法或資料進行預測,取其平均值作為預測值。
  • 焦點預測法(focus forecasts)
    • 同時使用多種預測技術,採用最近且預測效果最佳的方法作為本期之預測方法。
  • 誤差 = 實際值與預測值之間的差額
  • 平均絕對誤差(mean absolute deviation,MAD)
  • 均方誤差(mean squared error,MSE)
  • 平均絕對百分比誤差(mean absolute percent error,MAPE)
























  • 預測方法適用與否之判斷→預測誤差是否是隨機的。
  • 方法
    • 追蹤信號(tracking signal)
    • 管制圖










  • 其範圍通常從±3到±8
  • 一般採用±4
  • 管制中心線(center line, CL)=E(e)=0
  • 管制上限(upper control limit, UCL)=E(e)+zσe=z(MSE)1/2
  • 管制下限(lower control limit, LCL)=E(e)-zσe=-z(MSE)1/2
selecting the appropriate approach chambers mullick and smith cms
Selecting the Appropriate Approach (Chambers, Mullick, and Smith, CMS)
  • What is the purpose of the forecast?
    • Gross or detailed estimates?
  • What are the dynamics of the system being forecast?
    • Is it sensitive to economic data?
    • Is it seasonal? trending?
  • How important is the past in estimatingthe future?
product life cycle vs forecast techniques
Product life cycle vs. forecast techniques
  • Testing and intro: market research methods, judgment methods
  • Rapid growth: time series methods (with trend)
  • Mature: time series, causal methods (particularly for long-range planning)
  • It is typically effective to combine approaches. (Georgoff and Murdick)
  • 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