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OPER3208-001 Supply Chain Management. Fall 2006 Instructor: Prof. Setzler. Simchi-Levi, Chapters 3. Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi). Introduction

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Oper3208 001 supply chain management

OPER3208-001Supply Chain Management

Fall 2006

Instructor: Prof. Setzler


Oper3208 001 supply chain management

  • Simchi-Levi, Chapters 3


Chapter 3 inventory management and risk pooling simchi levi

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Introduction

    • Managing inventory in complex SCs is typically difficult, and may have a significant impact on the customer service level and SC systemwide cost

    • Inventory appears in the SC in several forms:

      • Raw materials

      • Work-in-process (WIP)

      • Finished products

        • Each needs its own inventory control mechanism

        • Shipment sizes (i.e., inventory policy)

        • Routes (i.e., transportation strategy)


Chapter 3 inventory management and risk pooling simchi levi1

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Introduction

    • Why hold inventory

      • Unexpected changes in customer demand

        • Short life cycle

        • Many competing products

      • Uncertainty in the quantity and quality of supply, supplier costs, and delivery times

      • Due to delivery lead times

      • Economies of scale of transportation cost


Chapter 3 inventory management and risk pooling simchi levi2

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Introduction

    • Two important issues in inventory management

      • Demand forecasting

      • Order quantity calculation

    • Since demand is uncertain in most situations, forecast demand is a critical element in determining order quantity


Chapter 3 inventory management and risk pooling simchi levi3

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • A single warehouse inventory example

    • What are the key factors affecting inventory policy?

      • Customer demand

        • May be known in advance, or may be random

      • Replenishment lead time

        • May be known at time of order, or may be uncertain

      • Number of different products

      • Length of the planning horizon

      • Costs, including order cost and inventory holding cost

        • Order cost = cost of the product + transportation cost

        • Inventory holding cost (a.k.a. inventory carrying cost = taxes and insurance + Maintenance + Obsolescence + Opportunity costs

      • Service level requirements

        • Management needs to specify an acceptable level of service


Chapter 3 inventory management and risk pooling simchi levi4

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • Model that illustrates the trade-offs between ordering and storage costs

    • Consider a warehouse facing constant demand for a single item

    • The warehouse orders from the supplier, who is assumed to have an unlimited quantity of the product


Chapter 3 inventory management and risk pooling simchi levi5

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • The economic lot size model assumes

      • Demand is constant at a rate of D items per day

      • Order quantities are fixed at Q items

      • A fixed cost (setup cost), K, is incurred every time an order is placed

      • Inventory carrying cost, h, is accrued per unit held in inventory per day that the unit is held

      • Lead time is zero

      • Initial inventory is zero

      • Planning horizon is long (infinite)


Chapter 3 inventory management and risk pooling simchi levi6

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • The goal is to find the optimal order policy that minimizes annual purchasing and carrying costs while meeting all demand

    • This is a simplified version of a real inventory system

      • The insight derived will help to develop inventory policies that are effective for more complex realistic systems


Chapter 3 inventory management and risk pooling simchi levi7

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • The optimal policy for this model is that orders should be received at the warehouse right when inventory drops to zero

      • Called the zero inventory ordering property


Chapter 3 inventory management and risk pooling simchi levi8

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • To find the optimal ordering policy is the economic lot size model, consider the inventory level as a function of time

      • This is called the saw-toothed inventory pattern

        • The time between two successive replenishments is referred to as a cycle time

        • Total inventory cost in a cycle of length T is


Chapter 3 inventory management and risk pooling simchi levi9

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • Since the inventory level changes from Q to 0 during a cycle of length T, and demand is constant at a rate of D units per unit time, it must be that Q = TD

    • Divide cost ( ) above by T, or, equivalently, Q/D, to get the average total cost per unit of time


Chapter 3 inventory management and risk pooling simchi levi10

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • Using simple calculus, it is easy to show that the order quantity Q* that minimizes the cost function above is

    • This quantity is referred to as the economic order quantity (EOQ)


Chapter 3 inventory management and risk pooling simchi levi11

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • Two important insights from this model

      • An optimal policy balances inventory holding cost per unit time with setup cost per unit time

        • Setup cost per unit time = KD/Q, while holding cost per unit time = hQ/2 (see Figure 3-2)

          • As Q increases, inventory holding costs per unit of time increases while K per unit of time decreases

        • The optimal order quantity is achieved at the point at which inventory setup cost per unit of time (KD/Q) equals inventory holding cost per unit of time (hQ/2)


Basic fixed order quantity eoq model formula

Total

Annual =

Cost

Annual

Purchase

Cost

Annual

Ordering

Cost

Annual

Holding

Cost

+

+

Basic Fixed-Order Quantity (EOQ) Model Formula

TC=Total annual cost

D =Demand

C =Cost per unit

Q =Order quantity

K =Cost of placing an order or setup cost

R =Reorder point

L =Lead time

H =Annual holding and storage cost per unit of inventory


Chapter 3 inventory management and risk pooling simchi levi12

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model


Chapter 3 inventory management and risk pooling simchi levi13

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The Economic Lot Size Model

    • Two important insights from this model

      • Total inventory cost is insensitive to order quantities

        • Changes in order quantities have a relatively small impact on annual setup costs and inventory holding costs

        • Consider a decision maker that places an order quantity Q that is a multiple b of the optimal order quantity Q*

        • Table 3-1 presents the impact of changes in b on total system cost


Chapter 3 inventory management and risk pooling simchi levi14

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • The previous model illustrates the trade-offs between setup and inventory holding costs

    • It ignores issues such as demand uncertainty and forecasting

    • Principles of all forecasts

      • Forecasts are always wrong

        • It is difficult to match supply and demand

      • The longer the forecast horizon, the worse the forecast

        • Even more difficult if one needs to predict customer demand for a long period of time

      • Aggregate forecasts are more accurate

        • While it is difficult to predict customer demand for individual SKUs, it is much easier to predict demand across all SKUs within one product family

          • This is an example of risk pooling


Chapter 3 inventory management and risk pooling simchi levi15

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • Six months prior to summer the swimsuit producer must commit to specific production quantities

        • The company needs to use various tools to predict demand

        • The trade-offs

          • Overestimating demand will result in unsold inventory

          • Underestimating demand will lead to inventory stockouts and loss of potential customers

        • Marketing department uses historical data from last 5 years, current economic conditions, and other factors to construct a probabilistic forecast

          • Identify several possible scenarios for sales based on such factors as possible weather patterns and competitors’ behavior, and assign each a probability, or chance of occurring


Chapter 3 inventory management and risk pooling simchi levi16

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

Average Demand = 13,000 units


Chapter 3 inventory management and risk pooling simchi levi17

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • Additional information

        • Fixed production cost = $100,000

        • Variable production cost = $80 per unit

        • Regular selling price = $125 per unit

        • Discount selling price = $20 per unit (i.e., salvage value)

      • To identify the best production quantity, the firm needs to understand the relationship between the production quantity, customer demand, and profit


Chapter 3 inventory management and risk pooling simchi levi18

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • Suppose manufacturer produces 10,000 units

      • Demand = 12,000 units

      • Profit = revenue from summer sales – variable production costs – fixed production costs

      • Profit = $125 (10,000) - $80 (10,000) - $100,000 = $350,000


Chapter 3 inventory management and risk pooling simchi levi19

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • Suppose manufacturer produces 10,000 units

      • Demand = 8,000 units

      • Profit = revenue from summer sales – variable production costs – fixed production costs

      • Profit = $125 (8,000) + $20 (2,000) - $80 (10,000) - $100,000 = $140,000


Chapter 3 inventory management and risk pooling simchi levi20

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • Probability that demand is

        8,000 is 11%

      • Probability that demand is

        12,000 is 27%

      • Therefore, producing 10,000 units leads to a profit of $350,000 with probability of 27%, and a profit of $140,00 with probability of 11%

      • The expected profit for a set production level (10,000 units above) is the total profit of all the scenarios weighted by the probability that each scenario will occur

        • Would like to find order quantity that maximizes average profit


Chapter 3 inventory management and risk pooling simchi levi21

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • What is the relationship between the optimal production quantity and average demand?

      • Should the optimal order quantity be equal to, more than, or less than the average demand?

        • The answer: evaluate the marginal profit and marginal cost of producing an additional unit

        • Marginal profit of a summer sale is $45 ($125 - $80 = $45)

        • Marginal cost of non-summer sale is $60 ($80 - $20 = $60)

          • The cost of a non-summer sale is larger than the profit obtained by a summer sale, therefore the best production quantity will be less than the average demand


Chapter 3 inventory management and risk pooling simchi levi22

$294,000

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

The optimal production quantity, or the quantity that maximizes average profit,

is about 12,000 units. 9,000 and 16,000 lead to the same average profit


Chapter 3 inventory management and risk pooling simchi levi23

$294,000

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • If had to decide between

        producing 9,000 or 16,000

        units, which should you do?

      • Need to better understand the risk associated with certain decisions

        • Construct a frequency histogram to provide information about potential profit for 9,000 and 16,000 units


Chapter 3 inventory management and risk pooling simchi levi24

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • The possible risk and possible reward increases as production

        size

        increases


Chapter 3 inventory management and risk pooling simchi levi25

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • The effect of demand uncertainty

    • Case: Swimsuit Production

      • Summary

        • The optimal order quantity is not necessarily equal to forecast, or average, demand

          • Optimal quantity depends on the relationship between marginal profit and marginal cost

          • Fixed cost has no impact on production quantity

        • As order quantity increases, average profit typically increases until the production quantity reaches a certain value, after which the average profit starts to decrease

        • As we increase the production quantity,

          • The risk (i.e., the probability of large losses) always increases

          • The probability of large gains also increases

          • This is the risk/reward trade-off


Chapter 3 inventory management and risk pooling simchi levi26

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • Buyers and suppliers typically agree on supply contracts

      • Contracts address issues that arise between a buyer and a supplier

      • Buyers and suppliers may agree on

        • Pricing and volume discounts

        • Minimum and maximum purchase quantities

        • Delivery lead time

        • Product or material quality

        • Product return policies

      • Supply contracts are very powerful tools that can be used for far more than to ensure adequate supply of, and demand for, goods


Chapter 3 inventory management and risk pooling simchi levi27

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • Sequential SC

      • A supply chain in which each party determines its own course of action independent of other parties

        • This cannot be an effective strategy of SC partners

      • We try to find mechanisms that enable SC entities to move beyond the sequential optimization and toward global optimization


Chapter 3 inventory management and risk pooling simchi levi28

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • A variety of supply contracts will allow for risk sharing, and increase profits across the SC

      • Buy-back contracts

      • Revenue-sharing contracts

      • Quantity-flexibility contracts

      • Sales rebate contracts

      • Global Optimization


Chapter 3 inventory management and risk pooling simchi levi29

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • A variety of supply contracts will allow for risk sharing, and increase profits across the SC

      • Buy-back contracts

        • The seller agrees to buy back unsold goods from the buyer for some agreed-upon price

        • Is effective because it allows the manufacturer to share some of the risk with the retailer, and motivates the retailer to increase the order quantity

        • The manufacturer compensates for its increase in risk by being able to sell more products at full price if demand out to be larger than expected


Chapter 3 inventory management and risk pooling simchi levi30

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts


Chapter 3 inventory management and risk pooling simchi levi31

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts


Chapter 3 inventory management and risk pooling simchi levi32

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • A variety of supply contracts will allow for risk sharing, and increase profits across the SC

      • Revenue-sharing contracts

        • In the sequential SC, one important reason for the retailer to order only the expected amount is the high wholesale price

        • If the retailer can convince the manufacturer to reduce the wholesale price, then the retailer will have an incentive to order more

          • A reduction in wholesale price will decrease the manufacturer’s profit if it is unable to sell more units

        • In revenue-sharing contracts, the buyer shares some of its revenue with the seller, in return for a discount on the wholesale price


Chapter 3 inventory management and risk pooling simchi levi33

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts


Chapter 3 inventory management and risk pooling simchi levi34

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts


Chapter 3 inventory management and risk pooling simchi levi35

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • A variety of supply contracts will allow for risk sharing, and increase profits across the SC

      • Quantity-flexibility contracts

        • Contracts in which the supplier provides full refund (unsold) items as long as the number of returns is no larger than a certain quantity

          • This contract gives full refund for all returned items


Chapter 3 inventory management and risk pooling simchi levi36

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • A variety of supply contracts will allow for risk sharing, and increase profits across the SC

      • Sales rebate contracts

        • 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


Chapter 3 inventory management and risk pooling simchi levi37

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • A variety of supply contracts will allow for risk sharing, and increase profits across the SC

      • Global Optimization

        • What is the most profit both the supplier and the buyer can hope to achieve?

        • Effective supply contracts provide incentives for supply chain partners to replace traditional strategies, in which each partner optimizes its own profit, global optimization is that it requires the firm to surrender decision-making power to an unbiased decision maker


Chapter 3 inventory management and risk pooling simchi levi38

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts


Chapter 3 inventory management and risk pooling simchi levi39

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts


Chapter 3 inventory management and risk pooling simchi levi40

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • Why supply contracts are so important

      • They help firms achieve global optimization by allowing buyers and suppliers to share the risk and the potential benefit

      • It’s not difficult to show that a more careful design of these contracts can achieve the exact same profit as the profit in global optimization

        • For revenue sharing this can be achieved by carefully selecting the wholesale price and the level of revenue sharing

        • For buy-back contract this can be achieved by choosing the buy-back price and the wholesale price


Chapter 3 inventory management and risk pooling simchi levi41

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts


Chapter 3 inventory management and risk pooling simchi levi42

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • The main drawback of global optimization is that it does not provide a mechanism to allocate supply chain profit between partners

      • It only provides information on the best, or optimal, set of actions that need to be taken by the supply chain to improve profit

      • Supply contracts allocate this profit among supply chain members


Chapter 3 inventory management and risk pooling simchi levi43

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Supply Contracts

    • Effective supply contracts allocate profit to each partner in a way that no partner can improve his profit by deciding to deviate from the optimal set of decisions

      • There is no incentive for either the buyer or the seller to deviate from the set of actions that will achieve the global optimal solution


Chapter 3 inventory management and risk pooling simchi levi44

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Multiple Order Opportunities

    • Recall the single-decision maker model discussed earlier

      • This model assumes that the decision maker can make only a single ordering decision for the entire horizon

        • In many practical situations, the decision maker may order products repeatedly at any time during the year


Chapter 3 inventory management and risk pooling simchi levi45

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Multiple Order Opportunities

    • Consider a distributor of TV sets

      • The distributor faces random demand for the product and receives supply from the manufacturer

      • The manufacturer can’t instantaneously satisfy distributor orders: there is a fixed lead time

      • Since demand is random and the manufacturer has a fixed delivery lead time, the distributor needs to hold inventory, even if no fixed setup cost is charged


Chapter 3 inventory management and risk pooling simchi levi46

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Multiple Order Opportunities

    • At lease 3 reasons explain why the distributor holds inventory

      • To satisfy demand occurring during lead time

      • To protect against uncertainty in demand

      • To balance annual inventory holding costs and annual fixed order costs

        • More frequent orders lead to lower inventory levels and therefore lower inventory holding costs, but they also lead to higher annual fixed order costs

      • The inventory policy for the distributor is not simple


Chapter 3 inventory management and risk pooling simchi levi47

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Multiple Order Opportunities

    • 2 types of policies

      • Continuous review policy

        • Inventory is reviewed every day and a decision is made about whether and how much to order

      • Periodic review policy

        • Inventory level is reviewed at regular intervals and an appropriate quantity is ordered after each review


Chapter 3 inventory management and risk pooling simchi levi48

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • Assumptions

      • Daily demand (d) is random and follows a normal distribution

      • Ordering cost: K = fixed cost + an amount proportional to the quantity ordered

      • Inventory holding cost: h = charge per item per unit time

      • Inventory level is reviewed at the end of every day. If an order is placed, it arrives after the specified lead time

      • If a customer order arrives when there is no inventory, the order is lost

      • The distributor specifies a required service level

        • The probability of not stocking out during lead time


Chapter 3 inventory management and risk pooling simchi levi49

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • Needed information

      • AVG = average daily demand

      • STD = standard deviation of daily demand

      • L = replenishment lead time

      • h = cost of holding 1 unit for 1 day

      • α = service level. This implies that the probability of stocking out is 1-α


Chapter 3 inventory management and risk pooling simchi levi50

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • Inventory position

      • Any point in time is the actual inventory on hand + items ordered that have not yet arrived – items that are backordered

      • s = the reorder point

      • S = the order-up-to level

      • An effective inventory policy in this case is an (s, S) policy where the difference between S and s is due to the fixed cost

        • When ever the inventory position level drops below level s, an order should be placed to raise the inventory position to level S


Chapter 3 inventory management and risk pooling simchi levi51

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • s = the reorder point

      • 2 components

        • Average inventory during lead time = average daily demand * lead time (i.e., L * AVG)

        • Safety stock, which is the amount of inventory to protect against deviations from average demand during lead time

        • The safety factor z is chosen from statistical tables to ensure that the probability of stockouts during lead time is exactly 1 -α

        • The reorder point must satisfy


Chapter 3 inventory management and risk pooling simchi levi52

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • Here is a list of z values for different values of the service level α


Chapter 3 inventory management and risk pooling simchi levi53

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • S = the order-up-to level

      • Recall that for the economic lot size model the order quantity Q is calculated as follows:

      • If there is no variability in demand, then Q items should be ordered whenever inventory is at the level L * AVG since it take L days to receive the order

      • Since there is most certainly variability in demand, an order for Q items should be placed whenever the inventory position is at the reorder point, s

      • The order-up-to level is S = Q + s


Chapter 3 inventory management and risk pooling simchi levi54

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • When (s, S) policies are employed, the inventory position may drop below the reorder point, in which case the (s, S) policy implies that the order size should be enough to raise the inventory position to the order-up-to level

      • This amount may be larger than Q


Chapter 3 inventory management and risk pooling simchi levi55

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy


Chapter 3 inventory management and risk pooling simchi levi56

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy


Chapter 3 inventory management and risk pooling simchi levi57

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy


Chapter 3 inventory management and risk pooling simchi levi58

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy


Chapter 3 inventory management and risk pooling simchi levi59

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • Variable lead time

      • Many times the assumption that delivery lead time is fixed and known in advanced doesn’t hold

        • The lead time may be assumed to be normally distributed with an average lead time denoted by AVGL and standard deviation by STDL

          • In this case, the reorder point, s, is calculated as follows


Chapter 3 inventory management and risk pooling simchi levi60

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • Variable lead time

    • Where AVG * AVGL represents average demand during lead time, while

    • Is the standard deviation of demand during lead time

    • Safety stock is equal to


Chapter 3 inventory management and risk pooling simchi levi61

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Continuous review policy

    • Variable lead time

      • The order-up-to level is the sum of the reorder point and Q


Chapter 3 inventory management and risk pooling simchi levi62

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Periodic review policy

    • Many times inventories are reviewed periodically, at regular intervals

      • Since inventory levels are reviewed at a periodic interval, the fixed cost of placing an order is a sunk cost and therefore can be ignored

        • The fixed cost was used to determine the review interval

        • Quantity ordered arrives after the appropriate lead time

      • This inventory policy is characterized by one parameter, the base-stock level

        • A target inventory level (a.k.a. base-stock level)

        • At each review period the inventory position is reviewed and enough product is ordered to raise the inventory position to the base-stock level


Chapter 3 inventory management and risk pooling simchi levi63

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Periodic review policy

    • Let r be the length of the review period

      • Assume that orders are placed every r period of time

      • L = lead time

      • AVG = average daily demand

      • STD = standard deviation of daily demand

      • At the time the order is placed, the order raises the inventory position to the base-stock level

        • This level of the inventory position should be enough to protect against shortages until the next order arrives

        • Since the next order arrives after a period of r + L days, the current order should be enough to cover demand during a period of r + L days


Chapter 3 inventory management and risk pooling simchi levi64

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Periodic review policy

    • The base-stock level should include 2 components

      • Average demand during an interval of r + L days, which is equal to (r + L) * AVG

      • Safety stock, which is the amount of inventory needed to protect against deviations from average demand during a period of r + L days


Chapter 3 inventory management and risk pooling simchi levi65

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Periodic review policy


Chapter 3 inventory management and risk pooling simchi levi66

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Periodic review policy

    • The expected level of inventory after receiving an order is equal to

    • While the expected level of inventory before an order arrives is just the safety stock

    • The average inventory level is the average of these two values


Chapter 3 inventory management and risk pooling simchi levi67

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Periodic review policy


Chapter 3 inventory management and risk pooling simchi levi68

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Risk pooling

    • Risk pooling suggests that demand variability is reduced if one aggregates demand across locations because, as demand is aggregated across different locations, it becomes more likely that high demand from one customer will be offset by low demand from another

    • This reduction in variability allows a decrease in safety sock and therefore reduces average inventory

    • In a centralized distribution system the warehouse serves all customers, which leads to a reduction in variability measured by either the standard deviation or the coefficient of variability


Chapter 3 inventory management and risk pooling simchi levi69

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Risk pooling

    • 3 critical points about risk pooling

      • Centralizing inventory reduces both safety stock and average inventory

        • The process of reallocating inventory is not possible in a decentralized distribution system

      • The higher the coefficient of variation, the greater the benefit obtained from centralized systems; that is, the greater the benefit from risk pooling

        • Since the reduction in average inventory is achieved mainly through a reduction in safety stock, the higher the coefficient of variation, the larger the impact of safety stock on inventory reduction

        • Coefficient of variation = Standard deviation/Average demand

      • The benefit from risk pooling depend on the behavior of demand from one market relative to demand from another

        • Demand from 2 markets are positively correlated if it is very likely that whenever demand from one market is greater than average, demand from the other market is also greater than average

        • The benefit from risk pooling decreases as the correlation between demand from the 2 markets becomes more positive


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Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Centralized versus decentralized systems

    • What are the trade-offs that need to be considered in comparing centralized distribution systems with decentralized distribution systems?

      • Safety stock

        • Decreases as move from decentralized to centralized systems

      • Service level

        • Safety stock levels held constant, service level provided by centralized systems is higher

      • Overhead costs

        • Typically much higher in decentralized systems because they have fewer economies of scale

      • Customer lead time

        • Response time is much shorter in decentralized systems since the warehouses are much closer to the customer

      • Transportation costs

        • Depend on specific situation

        • Decentralized systems outbound transportation costs decrease

        • Decentralized systems inbound transportation costs increase


Chapter 3 inventory management and risk pooling simchi levi71

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Managing inventory in the SC

    • Most inventory models considered so far assume a single facility

    • In this section, multifacility supply chain that belongs to a single firm are considered

    • The objective of the firm is to manage inventory to reduce systemwide cost

      • It is important to consider the interaction of the different facilities and the impact this interaction has on the inventory policy that should be employed by each facility


Chapter 3 inventory management and risk pooling simchi levi72

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Managing inventory in the SC

    • Consider a retail distribution system with a single warehouse serving a number of retailers

      • 2 assumptions

        • Inventory decisions are made by a single decision maker whose objective is to minimize systemwide cost

        • The decision maker has access to inventory information at each of the retailers and at the warehouse

      • Under these assumptions, an inventory policy based on the so-called echelon inventory is an effective way to manage the system


Chapter 3 inventory management and risk pooling simchi levi73

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Managing inventory in the SC

    • Echelon inventory

      • In a distribution system, each stage or level often is referred to as an echelon

        • The echelon inventory at any stage or level of the system is equal to the inventory on hand at the echelon, plus all downstream inventory

          • For example, the echelon inventory at the warehouse is equal to the inventory at the warehouse, plus all of the inventory in transit to and in stock at the retailers

          • 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


Chapter 3 inventory management and risk pooling simchi levi74

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Managing inventory in the SC

    • Echelon inventory


Chapter 3 inventory management and risk pooling simchi levi75

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Managing inventory in the SC

    • Effective approach to managing the single warehouse multiretailer system

      • The individual retailers are managed using the appropriate (s, S) inventory policy

      • The warehouse ordering decisions are based on the echelon inventory position at the warehouse

    • The reorder point, s, and order-up-to level, S, are calculated for each retailer

      • Whenever the inventory position at a retailer falls below the reorder point s, an order is placed to raise its inventory position to S

    • A reorder point s and an order-up-to level S is calculated for the warehouse

      • The warehouse policy controls its echelon inventory position

        • Whenever the inventory position for the warehouse is below s, and order is placed to raise the echelon inventory position to S


Chapter 3 inventory management and risk pooling simchi levi76

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Managing inventory in the SC

    • How should the reorder point associated with the warehouse echelon inventory position be calculated?

    • where

      • Le = echelon lead time

        • The lead time between the retailers and the warehouse plus the lead time between the warehouse and its supplier

      • AVG = average demand across all retailers (i.e., the average of the aggregate demand)

      • STD = standard deviation of (aggregate) demand across all retailers


Chapter 3 inventory management and risk pooling simchi levi77

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Managing inventory in the SC


Chapter 3 inventory management and risk pooling simchi levi78

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Practical issues

    • Top seven inventory reduction strategies

      • Periodic inventory review

        • Periodic inventory review policy makes it possible to identify slow-moving and obsolete products

      • Tight management of usage rates, lead times, and safety stock

        • Allows the firm to identify, for example, situations in which usage rates decrease for a few months

      • Reduce safety stock levels

        • Perhaps focusing on lead-time reduction

      • Introduce or enhance cycle counting practice

        • Replaces an annual inventory physical inventory count by a system where part of the inventory is counted every day, and each item is counted several times per year

      • ABC approach

        • Because Class A items account for the major part of the business, a high-frequency periodic review policy is appropriate.

      • Shift more inventory or inventory ownership to suppliers

      • Quantitative approaches

        • Approaches similar to determining the right balance between inventory holding cost and ordering cost


Chapter 3 inventory management and risk pooling simchi levi79

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Practical issues

    • There has been a significant effort by industry to increase the inventory turnover ratio

    • An increase in inventory turnover leads to a decrease in average inventory levels

      • High turnover ratio suggests a higher level of liquidity, smaller risk of obsolescence, and reduced investment in inventory


Chapter 3 inventory management and risk pooling simchi levi80

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Practical issues

    • What are the appropriate inventory turns that a firm should use in practice?


Chapter 3 inventory management and risk pooling simchi levi81

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Forecasting

    • 3 rules of forecasting

      • Forecasts are always wrong

      • The longer the forecast horizon, the worse the forecast

      • Aggregate forecasts are more accurate

    • Nevertheless, forecasting is a critical tool

      • By correctly managing inventory, managers can make the best possible use of forecasts


Chapter 3 inventory management and risk pooling simchi levi82

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi)

  • Forecasting

    • 4 general forecasting categories

      • Judgment method

        • Collection of expert opinions

      • Market research methods

        • Qualitative studies of customer behavior

      • Time-series methods

        • Mathematical methods in which future performance is extrapolated from past performance

      • Causal methods

        • Mathematical methods in which forecasts are generated based on different system variables


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