© 2015 McGraw-Hill Education. All rights reserved. Chapter 18 Inventory Theory.

© 2015 McGraw-Hill Education. All rights reserved.


Frederick S. Hillier Gerald J. Lieberman

Chapter 18

Inventory Theory


Introduction

• Scientific inventory management– Mathematical model describes system

behavior

– Goal: optimal inventory policy with respect to the model

– Computerized information processing system maintains inventory level records

– Apply the inventory policy to replenish inventory

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Introduction

• Demand– Number of units that will need to be withdrawn

from inventory

• Deterministic inventory model– Used when demand is known

• Stochastic inventory model– Used when demand cannot be predicted well

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18.1 Examples

• Example 1: manufacturing speakers for TV sets– One speaker needed per TV set

• Sets manufactured on continuous production line

– Speakers produced in batches• $12,000 setup cost per batch

– $10 unit production cost of a single speaker

– $0.30 per month holding cost per speaker

– $1.10 per month shortage cost

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Examples

• Example 2: wholesale bicycle distribution– Distributor purchases a specific bicycle model

from the manufacturer and supplies it to various bike shops

– Demand is uncertain

– Ordering cost includes administrative cost of $2000 and unit cost of $350 per bicycle

– $10 per bicycle holding cost

– $150 per bicycle shortage cost

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• Cost of ordering z units– Includes a static cost and a cost per unit

• K is the setup cost and c is the unit cost

• Holding cost– Represents all costs associated with holding a

unit in inventory until it is sold or used• Cost of tied-up capital

• Space

• Insurance

• Protection

18.2 Components of Inventory Models


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• Shortage cost– Also called unsatisfied demand cost

– Cost incurred when demand exceeds available stock

• Backlogging: demand not lost but delayed

• No backlogging: orders are canceled or met by priority shipment

– Revenue may or may not be included in the model

Components of Inventory Models


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• Salvage cost– Negative of the salvage value

– Included in the holding cost

• Discount rate– Accounts for the time value of money

• Classification of inventory model based on how often inventory is monitored– Continuous review

– Periodic review

Components of Inventory Models


18.3 Deterministic Continuous-Review Models

• Economic order quantity (EOQ) model – Stock levels are depleted over time

• Replenished by a batch shipment

• Basic EOQ model assumptions– Demand rate is constant at d units per unit

time

– Order quantity Q to replenish inventory levels arrives all at once when inventory drops to 0

– Planned shortages are not allowed

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Deterministic Continuous-Review Models

• Reorder point equals demand rate times lead time

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• Components of total cost per unit time T– Production or ordering cost per cycle,

– Holding cost per cycle,

• Total cost per unit time

• Value of Q, Q* that minimizes T

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• Cycle time, t*

• For the speaker example:

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• The EOQ model with planned shortages– Third assumption of basic EOQ model is

replaced:• When a shortage occurs, the affected customers

will wait for the product to become available again. Backorders are filled immediately when order quantity arrives to replenish inventory

• The EOQ model with quantity discounts– New assumption:

• Unit cost now depends on batch quantity

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• Different types of demand for a product– Independent demand

• Bicycle wholesaler experiences this type of demand

– Dependent demand• In the TV speaker example: speaker demand

varies with TV set demand

• Material requirements planning (MRP)– Technique for managing inventory of

dependent demand products16



• Just-in-time (JIT) inventory management– Emphasizes reducing inventory levels to the

bare minimum• Providing items just as they are needed

– Focuses on finding ways to reduce setup costs so that order quantities can be small

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18.4 A Deterministic Periodic-Review Model

• When demand varies from period to period– EOQ formula no longer ensures a minimum

cost solution

• Objective: minimize total cost over n periods

• Fixed costs are independent of the inventory policy– Minimize total variable costs over the n

periods

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A Deterministic Periodic-Review Model

• Example given on Pages 815-817 of the text

• An algorithm for an optimal inventory policy– An optimal policy produces only when the

inventory level is zero

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18.5 Deterministic Multiechelon Inventory Models for Supply Chain Management

• Echelon– Each stage in a multi-stage inventory system

• Supply chain– Network of facilities that take raw materials

and transform them into finished goods at the customer

– Includes procurement, manufacturing, and distribution

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Deterministic Multiechelon Inventory Models for Supply Chain Management

• A model for a serial, two-echelon system– Seven assumptions in this model outlined on

Page 822 of the text

• Echelon stock– Stock physically on hand and downstream at

subsequent echelons

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• Optimizing the two installations separately– A flawed approach

– Choosing order quantities for installation 2 must account for the resulting costs at installation 1

• Optimizing the two installations simultaneously– Correct approach

– Process outlined on Page 826-827 of the text

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• Model for a serial multiechelon system– Six assumptions outlined on Page 828 of the

text

– Difficult to solve for n > 2

– Simplifying approximations normally made to derive a solution

• Roundy’s 98 percent approximation property

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• Extension of serial multiechelon model can be formulated for a distribution system

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18.6 A Stochastic Continuous-Review Model

• Traditional method: a two-bin system– All units for a particular product held in two

bins

– Capacity of one bin equals the reorder point

– Units first withdrawn from the other bin

– Emptying second bin triggers a new order

• Newer approach: computerized inventory systems– Current inventory levels are always on record

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A Stochastic Continuous-Review Model

• Inventory system based on:– Reorder point, R

– Order quantity, Q

• Inventory policy: whenever inventory drops to R units, place an order for Q more units

• Ten model assumptions outlined on Page 839 of the text

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• Choosing the order quantity, Q– Use formula for EOQ model with planned

shortages

• d is the average demand per unit time

• See assumptions for definitions of K, h, and p

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• Choosing the reorder point, R– Based on manager’s desired level of service

to customers

• Alternative measures of service level– Probability that a stockout will not occur

between the time an order is placed and when the order quantity is received

– Average number of stockouts per year

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• Alternative measures of service level – Average percentage of annual demand that

can be filled immediately

– Average delay in filling backorders when a stockout occurs

– Overall average delay in filling orders• Where delay without a stockout is zero

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• Measure 1 is most convenient to use

• Procedure for choosing R under service level measure 1– Choose L

– Solve for R such that

• Example given on Page 841 of the text

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18.7 A Stochastic Single-Period Model for Perishable Products

• Stable product– Will remain sellable indefinitely

• Perishable product– Can be carried in inventory only a certain

amount of time

– Single period model is appropriate in this case

– Types of perishable products• Newspapers, flowers, seasonal greeting cards,

fashion goods, and airline reservations for a particular flight

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A Stochastic Single-Period Model for Perishable Products

• Seven assumptions of the model– Given on Pages 846-847 of the text

• Analysis of the model with no initial inventory and no setup cost– Simplest case to consider

– See Pages 847-849

– Application to the bicycle example

• Analysis extends to include setup cost and initial inventory levels

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18.8 Revenue Management

• Airlines started using revenue management in the late 1970s

• Overbooking– One of the oldest and most successful

revenue management practices

• Revenue management in the airline industry today– Pervasive, highly developed, and effective

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Revenue Management

• Model for capacity-controlled discount fares– Decision variable: inventory level that must be

reserved for highest-paying customers

– Key to solving: marginal analysis

• An overbooking model– Choose overbooking level to maximize profit

– Shortage cost (denied-boarding cost) is incurred if overbooking level is too high

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18.9 Conclusions

• Models presented in this chapter illustrate the general nature of inventory models

• EOQ models have been widely used

• Stochastic single-period model is appropriate for perishable products

• Multiechelon inventory models play an important role in supply chain management

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© 2015 McGraw-Hill Education. All rights reserved. Chapter 18 Inventory Theory.

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Transcript of © 2015 McGraw-Hill Education. All rights reserved. Chapter 18 Inventory Theory.