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

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1 © 2015 McGraw-Hill Education. All rights reserved. Chapter 18 Inventory Theory

2 © 2015 McGraw-Hill Education. All rights reserved. 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 2

3 © 2015 McGraw-Hill Education. All rights reserved. Introduction Demand –Number of units that will need to be withdrawn from inventory Deterministic inventory model –Used when demand is known Stochastic inventory model –Used when demand cannot be predicted well 3

4 © 2015 McGraw-Hill Education. All rights reserved 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 4

5 © 2015 McGraw-Hill Education. All rights reserved. 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 5

6 © 2015 McGraw-Hill Education. All rights reserved. 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 Components of Inventory Models

7 © 2015 McGraw-Hill Education. All rights reserved. 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 7 Components of Inventory Models

8 © 2015 McGraw-Hill Education. All rights reserved. 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 8 Components of Inventory Models

9 © 2015 McGraw-Hill Education. All rights reserved 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 9

10 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Continuous-Review Models Reorder point equals demand rate times lead time 10

11 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Continuous-Review Models 11

12 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Continuous-Review Models 12

13 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Continuous-Review Models 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 13

14 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Continuous-Review Models 14

15 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Continuous-Review Models 15

16 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Continuous-Review Models 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 products 16

17 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Continuous-Review Models 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 17

18 © 2015 McGraw-Hill Education. All rights reserved 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 18

19 © 2015 McGraw-Hill Education. All rights reserved. A Deterministic Periodic-Review Model Example given on Pages of the text An algorithm for an optimal inventory policy –An optimal policy produces only when the inventory level is zero 19

20 © 2015 McGraw-Hill Education. All rights reserved 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 20

21 © 2015 McGraw-Hill Education. All rights reserved. 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 21

22 © 2015 McGraw-Hill Education. All rights reserved. 22

23 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Multiechelon Inventory Models for Supply Chain Management 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 of the text 23

24 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Multiechelon Inventory Models for Supply Chain Management 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 24

25 © 2015 McGraw-Hill Education. All rights reserved. 25

26 © 2015 McGraw-Hill Education. All rights reserved. Deterministic Multiechelon Inventory Models for Supply Chain Management Extension of serial multiechelon model can be formulated for a distribution system 26

27 © 2015 McGraw-Hill Education. All rights reserved 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 27

28 © 2015 McGraw-Hill Education. All rights reserved. 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 28

29 © 2015 McGraw-Hill Education. All rights reserved. A Stochastic Continuous-Review Model 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 29

30 © 2015 McGraw-Hill Education. All rights reserved. A Stochastic Continuous-Review Model 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 30

31 © 2015 McGraw-Hill Education. All rights reserved. A Stochastic Continuous-Review Model 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 31

32 © 2015 McGraw-Hill Education. All rights reserved. A Stochastic Continuous-Review Model 32

33 © 2015 McGraw-Hill Education. All rights reserved 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 33

34 © 2015 McGraw-Hill Education. All rights reserved. A Stochastic Single-Period Model for Perishable Products Seven assumptions of the model –Given on Pages of the text Analysis of the model with no initial inventory and no setup cost –Simplest case to consider –See Pages –Application to the bicycle example Analysis extends to include setup cost and initial inventory levels 34

35 © 2015 McGraw-Hill Education. All rights reserved 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 35

36 © 2015 McGraw-Hill Education. All rights reserved. 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 36

37 © 2015 McGraw-Hill Education. All rights reserved 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 37


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