Planned Shortages with Back-Orders

Transcription

1 Planned Shortages with Back-Orders Shortage: when customer demand cannot be met Planned shortages could be beneficial Cost of keeping item is more expensive than the profit from selling it Ex: car 1

2 Customer Demands an item Alternatives for customers when their demand cannot be met from stock Customer demands an item The item is out of stock Back Order Customer waits for the next replenishment Lost Sales Customer moves to another suppliers 2 Customer keeps all future businesses Customer transfers some future business to another supplier Customer transfers some future business to another supplier Customer transfers all future business to another supplier

3 Planned Shortages with Back-Orders Optimal order size RC D Q o 2 HC SC ( HC + SC) Optimal amount to be backordered 2 RC HC D S o SC ( HC + SC) Time during which demand is met T 1 ( Q S ) o o / D Time during which demand is back-ordered T 2 S o / D Cycle time T T 1 + T 2 3

4 Ex 4: Back order Demand for an item is constant at 100 units a month. Unit cost is $50 Reorder cost is $50 Holding cost is 25% of value a year Shortage cost for back order is 40% of value a year Find an optimal inventory policy for the item 4

5 IM 322 Inventory Management Chapter 5 Models for Uncertain Demand -5- Textbook: Donald Waters, Inventory Control and Management, 2 nd ed

6 Chapter Outline ` ` ` ` ` ` Uncertainty in inventory management Variables that take uncertain value Probabilistic models for inventory model Uncertain demand Uncertain lead time Service level / safety stock 6

7 Areas of Uncertainty For example Changes in customer demand during leadtime Price uncertainty Operations change New products Disrupted supply chain Trading conditions etc 7

8 Uncertain Demand Inventory level Q Reorder point, R 0 LT Time LT 8 Lead time demand

9 Uncertain Demand Safety Stock Buffer added to on hand inventory during lead time Extra reserved stock To prevent stockout under uncertain demand Safety stock will not normally be used, but it is available under uncertain demand How much safety stock should we hold? Judgment on service level 9 Inventory level Q Reorder point, R 0 LT Safety Stock Time LT

10 Service Level 10

11 Service Level Several ways of measuring the service level Percentage of order completely satisfied from stock Percentage of units demanded that are delivered from stock Percentage of units demanded that are delivered on time Percentage of time there is stock available Percentage of stock cycles without shortages Percentages of item-months there is stock available 11

12 Reorder Level Reorder Level (ROL) LT x D Reorder Level (ROL) (LT x D) + Safety Stock Inventory level Q Reorder point, R 12 0 LT Safety Stock Time LT

13 Reorder Point for a Service Level Probability of meeting demand during lead time service level Average demand during lead time Probability of a stockout Safety stock zσ LT Demand R 13

14 Reorder Point with Uncertain Demand Reorder point with safety stock Service level probability of NO stockout zσ t σ d L t z L the safety ROL average lead standard number time service of stock demand level ( LT D) + zσ LT deviation standard of probabilit demand deviations y Safety Stock correspond σ L Standard deviation during leadtime ing to 14

15 Ex 1: Uncertain Demand PM Computers assembles microcomputers from generic components. It purchases its color monitors from a manufacturer in Taiwan. There is a long lead time of 25 days. Daily demand is normally distributed with a mean of 2.5 monitors and a standard deviation of 1.2 monitors. Determine the safety stock and reorder point corresponding to a 90% service level 15

16 Ex 2 Uncertain Demand ABC company finds that demand for an item is normally distributed with a mean of 2,000 units a year and standard deviation of 400 units. Unit cost is $100, reorder cost is $200, holding cost is 20% of value a year and lead time is fixed at 3 weeks. Describe an ordering policy that gives a 95% service level. What is the cost of safety stock? 16