Managing Facilitating Goods

1. Managing Facilitating Goods Replenishment order Replenishment order Customer order Replenishment order Factory Wholesaler Distributor Retailer Customer Production Delay Shipping Delay Shipping Delay Item Withdrawn Wholesaler Inventory Distributor Inventory Retailer Inventory

2. Learning Objectives • Discuss the role of information technology in managing inventories. • Describe the functions and costs of an inventory system. • Determine the order quantity. • Calculate the reorder point and safety stock for an inventory system. • Design a continuous or periodic review inventory-control system. • Conduct an ABC analysis of inventory items. • Determine the order size for the single-period inventory case. • Describe the rationale behind the retail discounting model.

3. Role of Inventory in Services • Decoupling inventories • Seasonal inventories • Speculative inventories • Cyclical inventories • In-transit inventories • Safety stocks

4. Considerations in Inventory Systems • Type of customer demand • Planning time horizon • Replenishment lead time • Constraints

5. Relevant Inventory Costs • Ordering costs • Receiving and inspections costs • Holding or carrying costs • Shortage costs

6. Inventory Management Questions • What should be the order quantity (Q)? • When should an order be placed, called a reorder point (ROP)? • How much safety stock (SS) should be maintained?

7. Inventory Models • Economic Order Quantity (EOQ) • Special Inventory Models With Quantity Discounts Planned Shortages • Demand Uncertainty - Safety Stocks • Inventory Control Systems Continuous-Review (Q,r) Periodic-Review (order-up-to) • Single Period Inventory Model

8. Inventory Levels For EOQ Model Units on Hand Q 0 Q Time D

9. Annual Costs For EOQ Model

10. EOQ Formula • NotationD = demand in units per yearH = holding cost in dollars/unit/yearS = cost of placing an order in dollarsQ = order quantity in units • Total Annual Cost for Purchase Lots • EOQ

11. Annual Costs for Quantity Discount Model 22,000 21000 20000 2000 1000 C = $20.00 C = $19.50 C = $18.75 Annual Cost, $ 0 100 200 300 400 500 600 700 Order quantity, Q

12. Inventory Levels For Planned Shortages Model Q-K Q TIME 0 -K T1 T2 T

13. Formulas for Special Models • Quantity Discount Total Cost Model • Model with Planned Shortages

14. Values for Q* and K* as AFunction of Backorder Cost B Q* K* Inventory Levels 0 0 0 undefined Q* 0

15. Demand During Lead Time Example = + + + u=3 u=3 u=3 u=3 ROP s s Demand During Lead time Four Days Lead Time

16. Safety Stock (SS) • Demand During Lead Time (LT) has Normal Distribution with - - • SS with r% service level • Reorder Point

17. Continuous Review System (Q,r) Amount used during first lead time Inventory on hand EOQ Reorder point, ROP Order quantity, EOQ d3 Average lead time usage, dL d1 d2 EOQ Safety stock, SS First lead time, LT1 LT2 LT3 Time Order 1 placed Order 3 placed Order 2 placed Shipment 1 received Shipment 2 received Shipment 3 received

18. Periodic Review System(order-up-to) Inventory on Hand Review period RP RP RP Target inventory level, TIL First order quantity, Q1 Q3 Q2 d3 d1 Amount used during first lead time d2 Safety stock, SS First lead time, LT1 LT2 LT3 Time Order 3 placed Order 2 placed Order 1 placed Shipment 3 received Shipment 1 received Shipment 2 received

19. Inventory Control Systems • Continuous Review System • Periodic Review System

20. ABC Classification of Inventory Items A B C

21. Inventory Items Listed in Descending Order of Dollar Volume Monthly Percent of Unit cost Sales Dollar Dollar Percent of Inventory Item ($) (units) Volume ($) Volume SKUs Class Computers 3000 50 150,000 74 20 A Entertainment center 2500 30 75,000 Television sets 400 60 24,000 Refrigerators 1000 15 15,000 16 30 B Monitors 200 50 10,000 Stereos 150 60 9,000 Cameras 200 40 8,000 Software 50 100 5,000 10 50 C Computer disks 5 1000 5,000 CDs 20 200 4,000 Totals 305,000 100 100

22. Single Period Inventory ModelNewsvendor Problem Example D = newspapers demanded p(D) = probability of demand Q = newspapers stocked P = selling price of newspaper, $10 C = cost of newspaper, $4 S = salvage value of newspaper, $2 Cu = unit contribution: P-C = $6 Co = unit loss: C-S = $2

23. Single Period Inventory Model Expected Value Analysis Stock Q p(D) D 6 7 8 9 10 .028 2 4 2 0 -2 -4 .055 3 12 10 8 6 4 .083 4 20 18 16 14 12 .111 5 28 26 24 22 20 .139 6 36 34 32 30 28 .167 7 36 42 40 38 36 .139 8 36 42 48 46 44 .111 9 36 42 48 54 52 .083 10 36 42 48 54 60 .055 11 36 42 48 54 60 .028 12 36 42 48 54 60 Expected Profit $31.54 $34.43 $35.77 $35.99 $35.33

24. Single Period Inventory Model Incremental Analysis E (revenue on last sale) E (loss on last sale) P ( revenue) (unit revenue) P (loss) (unit loss) (Critical Fractile) where: Cu = unit contribution from newspaper sale ( opportunity cost of underestimating demand) Co = unit loss from not selling newspaper (cost of overestimating demand) D = demand Q = newspaper stocked

25. Critical fractile for the newsvendor problem P(D<Q) (Co applies) P(D>Q) (Cu applies) 0.722

26. Topics for Discussion • Discuss the functions of inventory for different organizations in the distribution system. • How would one find values for inventory costs? • How can information technology create a competitive advantage through inventory management? • How valid are the assumptions for the EOQ model? • How is a service level determined for inventory items? • What inventory model would apply to service capacity such as seats on an aircraft?