1. Slide 1

2. Slide 2

3. Slide 3

4. Slide 4 Demand Distribution

5. Slide 5 Ideal depletion

6. Slide 6 Without Safety Stock

7. Slide 7 With Safety Stock

8. Slide 8 Inventory/Time with ROP

9. Slide 9 Lead Time Variability

10. Slide 10 Reorder Point With Variable Demand R = dL + z  d L where d=average daily demand L=lead time  d =the standard deviation of daily demand z=number of standard deviations corresponding to the service level probability z  d L=safety stock

11. Slide 11 Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z  d L

12. Slide 12 Economic Order Quantity (EOQ) Model

13. Slide 13 4 4 Demand = 20 units/day

14. Slide 14 4 5 Demand = 20 units/day

15. Slide 15 4 6 Demand = 20 units/day

16. Slide 16 Size of order Annual cost (dollars) Lowest total cost (EOQ) Total cost Inventory carrying cost Ordering cost Cost Trade-offs Required to Determine the Most Economic Order Quantity 4 8

17. Inventory Carrying Costing: based on % of Product Value Cost Percentage of Product Value Opportunity 12 % Shrinkage8 Tax/Insurance3 Storage/Handling2 Total 25 %

18. Slide 18 EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222

19. Slide 19 EOQ Cost Model TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = CoDQCoDQ CcQ2CcQ2 Q 2 = 2CoDCc2CoDCc Q opt = 2CoDCc2CoDCc

20. Slide 20 EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc 2(150)(10,000)(0.75) Q opt = 2,000 yards TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 (150)(10,000)2,000(0.75)(2,000)2 TC min = $750 + $750 = $1,500 Orders per year =D/Q opt =10,000/2,000 =5 orders/year Order cycle time =311 days/(D/Q opt ) =311/5 =62.2 store days

21. Economic Order Quantity (EOQ) Models  Orders arrive in a single shipment  No quantity discounts (i.e., single price)  Demand rate is constant  No constraints on order size  relevant costs include only holding and ordering/setup  Ordering decisions for items are independent from other items.  No uncertainty in lead time or supply  Basic EOQ Model: assumptions

22. Slide 22 Order Quantity Number of Orders (D/Q) Ordering Cost P*(D/Q) Inventory Carrying Cost 1/2 (Q*C*V) Total Cost 40 60 80 100 120 140 160 200 300 400 120 80 60 48 40 35 30 24 18 12 $ 4,800 3,200 2,400 1,920 1,600 1,400 1,200 960 720 480 $ 500 750 1,000 1,250 1,500 1,750 2,000 2,500 3,750 5,000 $ 5,300 3,950 3,400 3,170 3,100 3,150 3,200 4,460 4,470 5,480 Cost Trade-offs Required to Determine the Most Economic Order Quantity 4 9

23. Slide 23

24. Slide 24 Inventory Control Systems  Continuous system (fixed- order-quantity)  constant amount ordered when inventory declines to predetermined level  Periodic system (fixed-time- period)  order placed for variable amount after fixed passage of time

25. Slide 25 Objednávání fixního množství k proměnlivému okamžiku Continuous system - označení (B,Q) nebo (s,Q) s q0q0 q0q0 q0q0 S1S1 S2S2 s S3S3 Čas Stav t 1 t 2 t 3

26. Slide 26 Objednávání variabilního množství k pevně stanovenému okamžiku označení Periodic system - (s,S) nebo (R,S) S q1q1 q2q2 q3q3 Stav Čas t 0 t 0 t 0

27. Slide 27 Two Forms of Demand  Dependent  Demand for items used to produce final products  Tires stored at a Goodyear plant are an example of a dependent demand item  Independent  Demand for items used by external customers  Cars, appliances, computers, and houses are examples of independent demand inventory