1. ___________________________________________________________________________ Operations Research  Jan Fábry Deterministic Inventory Models

2. ___________________________________________________________________________ Operations Research  Jan Fábry Basic EOQ Model Deterministic Inventory Models

3. ___________________________________________________________________________ Operations Research  Jan Fábry Deterministic Inventory Models  How much to order? … Optimum quantity  When to order? … Optimum reorder point  What is the total cost?  What is the average inventory level?  What is the maximum inventory level? Basic Economic Order Quantity Model (EOQ Model)

4. ___________________________________________________________________________ Operations Research  Jan Fábry Basic Economic Order Quantity Model (EOQ Model) Assumptions  Single item  Deterministic demand (static)  Deterministic lead time (constant)  Uniform depletion of the inventory Deterministic Inventory Models

5. ___________________________________________________________________________ Operations Research  Jan Fábry Assumptions  Constant order quantity (OQ)  Purchasing cost is independent of the OQ  Unit holding cost is independent of the OQ  No shortages, no surpluses Basic Economic Order Quantity Model (EOQ Model) Deterministic Inventory Models

6. Time Inventory Level 0 q Maximum Level ___________________________________________________________________________ Operations Research  Jan Fábry Basic Economic Order Quantity Model (EOQ Model) Cycle 1Cycle 2Cycle 3 Depletion Replenishment Order Arrives Average Level q/2 Deterministic Inventory Models

7. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Monthly production of beer = 4 000 hl  Filling into glass bottles = 25% of production  Empty bottles stored in plastic cases (20 pcs.)  Annual holding cost per case = 20 CZK  Ordering cost – transportation = 11 000 CZK per order – other = 1 000 CZK per order  Lead time = ½ of month  Objective: minimize total annual cost Deterministic Inventory Models

8. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Annual demand Q = 120 000 cases  Annual holding cost c 1 = 20 CZK per case  Ordering cost c 2 = 12 000 CZK per order  Lead time d = 1/2 of month = 1/24 of year Deterministic Inventory Models

9. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Total annual cost Total annual HOLDING cost Total annual ORDERING cost Deterministic Inventory Models

10. Time Inventory Level 0 q Maximum Level Average Level q/2 Order quantity ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Deterministic Inventory Models

11. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Order quantity - q  Maximum inventory level  Average inventory level Deterministic Inventory Models

12. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Total annual HOLDING cost  Total annual ORDERING cost Deterministic Inventory Models

13. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Total annual cost Deterministic Inventory Models

14. Total cost q 0 ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery 120 000 1 212 000 60 000 624 000 10 000 244 000 OC HC TC Deterministic Inventory Models

15. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery Policy I Policy II Policy III Annual demand Q 120 000 Order quantity q 10 000 60 000 120 000 Annual unit holding cost c 1 202020 Average inventory level q/2 5 000 30 000 60 000 Total annual holding cost HC 100 000 600 000 1 200 000 Unit ordering cost c 2 12 000 Number of orders Q/q 1221 Total annual ordering cost OC 144 000 24 000 12 000 Total annual cost TC 244 000 624 000 1 212 000 Deterministic Inventory Models

16. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery 10 000 Inventory Level Time 0 12 6 Policy I Deterministic Inventory Models

17. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery 60 000 Inventory Level Time0 12 6 Policy II Deterministic Inventory Models

18. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery 0 Policy III Time Inventory Level 120 000 6 12 Deterministic Inventory Models

19. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Optimum order quantity Deterministic Inventory Models

20. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Optimum total annual cost Deterministic Inventory Models

21. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery 12 000 0 cost q 240 000 OC HC TC Deterministic Inventory Models

22. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery  Optimum length of inventory cycle

23. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery Inventory Level Time (days) 073 36.5109.5 146 182.5 219 255.5 292 328.5 365 12 000 6 000 Deterministic Inventory Models

24. Time Inventory Level q*q* t*t* ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery r*r* d OrderDelivery Deterministic Inventory Models

25. ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery q*q* t*t* r*r* d  Optimum reorder point

26. Time Inventory Level q*q* t*t* r*r* d ___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model Example – Brewery d > t * Deterministic Inventory Models