___________________________________________________________________________

1. Deterministic Inventory Models ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

2. Deterministic Inventory Models Basic EOQ Model ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

3. Deterministic Inventory Models Basic Economic Order Quantity Model (EOQ Model) • 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? ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

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

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

6. Inventory Level Replenishment Depletion MaximumLevel q Average Level q/2 Order Arrives 0 Time Deterministic Inventory Models Basic Economic Order Quantity Model (EOQ Model) Cycle 1 Cycle 2 Cycle 3 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

7. Deterministic Inventory Models 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 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

8. Deterministic Inventory Models EOQ Model Example – Brewery • Annual demand Q = 120 000 cases • Annual holding cost c1 = 20 CZK per case • Ordering cost c2 = 12 000 CZK per order • Lead time d = 1/2 of month = 1/24 of year ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

9. Total annual ORDERING cost Total annual HOLDING cost Deterministic Inventory Models EOQ Model Example – Brewery • Total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

10. Inventory Level MaximumLevel q Orderquantity Average Level q/2 0 Time Deterministic Inventory Models EOQ Model ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

11. Deterministic Inventory Models EOQ Model Example – Brewery • Order quantity - q • Maximum inventory level • Average inventory level ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

12. Deterministic Inventory Models EOQ Model Example – Brewery • Total annual HOLDING cost • Total annual ORDERING cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

13. Deterministic Inventory Models EOQ Model Example – Brewery • Total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

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

15. Deterministic Inventory Models EOQ Model Example – Brewery ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

16. Inventory Level Policy I 10 000 Time 0 6 12 Deterministic Inventory Models EOQ Model Example – Brewery ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

17. Inventory Level Policy II 60 000 0 6 12 Time Deterministic Inventory Models EOQ Model Example – Brewery ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

18. Inventory Level 120 000 Policy III 0 6 12 Time Deterministic Inventory Models EOQ Model Example – Brewery ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

19. Deterministic Inventory Models EOQ Model Example – Brewery • Optimum order quantity ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

20. Deterministic Inventory Models EOQ Model Example – Brewery • Optimum total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

21. cost TC 240 000 HC OC q 0 12 000 Deterministic Inventory Models EOQ Model Example – Brewery ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

22. EOQ Model Example – Brewery • Optimum length of inventory cycle ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

23. Inventory Level 12 000 6 000 0 73 146 219 292 365 Time(days) 36.5 109.5 182.5 255.5 328.5 Deterministic Inventory Models EOQ Model Example – Brewery ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

24. InventoryLevel Order q* Delivery r* Time d t* Deterministic Inventory Models EOQ Model Example – Brewery ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

25. q* r* d t* EOQ Model Example – Brewery • Optimum reorder point ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

26. InventoryLevel q* r* Time d t* Deterministic Inventory Models EOQ Model Example – Brewery d > t* ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry