___________________________________________________________________________

1. Inventory Models EOQ Model with Planned Shortages Assumptions • Assumptions of EOQ model • Shortages are allowed ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

2. Deterministic Inventory Models EOQ Model with Quantity Discounts ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

3. Inventory Models EOQ Model with Quantity Discount Assumptions • Assumptions of EOQ model • Purchase cost is NOT independent of the order quantity • Unit holding cost is NOT independent of the order quantity ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

4. Inventory Models EOQ Model with Quantity Discount Example – Brewery • Monthly production of beer = 4 000 hl • Filling into glass bottles = 25% of production • Empty bottles stored in plastic cases (20 pcs.) • 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

5. Inventory Models EOQ Model with Quantity Discount Example – Brewery • Unit purchase price – quantity discount schedule: • Annual holding cost per case = = 50% of unit purchase price ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

6. Inventory Models EOQ Model with Quantity Discount Example – Brewery • Annual demand Q = 120 000 cases • Purchase price cq = 46/40/36 CZK per case • Annual holding cost c1 = 23/20/18 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

7. Total annual PURCHASE cost Total annual ORDERING cost Total annual HOLDING cost Inventory Models EOQ Model with Quantity Discount Example – Brewery • Total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

8. Inventory Models EOQ Model with Quantity Discount Example – Brewery • Total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

9. cq= 46 cq= 40 cq= 36 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

10. Inventory Models EOQ Model with Quantity Discount Example – Brewery • Optimum order quantity for EACH CATEGORY ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

11. cq= 46 4 999 11 191 cq= 40 cq= 36 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

12. cq= 46 cq= 40 cq= 36 12 000 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

13. cq= 46 cq= 40 cq= 36 15 000 12 650 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

14. TC = 5 865546 TC = 5  040 000 TC = 4 551 000 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

15. Deterministic Inventory Models Economic Production Lot Size Model ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

16. Inventory Models Economic Production Lot Size Model Assumptions • Assumptions of EOQ model • Inventory is NOT replenished through the single batch ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

17. InventoryLevel ProductionPhase NonproductionPhase Maximal Inventory Level Average Inventory Level 0 t1 t2 Time t Inventory Models Economic Production Lot Size Model ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

18. Inventory Models Economic Production Lot Size Model Assumptions • Production phase - production (production rate) - demand (demand rate) - replenishment • Nonproduction phase - demand (demand rate) - depletion ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

19. Inventory Models Economic Production Lot Size Model Assumptions Production rate  Demand rate ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

20. Inventory Models Economic Production Lot Size Model Cost • Holding cost • Production setup cost • Objective: minimize total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

21. Inventory Models Economic Production Lot Size Model Example – Brewery • Monthly production of beer = 4 000 hl • Filling into glass bottles = 25% of production • Empty bottles are processed on the cleaning line (daily output = 8 000 bottles) • Setup cost – 12 000 CZK per one cleaning process • Annual holding cost per case = 20 CZK • Lead time (preparation of cleaning line) = ½ of month • Objective: minimize total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

22. Fillingbottles Cleaning line Store Inventory Models Economic Production Lot Size Model Example – Brewery Production phase ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

23. Fillingbottles Store Inventory Models Economic Production Lot Size Model Example – Brewery Nonproduction phase Cleaning line ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

24. Inventory Models Economic Production Lot Size Model Example – Brewery • What is the optimum LOT SIZE? • What is the maximum inventory level? • What is the minimum total annual cost ? • How long time does a cleaning run take? • When to start the preparation process for the cleaning run? ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

25. Inventory Models Economic Production Lot Size Model Example – Brewery • Demand rate h = 120 000 cases per year • Production rate p = 146 000 cases per year • Annual holding cost c1 = 20 CZK per case • Setup cost c2 = 12 000 CZK per cleaning lot • Lead time d = 1/2 of month = 1/24 of year ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

26. Total annual SETUP cost Total annual HOLDING cost Inventory Models Economic Production Lot Size Model Example – Brewery • Total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

27. Inventory Models Economic Production Lot Size Model Example – Brewery • Production lot size – number of cleaned cases in a cleaning lot (within period t1) • Demand withinperiod t1 – • Maximum inventory level ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

28. Inventory Models Economic Production Lot Size Model Example – Brewery • Average inventory level • Total annual HOLDING cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

29. Inventory Models Economic Production Lot Size Model Example – Brewery • Number of production lots within a year • Total annual SETUP cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

30. Inventory Models Economic Production Lot Size Model Example – Brewery • Total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

31. Inventory Models Economic Production Lot Size Model Example – Brewery • Optimum (economic) lot size ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

32. Inventory Models Economic Production Lot Size Model Example – Brewery • Maximum inventory level ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

33. Inventory Models Economic Production Lot Size Model Example – Brewery • Optimum total annual cost ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

34. Inventory Models Economic Production Lot Size Model Example – Brewery • Optimum length of production period ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

35. Inventory Models Economic Production Lot Size Model Example – Brewery • Optimum length of depletion period ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

36. Inventory Models Economic Production Lot Size Model Example – Brewery • Optimum cycle or ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

37. InventoryLevel InventoryLevel Time Time • Optimum starting setup point ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry

38. Inventory Models Economic Production Lot Size Model Example – Brewery • Optimum starting setup point ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry