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

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

3. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry 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

4. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Inventory Models 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 EOQ Model with Quantity Discount

5. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Inventory Models Example – Brewery Unit holding cost [CZK per case] 23 20 18 EOQ Model with Quantity Discount  Annual holding cost per case = = 50% of unit purchase price  Unit purchase price – quantity discount schedule: Discount category Order quantity [cases] Purchase price [CZK per case] 1 1 – 4 999 46 2 5 000 – 14 999 40 3 15 000 + 36

6. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Inventory Models Example – Brewery  Annual demand Q = 120 000 cases  Annual holding cost c 1 = 23/20/18 CZK per case  Lead time d = 1/2 of month = 1/24 of year EOQ Model with Quantity Discount  Ordering cost c 2 = 12 000 CZK per order  Purchase price c q = 46/40/36 CZK per case

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

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

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

10. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Inventory Models Example – Brewery EOQ Model with Quantity Discount  Optimum order quantity for EACH CATEGORY Discount category q*q*q*q*1 11 191 2 12 000 3 12 650

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

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

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

14. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry TC = 5 865 546 TC = 5 040 000 TC = 4 551 000

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

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

17. Time Inventory Level 0 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Inventory Models Economic Production Lot Size Model t 1 t 2 Maximal Inventory Level t Nonproduction Phase Production Phase Average Inventory Level

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

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

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

21. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Inventory Models 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  Lead time (preparation of cleaning line) = ½ of month  Objective: minimize total annual cost Economic Production Lot Size Model  Annual holding cost per case = 20 CZK

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

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

24. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Inventory Models  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? Economic Production Lot Size Model Example – Brewery

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

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

27. ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Inventory Models Example – Brewery  Production lot size – number of cleaned cases in a cleaning lot (within period t 1 ) Economic Production Lot Size Model  Demand within period t 1 –  Maximum inventory level

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

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

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

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

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

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

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

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

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

37. Time Inventory Level Time Inventory Level ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry  Optimum starting setup point

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