1. Inventory Models Assumptions of EOQ model Shortages are allowed

2. EOQ Model with Quantity Discounts
Deterministic Inventory Models
EOQ Model with Quantity Discounts

3. Inventory Models Assumptions of EOQ model
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. Inventory Models Example – Brewery
EOQ Model with Quantity Discount
Example – Brewery
Monthly production of beer = hl
Filling into glass bottles = 25% of production
Empty bottles stored in plastic cases (20 pcs.)
Ordering cost – transportation = CZK per order – other = CZK per order
Lead time = ½ of month
Objective: minimize total annual cost

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

6. Inventory Models Example – Brewery Annual demand Q = 120 000 cases
EOQ Model with Quantity Discount
Example – Brewery
Annual demand
Q = cases
Purchase price
cq = 46/40/36 CZK per case
Annual holding cost
c1 = 23/20/18 CZK per case
Ordering cost
c2 = CZK per order
Lead time
d = 1/2 of month = 1/24 of year

7. Inventory Models Example – Brewery Total annual cost
EOQ Model with Quantity Discount
Example – Brewery
Total annual cost
Total annual HOLDING cost
Total annual ORDERING cost
Total annual PURCHASE cost

8. Inventory Models Example – Brewery Total annual cost
EOQ Model with Quantity Discount
Example – Brewery
Total annual cost

9. cq= 46
cq= 40
cq= 36

10. Inventory Models q* Example – Brewery
EOQ Model with Quantity Discount
Example – Brewery
Optimum order quantity for EACH CATEGORY
Discount category q* 1
11 191 2
12 000 3
12 650

11. cq= 46
4 999
11 191
cq= 40
cq= 36

12. cq= 46
cq= 40
cq= 36
12 000

13. cq= 46
cq= 40
cq= 36
15 000
12 650

14. TC = 5 
TC = 5  040  000
TC = 4  551  000

15. Economic Production Lot Size Model
Deterministic Inventory Models
Economic Production Lot Size Model

16. Inventory Models Assumptions of EOQ model
Economic Production Lot Size Model
Assumptions
Assumptions of EOQ model
Inventory is NOT replenished through the single batch

17. Inventory Models Time Inventory Level Maximal Inventory Level
Economic Production Lot Size Model
Time
Inventory Level
Maximal
Inventory Level
Production Phase
Nonproduction Phase
Average
Inventory Level t t1 t2

18. Inventory Models Production phase - production (production rate)
Economic Production Lot Size Model
Assumptions
Production phase
- production (production rate)
- demand (demand rate)
- replenishment
Nonproduction phase
- demand (demand rate)
- depletion

19. Production rate  Demand rate
Inventory Models
Economic Production Lot Size Model
Assumptions
Production rate  Demand rate

20. Inventory Models Holding cost Production setup cost
Economic Production Lot Size Model
Cost
Holding cost
Production setup cost
Objective: minimize total annual cost

21. Inventory Models Example – Brewery
Economic Production Lot Size Model
Example – Brewery
Monthly production of beer = hl
Filling into glass bottles = 25% of production
Empty bottles are processed on the cleaning line (daily output = bottles)
Setup cost – 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

22. Inventory Models Filling bottles Example – Brewery Store
Economic Production Lot Size Model
Example – Brewery
Production phase
Filling bottles
Cleaning line
Store

23. Inventory Models Filling bottles Example – Brewery Store
Economic Production Lot Size Model
Example – Brewery
Nonproduction phase
Filling bottles
Cleaning line
Store

24. Inventory Models Example – Brewery What is the optimum LOT SIZE?
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?

25. Inventory Models Example – Brewery Demand rate
Economic Production Lot Size Model
Example – Brewery
Demand rate
h = cases per year
Production rate
p = cases per year
Annual holding cost
c1 = 20 CZK per case
Setup cost
c2 = CZK per cleaning lot
Lead time
d = 1/2 of month = 1/24 of year

26. Inventory Models Example – Brewery Total annual cost
Economic Production Lot Size Model
Example – Brewery
Total annual cost
Total annual HOLDING cost
Total annual SETUP cost

27. Inventory Models Example – Brewery
Economic Production Lot Size Model
Example – Brewery
Production lot size – number of cleaned cases in a cleaning lot (within period t1)
Demand within period t1 –
Maximum inventory level

28. Inventory Models Example – Brewery Average inventory level
Economic Production Lot Size Model
Example – Brewery
Average inventory level
Total annual HOLDING cost

29. Inventory Models Example – Brewery
Economic Production Lot Size Model
Example – Brewery
Number of production lots within a year
Total annual SETUP cost

30. Inventory Models Example – Brewery Total annual cost
Economic Production Lot Size Model
Example – Brewery
Total annual cost

31. Inventory Models Example – Brewery Optimum (economic) lot size
Economic Production Lot Size Model
Example – Brewery
Optimum (economic) lot size

32. Inventory Models Example – Brewery Maximum inventory level
Economic Production Lot Size Model
Example – Brewery
Maximum inventory level

33. Inventory Models Example – Brewery Optimum total annual cost
Economic Production Lot Size Model
Example – Brewery
Optimum total annual cost

34. Inventory Models Example – Brewery Optimum length of production period
Economic Production Lot Size Model
Example – Brewery
Optimum length of production period

35. Inventory Models Example – Brewery Optimum length of depletion period
Economic Production Lot Size Model
Example – Brewery
Optimum length of depletion period

36. Inventory Models Example – Brewery or Optimum cycle
Economic Production Lot Size Model
Example – Brewery
Optimum cycle or

37. Optimum starting setup point
Time
Inventory Level
Time
Inventory Level

38. Inventory Models Example – Brewery Optimum starting setup point
Economic Production Lot Size Model
Example – Brewery
Optimum starting setup point