1. 1 Inventory Control

2. 2  Week 1Introduction to Production Planning and Inventory Control  Week 2Inventory Control – Deterministic Demand  Week 3Inventory Control – Stochastic Demand  Week 4Inventory Control – Stochastic Demand  Week 5Inventory Control – Stochastic Demand  Week 6Inventory Control – Time Varying Demand  Week 7Inventory Control – Multiple Echelons Lecture Topics

3. 3  Week 8Production Planning and Scheduling  Week 9Production Planning and Scheduling  Week 12Managing Manufacturing Operations  Week 13Managing Manufacturing Operations  Week 14 Managing Manufacturing Operations  Week 10Demand Forecasting  Week 11Demand Forecasting  Week 15Project Presentations Lecture Topics (Continued…)

4. 4 Inventory in the US Economy $290.40 billion Wholesale (23.2%) $122.10 billion Other (9.8% $98.60 billion Farm (7.9%) $424.60 billion Manufacturing (33.9%) $316.00 billion Retail (25.2%)

5. 5 Inventory Types

6. 6  Raw Materials  Work-in-process (WIP)  Finished goods inventory (FGI)

7. 7 Inventory Location

8. 8  Manufacturing Facility  In-Transit  Warehouse  Retailer  Customer

9. 9 Benefits of Inventory

10. 10 Benefits of Inventory  Reduces ordering, setup & transportation costs (economies of scale)  Buffer against demand fluctuations  Buffer against supply fluctuations  Supply shortages  Variability in supply lead times

11. 11 Benefits of Inventory (continued…)  Buffer against price fluctuations  Benefits from quantity discounts  Protects production capacity  Allows production smoothing  Reduces managerial complexity (eliminates the need for coordination)  Can increase demand

12. 12 The Cost of Inventory

13. 13 The Cost of Inventory  Tied up capital  Warehousing cost  Deterioration  Obsolescence  Demand shortfall  Quality defects  Changes in raw material prices  Changes in product design specifications

14. 14  What if demand uncertainty and variability are eliminated?

15. 15  What if demand uncertainty and variability are eliminated?  What if replenishment lead times are made insignificant?

16. 16  What if demand uncertainty and variability are eliminated?  What if replenishment lead times are made insignificant?  What if ordering & setup costs are made negligible?

17. 17  What if demand uncertainty and variability are eliminated?  What if replenishment lead times are made insignificant?  What if ordering & setup costs are made negligible?  What if production capacity is never a constraint?

18. 18  Demand  Constant  Time varying  Stochastic  Supply lead time  Deterministic  Stochastic  Load-dependent  Review  Continuous review  Periodic review Characteristics of Inventory Systems

19. 19  Excess Demand  Backordering  Lost sales  Impatient customers  Item substitution  Capacity  Unlimited  Limited  Deterministic  Stochastic Characteristics of Inventory Systems (continued…)

20. 20  Number of items & customer classes  Single item  Multiple items  Single customer class  Multiple customer classes  Inventory quality  Perishability  Obsolescence  Imperfect yield Characteristics of Inventory Systems (continued…)

21. 21  Holding cost ( h )  Capital cost  Taxes and insurance  Deterioration, spoilage, obsolescence  Ordering (setup) cost ( A )  Purchasing (production) costs ( c )  Shortage cost ( p )  backordering cost  lost sale cost Cost Measures

22. 22 h = ic (cost per unit per time period) 28% = cost of capital 2% = taxes and insurance 6% = storage cost 1% = breakage cost 37% = total interest charge ( i ) per year If c = $100, then h = ic = $37 Example

23. 23 The Economic Order Quantity (EOQ) Model

24. 24 Assumptions of the Basic Model  Demand occurs continuously over time with a constant rate  Inventory can be replenished instantaneously  There are no capacity limits or limits on the size of replenishment orders  A replenishment order incurs a fixed ordering (or setup) cost  Multiple products can be analyzed independently of each other  No backorders are allowed

25. 25 Notation  D : demand rate (units per unit time)  c : unit purchase/production cost (dollars per unit)  A : fixed cost to place an order (dollars)  h : holding cost (dollars per unit per unit time); if the holding cost consists entirely of interest on money tied up in inventory, then h = ic where i is an interest rate.  Q : the size of the order (a decision variable)

26. 26 Inventory versus Time Q Inventory Time

27. 27 Inventory versus Time Q/D 2 Q/D 3 Q/D 4 Q/D Q Inventory Time

28. 28 Costs  Holding cost:

29. 29 Costs  Holding cost:  Ordering/setup cost:

30. 30 Costs  Holding cost:  Ordering/setup cost:  Production cost: c per unit

31. 31 Total Cost  Total cost per unit time:

32. 32 Total Cost  Total cost per unit time:  Total cost per unit:

33. 33 Economic Order Quantity hQ/2 AD/Q Q Y(Q)Y(Q)

34. 34 The Economic Order Quantity

35. 35 The Economic Order Quantity

36. 36 Optimal Cost  Optimal average cost per unit:  Optimal average cost per unit time (e.g., per year):

37. 37 Sensitivity to Order Quantity  Ordering and holding cost from using Q’:  Ratio

38. 38 Sensitivity to Order Quantity  Ordering and holding cost from using Q’:  Ratio  Example Q' = 2 Q*, then the ratio of the actual to optimal cost is (1/2)[2 + (1/2)] = 1.25

39. 39 Sensitivity to Order Quantity Large deviations from the optimal order quantity lead to relatively small deviations from the optimal cost.

40. 40 Order Quantity versus Order Interval  Order Interval: Let T represent time between orders, then  Total cost:  Optimal Order Interval:

41. 41 Some Limitations of the EOQ Model  Demand is deterministic and constant  Instantaneous replenishments  Ordering costs are constant and independent of order size  No accounting for interactions among multiple items  No backordering

42. 42 Extensions  Non-zero order replenishment lead times  Non-zero safety stocks  Finite supply capacity  Backordering

43. 43 Non-Zero Replenishment Lead Times

44. 44 Non-Zero Replenishment Lead Times  If L is the lead time and r is the reorder point, then r = D L  A non-zero lead time has no effect on Q * or Y ( Q )

45. 45 Non-Zero Safety Stocks  If ss is the safety stock, then  A non-zero safety stock affects Y ( Q ) but has no effect on Q *