Chapter 10:

1. Chapter 10: Inventory Decision Making

2. Learning Objectives - After reading this chapter, you should be able to do the following: • Understand the fundamental differences among approaches to managing inventory. • Appreciate the rationale and logic behind the Economic Order Quantity (EOQ) approach to inventory decision making, and be able to solve some problems of a relatively straightforward nature. • Understand alternative approaches to managing inventory --- JIT, MRP, and DRP.

3. Learning Objectives • Realize how variability in demand and order cycle length affects inventory decision making. • Know how inventory will vary as the number of stocking points decreases or increases. • Recognize the contemporary interest in and relevance of time-based approaches to inventory management.

4. Learning Objectives • Make needed adjustments to the basic EOQ approach to respond to several special types of applications.

5. Fundamental Approaches to Managing Inventory • Basic issues are simple…how much to order and when to order. • Additional issues are…where to store inventory and what items to order. • Traditionally, conflicts were usually present…as customer service levels increased, investment in inventory also increased. • Recent emphasis is on increasing customer service and reducing inventory investment.

6. Fundamental Approaches to Managing Inventory • Four factors might permit this apparent paradox, that is, the firm can achieve higher levels of customer service without actually increasing inventory: • More responsive order processing • Ability to strategically manage logistics data • More capable and reliable transportation • Improvements in the location of inventory

7. Figure 10-1 Relationship between Inventory and Customer Service Level

8. Key Differences among Approaches to Managing Inventory • Dependent versus Independent Demand • Dependent demand is directly related to the demand for another product. • Independent demand is unrelated to the demand for another product. • For many manufacturing processes, demand is dependent. • For many end-use items, demand is independent.

9. Key Differences among Approaches to Managing Inventory • Of the inventory management processes in this chapter, JIT, MRP and MRPII are generally associated with items having dependent demand. • Alternatively, DRP and the EOQ models are generally associated with items exhibiting independent demand.

10. Key Differences among Approaches to Managing Inventory • Pull versus Push • Pull approach is a “reactive” system, relying on customer demand to “pull” product through a logistics system. MacDonald’s is an example. • Push approach is a “proactive” system, and uses inventory replenishment to anticipate future demand. Catering businesses are examples of push systems.

11. Key Differences among Approaches to Managing Inventory • Pull versus Push • Pull systems respond quickly to sudden or abrupt changes in demand, involve one-way communications, and apply more to independent demand situations. • Push systems use an orderly and disciplined master plan for inventory management, and apply more to dependent demand situations.

12. On the Line: American Cancer Society • ACS constructed a world class automated order fulfillment center in Atlanta. • Order cycle time was reduced to five business days. • Centralized storage reduced waste and obsolescence of educational materials. • Centralized shipment reduced freight rates. • The new center saved $8 million in the first year alone.

13. Fixed Order Quantity Approach (Condition of Certainty): Inventory Cycles • In this example, each cycle starts with 4,000 units: • Demand is constant at the rate of 800 units per day. • When inventory falls below 1,500 units, an order is placed for an additional 4,000 units. • After 5 days the inventory is completely used. • Just as the 4,000th unit is sold, the next order of 4,000 units arrives and a new cycle begins.

14. Figure 10-2 Fixed Order Quantity Model under the Condition of Certainty

15. Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model • Simple EOQ Model Assumptions • Continuous, constant, known and infinite rate of demand on one item of inventory. • A constant and known replenishment time. • Satisfaction of all demand. • Constant cost, independent of order quantity or time. • No inventory in transit costs. • No limits on capital availability.

16. Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model • Simple EOQ Model Variables • R = annual rate of demand • Q = quantity ordered (lot size in units) • A = order or setup cost • V = value or cost of one unit in dollars • W = carrying cost per dollar value in percent • S = VW = annual storage cost in $/unit per year • t = time in days • TAC = total annual costs in dollars per year

17. Figure 10-3 Inventory Carrying Cost

18. Figure 10-4 Order or Setup Cost

19. Figure 10-5 Inventory Costs

20. Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model TAC = QVW + AR or TAC = QS+ AR 2Q2Q First term is the average carrying cost Second term is order or setup costs per year

21. Figure 10-6 Sawtooth Model

22. Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model TAC = QVW + AR or TAC = QS+ AR 2Q2Q Solving for Q gives the following expressions: Q= √2 RAor Q = √2RA or Q = √2RA VW or S VW S

23. Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model Where R = 3600 units V = $100; W = 25%; S (or VW)= $25; A = $200 per order Q= √2 RA or Q = √2RA or Q = √2RA VW or SVWS √ 2*3600*$200√2*3600*$200 $100*25% $25 Q = 240 units Q = 240 units

24. Figure 10-7 Sawtooth Models

25. Table 10-1 Total Costs for Various EOQ Amounts

26. Figure 10-8 Graphical Representation of the EOQ Example

27. Fixed Order Quantity Approach (Condition of Certainty) • Summary and Evaluation of the Fixed Order Quantity Approach: • EOQ is a popular inventory model. • EOQ doesn’t handle multiple locations as well as a single location. • EOQ doesn’t do well when demand is not constant. • Minor adjustments can be made to the basic model. • Newer techniques will ultimately take the place of EOQ.

28. Fixed Order Quantity Approach (Condition of Uncertainty) • Uncertainty is a more normal condition. • Demand is often affected by exogenous factors---weather, forgetfulness, etc. • Lead times often vary regardless of carrier intentions. • Examine out Figure 10-9. • Note the variability in lead times and demand.

29. Figure 10-9 Fixed Order Quantity Model under Conditions of Uncertainty

30. Fixed Order Quantity Approach (Condition of Uncertainty) • Reorder Point – A Special Note • With uncertainty of demand, the reorder point becomes the average daily demand during lead time plus the safety stock. • Examine Figure 10-9 again.

31. Fixed Order Quantity Approach (Condition of Uncertainty) • Uncertainty of Demand Affects Simple EOQ Model Assumptions: • a constant and known replenishment time. • constant cost/price, independent of order quantity or time. • no inventory in transit costs. • one item and no interaction among the inventory items. • infinite planning horizon. • no limit on capital availability.

32. Table 10-2 Probability Distribution of Demand during Lead Time

33. Table 10-3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points

34. Table 10-3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points

36. Fixed Order Quantity Approach (Condition of Certainty): Expanded EOQ Model Where R = 3600 units V = $100; W = 25%; A = $200 per order; G = 8 Q= √2 R(A + G) VW √ 2 * 3600 * ($200 + 8) $100 * 25% Q = approximately 242 units

37. Fixed Order Quantity Approach (Condition of Certainty): Expanded EOQ Model Where R = 3600 units V = $100; W = 25%; A = $200 per order; G = 8; Q = 242; e = 10.8 TAC = QVW + AR + eVW + GR 2 Q Q TAC = (242*$100*25%) + (200*3600) + (10.8*$100*25%) + (8*3600) 2 242 242 TAC = $3025 + $2975 + $270 + $119 TAC = $6389 (New value for TAC when uncertainty introduced)

38. Fixed Order Quantity Approach (Condition of Uncertainty): Conclusions • Following costs will rise to cover the uncertainty: • Stockout costs. • Inventory carrying costs of safety stock • Results may or may not be significant. • In text example, TAC rose $389 or approximately 6.5%. • The greater the dispersion of the probability distribution, the greater the cost disparity.

39. Figure 10-10 Area under the Normal Curve

40. Table 10-5 Reorder Point Alternatives and Stockout Possibilities

41. Fixed Order Interval Approach • A second basic approach • Involves ordering at fixed intervals and varying Q depending upon the remaining stock at the time the order is placed. • Less monitoring than the basic model • Examine Figure 10-11. • Amount ordered over each five weeks in the example varies each week.

42. Figure 10-11 Fixed Order Interval Model (with Safety Stock)

43. Summary and Evaluation of EOQ Approaches to Inventory Management • Four basic inventory models: • Fixed quantity/fixed interval • Fixed quantity/irregular interval • Irregular quantity/fixed interval • Irregular quantity/irregular interval • Where demand and lead time are known, basic EOQ or fixed order interval model best. • If demand or lead time varies, then safety stock model should be used

44. Summary and Evaluation of EOQ Approaches to Inventory Management • Relationship to ABC analysis • “A” items suited to a fixed quantity/irregular interval approach. • “C” items best suited to a irregular quantity/fixed interval approach. • Importance of trade-offs • Familiarity with EOQ approaches assists the manager in trade-offs inherent in inventory management.

45. Summary and Evaluation of EOQ Approaches to Inventory Management • New concepts • JIT, MRP, MRPII, DRP, QR, and ECR also take into account a knowledge and understanding of applicable logistics trade-offs. • Number of DCs • The issue of inventory at multiple locations in a logistics network raises some interesting questions concerning the number of DCs, the SKUs at each, and their strategic positioning.

46. Additional Approaches to Inventory Management • Three approaches to inventory management that have special relevance to supply chain management: • JIT (Just in Time) • MRP (Materials Requirements into Planning) • DRP (Distribution Resource Planning)

47. Time-Based Approaches to Replenishment Logistics: JIT • Definition and Components of JIT Systems - designed to manage lead times and eliminate waste. • Kanban - refers to the informative signboards on carts in a Toyota system of delivering parts to the production line. Each signboard details the exact quantities and necessary time of replenishment. • JIT operations - Kanban cards and light warning system communicate possible production interruptions. • Fundamental concepts - JIT can substantially reduce inventory and related costs.

48. Time-Based Approaches to Replenishment Logistics: JIT • Definition and Components of JIT Systems - designed to manage lead times and eliminate waste. • Goal is zero inventory, and zero defects. • Similarity to the two-bin system - one bin fills demand for part, the other is used when the first is empty. • Reduces lead times through requiring small and frequent replenishment.

49. Time-Based Approaches to Replenishment Logistics: JIT • JIT is a widely used and effective strategy for managing the movement of parts, materials, semi-finished products from points of supply to production facilities. • Product should arrive exactly when a firm needs it, with no tolerance for early or late deliveries. • JIT systems place a high priority on short, consistent lead times.

50. JIT versus EOQ Approaches to Inventory Management • Six major differences: • First, JIT attempts to eliminate excess inventories for both buyer and seller. • Second, JIT systems involve short production runs with frequent changeovers. • Third, JIT minimizes waiting lines by delivering goods when and where needed.