Chapter 7: Inventory Decision Making
Learning Objectives - After reading this chapter, you should be able to do the following: n n n 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. Chapter 7 Management of Business Logistics, 7 th Ed. 2
Learning Objectives n n n Realize how variability in demand 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. Chapter 7 Management of Business Logistics, 7 th Ed. 3
Learning Objectives n Make needed adjustments to the basic EOQ approach to respond to several special types of applications. Chapter 7 Management of Business Logistics, 7 th Ed. 4
Fundamental Approaches to Managing Inventory n n 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. Chapter 7 Management of Business Logistics, 7 th Ed. 5
Fundamental Approaches to Managing Inventory n Four factors might permit this apparent paradox, that is, the firm can achieve higher levels of customer service without actually increasing inventory: n More responsive order processing n Ability to strategically manage logistics data n More capable and reliable transportation n Improvements in the location of inventory Chapter 7 Management of Business Logistics, 7 th Ed. 6
Relationship between Inventory and Customer Service Level Figure 7 -1 Chapter 7 Management of Business Logistics, 7 th Ed. 7
Key Differences among Approaches to Managing Inventory n Dependent versus Independent Demand n Dependent demand is directly related to the demand for another product. n Independent demand is unrelated to the demand for another product. n For many manufacturing processes, demand is dependent. n For many end-use items, demand is independent. Chapter 7 Management of Business Logistics, 7 th Ed. 8
Key Differences among Approaches to Managing Inventory n n Chapter 7 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. Management of Business Logistics, 7 th Ed. 9
Key Differences among Approaches to Managing Inventory n Pull versus Push n Pull approach is a “reactive” system, relying on customer demand to “pull” product through a logistics system. Mac. Donald’s is an example. n Push approach is a “proactive” system, and uses inventory replenishment to anticipate future demand. Catering businesses are examples of push systems. Chapter 7 Management of Business Logistics, 7 th Ed. 10
Key Differences among Approaches to Managing Inventory n Pull versus Push n Pull systems respond quickly to sudden or abrupt changes in demand, involve one-way communications, and apply more to independent demand situations. n Push systems use an orderly and disciplined master plan for inventory management, and apply more to dependent demand situations. Chapter 7 Management of Business Logistics, 7 th Ed. 11
On the Line: American Cancer Society n n n 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. Chapter 7 Management of Business Logistics, 7 th Ed. 12
Fixed Order Quantity Approach (Condition of Certainty): Inventory Cycles n In this example, each cycle starts with 4, 000 units: n Demand is constant at the rate of 800 units per day. n When inventory falls below 1, 500 units, an order is placed for an additional 4, 000 units. n After 5 days the inventory is completely used. n Just as the 4, 000 th unit is sold, the next order of 4, 000 units arrives and a new cycle begins. Chapter 7 Management of Business Logistics, 7 th Ed. 13
Fixed Order Quantity Model under the Condition of Certainty Figure 7 -2 Chapter 7 Management of Business Logistics, 7 th Ed. 14
Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model n Simple EOQ Model Assumptions n n n Chapter 7 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. Management of Business Logistics, 7 th Ed. 15
Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model n Simple EOQ Model Variables n n n n Chapter 7 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 Management of Business Logistics, 7 th Ed. 16
Figure 7 -3 Inventory Carrying Cost Chapter 7 Management of Business Logistics, 7 th Ed. 17
Figure 7 -4 Order or Setup Cost Chapter 7 Management of Business Logistics, 7 th Ed. 18
Figure 7 -5 Inventory Costs Chapter 7 Management of Business Logistics, 7 th Ed. 19
Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model TAC = QVW + AR 2 Q or TAC = QS + AR 2 Q First term is the average carrying cost Second term is order or setup costs per year Chapter 7 Management of Business Logistics, 7 th Ed. 20
Figure 7 -6 Sawtooth Model Chapter 7 Management of Business Logistics, 7 th Ed. 21
Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model TAC = QVW + AR 2 Q or TAC = QS + AR 2 Q Solving for Q gives the following expressions: Q= √ 2 RA Chapter 7 or Q = VW or S √ 2 RA or Q = VW Management of Business Logistics, 7 th Ed. √ 2 RA S 22
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 VW or S or Q= √ 2 RA VW S √ 2*3600*$200 $100*25% Q = 240 units Chapter 7 $25 Q = 240 units Management of Business Logistics, 7 th Ed. 23
Figure 7 -7 Sawtooth Models Chapter 7 Management of Business Logistics, 7 th Ed. 24
Table 7 -1 Total Costs for Various EOQ Amounts Chapter 7 Management of Business Logistics, 7 th Ed. 25
Figure 7 -8 Graphical Representation of the EOQ Example Chapter 7 Management of Business Logistics, 7 th Ed. 26
Fixed Order Quantity Approach (Condition of Certainty) n Summary and Evaluation of the Fixed Order Quantity Approach: n n n 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. Chapter 7 Management of Business Logistics, 7 th Ed. 27
Fixed Order Quantity Approach (Condition of Uncertainty) n n Uncertainty is a more normal condition. n Demand is often affected by exogenous factors---weather, forgetfulness, etc. n Lead times often vary regardless of carrier intentions. Examine out Figure 7 -9. n Note the variability in lead times and demand. Chapter 7 Management of Business Logistics, 7 th Ed. 28
Figure 7 -9 Fixed Order Quantity Model under Conditions of Uncertainty Chapter 7 Management of Business Logistics, 7 th Ed. 29
Fixed Order Quantity Approach (Condition of Uncertainty) n Reorder Point – A Special Note n With uncertainty of demand, the reorder point becomes the average daily demand during lead time plus the safety stock. n Examine Figure 7 -9 again. Chapter 7 Management of Business Logistics, 7 th Ed. 30
Fixed Order Quantity Approach (Condition of Uncertainty) n Uncertainty of Demand Affects Simple EOQ Model Assumptions: n n n Chapter 7 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 inventory items. infinite planning horizon. no limit on capital availability. Management of Business Logistics, 7 th Ed. the 31
Table 7 -2 Probability Distribution of Demand during Lead Time Demand Probability 100 units 110 0. 06 120 0. 24 130 0. 38 140 0. 24 150 0. 06 160 Chapter 7 0. 01 Management of Business Logistics, 7 th Ed. 32
Table 7 -3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points Actual Demand 100 0 110 -10 120 130 140 150 160 Chapter 7 -20 -30 -40 -50 -60 110 10 0 Reorder Points 120 130 140 20 30 40 10 20 30 150 50 40 160 60 50 -10 -20 -30 -40 -50 0 -10 -20 -30 -40 30 20 10 0 -10 -20 -30 20 10 0 -10 -20 Management of Business Logistics, 7 th Ed. 33
Table 7 -3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points Actual Demand Probability 100 110 120 130 140 150 160 100 0. 01 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 110 0. 06 -0. 6 0 0. 6 1. 2 1. 8 2. 4 3. 0 120 0. 24 -4. 8 -2. 4 0 2. 4 4. 8 7. 2 9. 6 130 0. 38 -11. 4 -7. 6 -3. 8 0 3. 8 7. 6 11. 4 140 0. 24 -9. 6 -7. 2 -4. 8 -2. 4 0 2. 4 4. 8 150 0. 06 -3. 0 -2. 4 -1. 8 -1. 2 -0. 6 0 0. 6 -0. 1 0 160 7 0. 01 Chapter -0. 6 -0. 5 of Business Logistics, 7 -0. 2 -0. 4 -0. 3 Ed. Management th 34
Table 7 -4 Calculation of Lowest-Cost Reorder Point Dmnd 100 110 120 130 140 150 160 (e) 0. 0 0. 1 0. 8 3. 9 10. 8 20. 1 30. 0 (VW) 0 $2. 50 $20 $97. 50 (g) 30 20. 1 10. 8 3. 9 0. 8 0. 1 0. 0 G=gw $300 $201 $108 $39 $8 $1 $0 GR/Q $4500 $3015 $1620 $585 $120 $15 $0 TAC $4500 $3018 $1640 $682. 50 $390 $517. 50 $750 Chapter 7 $270 $502. 50 $750 Management of Business Logistics, 7 th Ed. 35
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 Chapter 7 Management of Business Logistics, 7 th Ed. 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 = 242; e = 10. 8 TAC = QVW + AR + e. VW + GR 2 Q Q TAC = (242*$100*25%) + (200*3600) + (10. 8*$100*25%) + (8*3600) 2 242 TAC = $3025 TAC = $6389 (New value for TAC when uncertainty introduced) Chapter 7 + $2975 + $270 Management of Business Logistics, 7 th Ed. + $119 37
Fixed Order Quantity Approach (Condition of Uncertainty): Conclusions n n Following costs will rise to cover the uncertainty: n Stockout costs. n Inventory carrying costs of safety stock Results may or may not be significant. n In text example, TAC rose $389 or approximately 6. 5%. n The greater the dispersion of the probability distribution, the greater the cost disparity. Chapter 7 Management of Business Logistics, 7 th Ed. 38
Figure 7 -10 Area under the Normal Curve Chapter 7 Management of Business Logistics, 7 th Ed. 39
Table 7 -5 Reorder Point Alternatives and Stockout Possibilities Chapter 7 Management of Business Logistics, 7 th Ed. 40
Fixed Order Interval Approach n n n 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 7 -11. Amount ordered over each five weeks in the example varies each week. Chapter 7 Management of Business Logistics, 7 th Ed. 41
Figure 7 -11 Fixed Order Interval Model (with Safety Stock) Chapter 7 Management of Business Logistics, 7 th Ed. 42
Summary and Evaluation of EOQ Approaches to Inventory Management n Four basic inventory models: n n n Fixed quantity/fixed interval Fixed quantity/irregular interval Irregular quantity/fixed interval Irregular quantity/irregular interval Where demand 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 Chapter 7 Management of Business Logistics, 7 th Ed. 43
Summary and Evaluation of EOQ Approaches to Inventory Management n n Relationship to ABC analysis n “A” items suited to a fixed quantity/irregular interval approach. n “C” items best suited to a irregular quantity/fixed interval approach. Importance of trade-offs n Familiarity with EOQ approaches assists the manager in trade-offs inherent in inventory management. Chapter 7 Management of Business Logistics, 7 th Ed. 44
Summary and Evaluation of EOQ Approaches to Inventory Management n n New concepts n JIT, MRPII, DRP, QR, and ECR also take into account a knowledge and understanding of applicable logistics trade-offs. Number of DCs n 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. Chapter 7 Management of Business Logistics, 7 th Ed. 45
Additional Approaches to Inventory Management n Three approaches to inventory management that have special relevance to supply chain management: n JIT (Just in Time) n MRP (Materials Requirements into Planning) n DRP (Distribution Resource Planning) Chapter 7 Management of Business Logistics, 7 th Ed. 46
Time-Based Approaches to Replenishment Logistics: JIT n Definition and Components of JIT Systems - designed to manage lead times and eliminate waste. n 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. n JIT operations - Kanban cards and light warning system communicate possible production interruptions. n Fundamental concepts - JIT can substantially reduce inventory and related costs. Chapter 7 Management of Business Logistics, 7 th Ed. 47
Time-Based Approaches to Replenishment Logistics: JIT n Definition and Components of JIT Systems designed to manage lead times and eliminate waste. n Goal is zero inventory, and zero defects. n Similarity to the two-bin system - one bin fills demand for part, the other is used when the first is empty. n Reduces lead times through requiring small and frequent replenishment. Chapter 7 Management of Business Logistics, 7 th Ed. 48
Time-Based Approaches to Replenishment Logistics: JIT n n n 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. Chapter 7 Management of Business Logistics, 7 th Ed. 49
JIT versus EOQ Approaches to Inventory Management n Six major differences: n First, JIT attempts to eliminate excess inventories for both buyer and seller. n Second, JIT systems involve short production runs with frequent changeovers. n Third, JIT minimizes waiting lines by delivering goods when and where needed. Chapter 7 Management of Business Logistics, 7 th Ed. 50
JIT versus EOQ Approaches to Inventory Management n n n Chapter 7 Fourth, JIT uses short, consistent lead times to satisfy inventory needs in a timely manner. Fifth, JIT relies on high-quality incoming products and on exceptionally high-quality inbound logistics operations. Sixth, JIT requires a strong, mutual commitment between buyer and seller, emphasizing quality and win-win outcomes for both partners. Management of Business Logistics, 7 th Ed. 51
Table 7 -6 EOQ versus JIT Attitudes and Behaviors Chapter 7 Management of Business Logistics, 7 th Ed. 52
Time-Based Approaches to Replenishment Logistics: JIT n JIT versus Traditional Inventory Management n Reduces excess inventories n Shorter, more frequent production runs n Minimize waiting lines by delivering materials when and where needed n Short, consistent lead times through proximate location n Quality stressed throughout supply chain n Win-win relationships necessary to a healthy supply chain Chapter 7 Management of Business Logistics, 7 th Ed. 53
Time-Based Approaches to Replenishment Logistics: JIT n Examples of JIT Successes: n n Chapter 7 Apple Computer’s increase in IT from 10 weeks to 2 weeks resulted in 18 -month $20 million payback on plant. GM increased production by 100%, but inventories increased by only 6%. Norfolk Southern mini-train hauls direct from one GM plant to another without switching delays. Ryder handles all inbound logistics for Saturn. Management of Business Logistics, 7 th Ed. 54
Figure 7 -12 The Orderly Pickup Concept Chapter 7 Management of Business Logistics, 7 th Ed. 55
Time-Based Approaches to Replenishment Logistics: MRP n n A Materials Requirements Planning (MRP) system consists of a set of logically related procedures, decision rules, and records designed to translate a master production schedule into time-phased net inventory requirements for each component item needed to implement this schedule. MRPs re-plan net requirements based on changes in schedule, demand, etc. Chapter 7 Management of Business Logistics, 7 th Ed. 56
Time-Based Approaches to Replenishment Logistics: MRP n Goals of an MRP: n Ensure the availability of materials, components, and products for planned production. n Maintain lowest possible inventory n Plan manufacturing activities, delivery schedules, and purchasing activities. Chapter 7 Management of Business Logistics, 7 th Ed. level. 57
Time-Based Approaches to Replenishment Logistics: MRP n Key elements of an MRP: n Master production schedule n Bill of materials file n Inventory status file n MRP program n Outputs and reports Chapter 7 Management of Business Logistics, 7 th Ed. 58
Figure 7 -13 An MRP System Demand Forecasts Customer Orders Master Production Schedule Bill of Material File MRP Program Inventory Status File Output and Reports Chapter 7 Management of Business Logistics, 7 th Ed. 59
Figure 7 -14 Relationship of Parts to Finished Product: MRP Egg Timer Example 1 Egg Timer 2 Ends 1 Bulb 3 Supports 1 Gram of Sand Chapter 7 Management of Business Logistics, 7 th Ed. 60
Table 7 -7 Inventory Status File: MRP Egg Timer Example Product Gross Req. Inventory Net Req. Lead Time Egg Timers 1 0 1 1 Ends 2 0 2 5 Supports 3 2 1 1 Bulbs 1 0 1 1 Sand 1 0 1 4 Chapter 7 Management of Business Logistics, 7 th Ed. 61
Figure 7 -15 Timer Example Chapter 7 Master Schedule: MRP Egg Management of Business Logistics, 7 th Ed. 62
Time-Based Approaches to Replenishment Logistics: MRP n Principal advantages of MRP: n Maintain reasonable safety stock. n Minimize or eliminate inventories. n Identification of process problems. n Production schedules based on actual demand. n Coordination of materials ordering. n Most suitable for batch or intermittent production schedules. Chapter 7 Management of Business Logistics, 7 th Ed. 63
Time-Based Approaches to Replenishment Logistics: MRP n Principal shortcomings of MRP: n Computer intensive. n Difficult to make changes once operating. n Ordering and transportation costs may rise. n Not usually as sensitive to short-term fluctuations in demand. n Frequently become quite complex. n May not work exactly as intended. Chapter 7 Management of Business Logistics, 7 th Ed. 64
Time-Based Approaches to Replenishment Logistics: Distribution Resource Planning n n n MRP sets a master production schedule and “explodes” into gross and net requirements. DRP starts with customer demand works backwards toward establishing a realistic system-wide plan for ordering the necessary finished products. Then DRP works to develop a time-phased plan for distributing product from plants and warehouses to the consumer. Chapter 7 Management of Business Logistics, 7 th Ed. 65
Time-Based Approaches to Replenishment Logistics: Distribution Resource Planning n DRP develops a projection for each SKU and requires 17: n Forecast of demand for each SKU. n Current inventory level for each SKU. n Target safety stock. n Recommended replenishment quantity. n Lead time for replenishment. Chapter 7 Management of Business Logistics, 7 th Ed. 66
Table 7 -8 DRP Table for Chicken Noodle Soup Columbus Distribution Center–Distribution Resource Planning Month Week CN Soup Forecast Schedule Receipt BOH-End Planned Order Chapter 7 January 1 2 3 February 4 5 6 7 March 8 9 Current BOH=4314; Q=3800; SS=1956; LT=1 974 974 989 1002 1061 0 0 3800 0 0 2227 5025 4023 2962 3800 0 0 3800 3340 2366 5192 4218 3229 0 3800 0 Management of Business Logistics, 7 th Ed. 67
Figure 7 -16 Combining DRP Tables Chapter 7 Management of Business Logistics, 7 th Ed. 68
Inventory at Multiple Locations – The Square Root Law (SQL) n n n Used to reduce inventory at multiple locations. As locations increase, inventory also increases, but not in the same ratio as the growth in facilities. The square root law (SRL) states that total safety stock can be approximated by multiplying the total inventory by the square root of the number of future facilities divided by the current number of facilities. Chapter 7 Management of Business Logistics, 7 th Ed. 69
Inventory at Multiple Locations – The Square Root Law n n X 2= (X 1) * √(n 2/n 1) Where: n n 1 = number of existing facilities n n 2 = number of future facilities n X 1 = total inventory in existing facilities n X 2 = total inventory in future facilities Chapter 7 Management of Business Logistics, 7 th Ed. 70
Square Root Law Example n n n Current distribution 40, 000 units Eight facilities shrinking to two Using the square root law: √(2/8) n X 2 = (40, 000) * n X 2 = 20, 000 units Chapter 7 Management of Business Logistics, 7 th Ed. 71
Table 7 -9 Example Impacts of Square Root Law on Logistics Inventories Warehouses 1 2 3 √n 1. 0000 1. 4142 1. 7321 Total Av Inv 3, 885 5, 494 6, 729 % Change --141% 173% 4 5 10 15 20 23 25 2. 0000 2. 2361 3. 1623 3. 8730 4. 4721 4. 7958 5. 0000 7, 770 8, 687 12, 285 15, 047 17, 374 18, 632 19, 425 200% 224% 316% 387% 447% 480% 500% Chapter 7 Management of Business Logistics, 7 th Ed. 72
Four Directions for Replenishment Logistics Figure 7 -17 Chapter 7 Management of Business Logistics, 7 th Ed. 73
Time-Based Approaches to Replenishment Logistics: Quick Response (QR) n Structure of QR n Shorter, compressed time horizons. n Real-time information available by SKU. n Seamless, integrated logistics networks with rapid transportation, cross-docking and effective store receipt and distribution systems. Chapter 7 Management of Business Logistics, 7 th Ed. 74
Time-Based Approaches to Replenishment Logistics: Quick Response (QR) n Structure of QR n Partnership relationships present among supply chain members. n Redesign of manufacturing processes to reduce lot sizes, changeover times and enhanced flexibility. n Commitment to TQM. Chapter 7 Management of Business Logistics, 7 th Ed. 75
Figure 7 -18 Basic Elements of Quick Response (QR) Chapter 7 Management of Business Logistics, 7 th Ed. 76
Time-Based Approaches to Replenishment Logistics: Efficient Consumer Response (ECR) n Structure of ECR n n Grocery industry estimates U. S. savings at approximately $30 billion. “Ultimate goal is a responsive, consumer-driven system in which distributors and suppliers work together as business allies to maximize consumer satisfaction and minimize cost. Accurate information and high-quality products flow through a paperless system between manufacturing and check-out counter with minimum degradation or interruption…” Chapter 7 Management of Business Logistics, 7 th Ed. 77
Figure 7 -19 Efficient Consumer Response: Broad Operating Capabilities Tailored to Each Unique Partner Chapter 7 Management of Business Logistics, 7 th Ed. 78
Chapter 7: Summary and Review Questions Students should review their knowledge of the chapter by checking out the Summary and Study Questions for Chapter 7. This is the last slide for Chapter 7
Figure A 7 -1 Sawtooth Model Modified for Inventory in Transit Chapter 7 Management of Business Logistics, 7 th Ed. 80
Figure A 7 -2 EOQ Costs Considering Volume Transportation Rate Chapter 7 Management of Business Logistics, 7 th Ed. 81
Table 7 A-1 Annual Savings, Annual Cost, and Net Savings by Various Quantities Using Incentive Rates Chapter 7 Management of Business Logistics, 7 th Ed. 82
Figure A 7 -3 Net Savings Function for Incentive Rate Chapter 7 Management of Business Logistics, 7 th Ed. 83
End of Chapter 7 and 7 A Slides Inventory Decision Making
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