Chapter 7: Inventory Decision Making Fundamental Approaches to Managing Inventory Basic issues are simple… how much to order and when to order 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, 7th Ed. 2 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: 1. More responsive order processing 2. Ability to strategically manage logistics data 3. More capable and reliable transportation 4. Improvements in the location of inventory Chapter 7 Management of Business Logistics, 7th Ed. 3 Relationship between Inventory and Customer Service Level Figure 7-1 Chapter 7 Management of Business Logistics, 7th Ed. 4 Key Differences among Approaches to Managing Inventory Three differences of approach: 1. 2. 3. Dependent versus Independent Demand Pull versus Push Systemwide versus single-facility solutions Each approach has models developed for approach solution to the inventory problem. Chapter 7 Management of Business Logistics, 7th Ed. 5 Key Differences among Approaches to Managing Inventory 1. 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. Chapter 7 Management of Business Logistics, 7th Ed. 6 Key Differences among Approaches to Managing Inventory 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, 7th Ed. 7 Key Differences among Approaches to Managing Inventory 2. 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. Chapter 7 Management of Business Logistics, 7th Ed. 8 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. Chapter 7 Management of Business Logistics, 7th Ed. 9 Key Differences among Approaches to Managing Inventory 3. systemwide versus single-facility approach Is to estimate whether the selected approach would apply to the whole system, or is appropriate to a single facility Chapter 7 Management of Business Logistics, 7th Ed. 10 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. Chapter 7 Management of Business Logistics, 7th Ed. 11 We now look at models of 1. 2. Chapter 7 Fixed order cost with condition of Certainty Fixed order cost with condition of Uncertainty Management of Business Logistics, 7th Ed. 12 1. 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. Chapter 7 Management of Business Logistics, 7th Ed. 13 Fixed Order Quantity Model under the Condition of Certainty Figure 7-2 Chapter 7 Management of Business Logistics, 7th Ed. 14 Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model Simple EOQ Model Assumptions 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, 7th Ed. 15 Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ Model Simple EOQ Model Variables 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, 7th Ed. 16 Figure 7-3 Inventory Carrying Cost Chapter 7 Management of Business Logistics, 7th Ed. 17 Figure 7-4 Order or Setup Cost Chapter 7 Management of Business Logistics, 7th Ed. 18 Figure 7-5 Inventory Costs Chapter 7 Management of Business Logistics, 7th 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, 7th Ed. 20 Figure 7-6 Sawtooth Model Chapter 7 Management of Business Logistics, 7th 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 √ 2RA or Q = VW Management of Business Logistics, 7th Ed. √ 2RA 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= √ 2RA or Q= √ 2RA VW S √ 2*3600*$200 √ 2*3600*$200 $100*25% Q = 240 units Chapter 7 $25 Q = 240 units Management of Business Logistics, 7th Ed. 23 Figure 7-7 Sawtooth Models Chapter 7 Management of Business Logistics, 7th Ed. 24 Table 7-1 Total Costs for Various EOQ Amounts Chapter 7 Management of Business Logistics, 7th Ed. 25 Figure 7-8 Graphical Representation of the EOQ Example Chapter 7 Management of Business Logistics, 7th Ed. 26 1. 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. Chapter 7 Management of Business Logistics, 7th Ed. 27 2. 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 7-9. Note the variability in lead times and demand. Chapter 7 Management of Business Logistics, 7th Ed. 28 Figure 7-9 2. Fixed Order Quantity Model under Conditions of Uncertainty Chapter 7 Management of Business Logistics, 7th Ed. 29 2. 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. Chapter 7 Based on rate of probability Examine Figure 7-9 again. Management of Business Logistics, 7th Ed. 30 Fixed Order Quantity Approach (Condition of Uncertainty) Uncertainty of Demand Affects Simple EOQ Model Assumptions: 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 the inventory items. infinite planning horizon. no limit on capital availability. Management of Business Logistics, 7th Ed. 31 Notes for the following tables Assume k =10, each unit,v =$100, carrying cost,w =25%, A=200,R=3600 Table 7-1 shortage Table 7-2 Table 7-3 Table 7-4 Chapter 7 illustrates the rate of probability of shows the units of shortage combines Tables 7-1 and 7-2 computes all relevant values Management of Business Logistics, 7th Ed. 32 Table 7-2 Probability Distribution of Demand during Lead Time Demand Chapter 7 Probability 100 units 0.01 110 0.06 120 0.24 130 0.38 140 0.24 150 0.06 160 0.01 Management of Business Logistics, 7th Ed. 33 Table 7-3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points Actual Demand 100 100 0 110 -10 110 10 0 Reorder Points 120 130 140 20 30 40 10 20 30 150 50 40 160 60 50 120 130 140 -20 -30 -40 -10 -20 -30 0 -10 -20 10 0 -10 20 10 0 30 20 10 40 30 20 150 160 -50 -60 -40 -50 -30 -40 -20 -30 -10 -20 0 -10 10 0 Chapter 7 Management of Business Logistics, 7th Ed. 34 Table 7-3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points 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 0.01 Chapter 7 -0.6Management -0.5 of Business -0.4 Logistics, -0.3 7 -0.2 Ed. th 35 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)* e=2 0 $2.50 $20 $97.50 (g)=3 30 20.1 10.8 3.9 0.8 0.1 0.0 G=gw =4= 3*100 $300 $201 $108 $39 $8 $1 $0 GR/Q $4500 $3015 $1620 $585 $120 $15 $0 =5 =1 $270 $502.50 $750 TAC $4500 $3018 Management $1640 of$682.50 $390 $517.50 $750 Chapter 7 Business Logistics, 7 Ed. 36 = 2+5 th Note for Table 7-4 e = expected excess per cycle =of values above diagonal line of Table 7.4 g = expected shorts per cycle =of values below diagonal line of Table 7.4 K = stockout cost in dollars G =gk =expected stockout cost per cycle G (R/Q) = 5 = expected stockout per year Refer to page 241 of text for calculation. Chapter 7 Management of Business Logistics, 7th Ed. 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= √ 2 R(A + G) VW √ 2 * 3600 * ($200 + 8) $100 * 25% Q = approximately 242 units Chapter 7 Management of Business Logistics, 7th Ed. 38 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 TAC = $6389 (New value for TAC when uncertainty introduced) Chapter 7 + $2975 + $270 Management of Business Logistics, 7th Ed. + $119 39 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. Chapter 7 Management of Business Logistics, 7th Ed. 40 Figure 7-10 Area under the Normal Curve Chapter 7 Management of Business Logistics, 7th Ed. 41 Table 7-5 Reorder Point Alternatives and Stockout Possibilities Chapter 7 Management of Business Logistics, 7th Ed. 42 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 7-11. Amount ordered over each five weeks in the example varies each week. Chapter 7 Management of Business Logistics, 7th Ed. 43 Figure 7-11 Fixed Order Interval Model (with Safety Stock) Chapter 7 Management of Business Logistics, 7th Ed. 44 Summary and Evaluation of EOQ Approaches to Inventory Management Four basic inventory models: 1. 2. 3. 4. 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 Chapter 7 Management of Business Logistics, 7th Ed. 45 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. Chapter 7 Management of Business Logistics, 7th Ed. 46 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 (distribution centers) 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, 7th Ed. 47 Additional Approaches to Inventory Management Five approaches to inventory management that have special relevance to supply chain management: 1. JIT (Just in Time) 2. MRP (Materials Requirements into Planning) 3. DRP (Distribution Resource Planning) 4. QR (Quick Response) 5. ECR (Efficient Consumer Response) Chapter 7 Management of Business Logistics, 7th Ed. 48 1. JIT: Time-Based Approaches to Replenishment Logistics 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. Chapter 7 Management of Business Logistics, 7th Ed. 49 1. JIT (cont.) 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. Chapter 7 Management of Business Logistics, 7th Ed. 50 1. JIT (cont.) 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, 7th Ed. 51 1. JIT versus EOQ Approaches to Inventory Management Six major differences: 1. JIT attempts to eliminate excess inventories for both buyer and seller. 2. JIT systems involve short production runs with frequent changeovers. 3. JIT minimizes waiting lines by delivering goods when and where needed. Chapter 7 Management of Business Logistics, 7th Ed. 52 1. JIT versus EOQ Approaches to Inventory Management Chapter 7 4. JIT uses short, consistent lead times to satisfy inventory needs in a timely manner. 5. JIT relies on high-quality incoming products and on exceptionally high-quality inbound logistics operations. 6. JIT requires a strong, mutual commitment between buyer and seller, emphasizing quality and win-win outcomes for both partners. Management of Business Logistics, 7th Ed. 53 Table 7-6 EOQ versus JIT Attitudes and Behaviors Chapter 7 Management of Business Logistics, 7th Ed. 54 1. JIT (cont.) JIT versus Traditional Inventory Management Reduces excess inventories Shorter, more frequent production runs Minimize waiting lines by delivering materials when and where needed Short, consistent lead times through proximate location Quality stressed throughout supply chain Win-win relationships necessary to a healthy supply chain Chapter 7 Management of Business Logistics, 7th Ed. 55 2. JIT (cont.) Examples of JIT Successes: 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, 7th Ed. 56 Note for Figure 7-12 (next) It shows JIT-based manufacturing use timesequenced motor carrier pickup from suppliers in conjunction with rail-motor to meet JIT requirements. Chapter 7 Management of Business Logistics, 7th Ed. 57 Figure 7-12 The Orderly Pickup Concept Chapter 7 Management of Business Logistics, 7th Ed. 58 2: MRP: Time-Based Approaches to Replenishment Logistics 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, 7th Ed. 59 2. MRP (cont.) Goals of an MRP: Ensure the availability of materials, components, and products for planned production. Maintain lowest possible inventory level. Plan manufacturing activities, delivery schedules, and purchasing activities. Chapter 7 Management of Business Logistics, 7th Ed. 60 2. MRP (cont.) Key elements of an MRP: Master production schedule Bill of materials file Inventory status file MRP program Outputs and reports Chapter 7 Management of Business Logistics, 7th Ed. 61 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, 7th Ed. 62 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, 7th Ed. 63 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, 7th Ed. 64 Master Schedule: MRP Egg Timer Example Figure 7-15 Chapter 7 Management of Business Logistics, 7th Ed. 65 Time-Based Approaches to Replenishment Logistics: MRP Principal advantages of MRP: 1. Maintain reasonable safety stock. 2. Minimize or eliminate inventories. 3. Identification of process problems. 4. Production schedules based on actual demand. 5. Coordination of materials ordering. 6. Most suitable for batch or intermittent production schedules. Chapter 7 Management of Business Logistics, 7th Ed. 66 2. MRP (cont.) Principal shortcomings of MRP: 1. Computer intensive. 2. Difficult to make changes once operating. 3. Ordering and transportation costs may rise. 4. Not usually as sensitive to short-term fluctuations in demand. 5. Frequently become quite complex. 6. May not work exactly as intended. Chapter 7 Management of Business Logistics, 7th Ed. 67 3: Distribution Resource Planning MRP sets a master production schedule and “explodes” into gross and net requirements. DRP starts with customer demand and 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, 7th Ed. 68 3. Distribution Resource Planning (cont.) DRP develops a projection for each SKU (stock 17 keep unit) and requires : Forecast of demand for each SKU. Current inventory level for each SKU. Target safety stock. Recommended replenishment quantity. Lead time for replenishment. Chapter 7 Management of Business Logistics, 7th Ed. 69 Table 7-8 DRP Table for Chicken Noodle Soup Columbus Distribution Center–Distribution Resource Planning Month Week CN Soup Forecast January 1 2 3 February 4 5 6 Chapter 7 8 9 Current BOH=4314; Q=3800; SS=1956; LT=1 974 974 974 974 989 1002 Schedule 0 0 3800 0 0 0 Receipt BOH-End 3340 2366 5192 4218 3229 2227 Planned Order 7 March 0 3800 0 0 0 1002 1002 1061 3800 0 0 5025 4023 2962 0 0 3800 3800 Management of Business Logistics, 7th Ed. 70 Figure 7-16 Combining DRP Tables Chapter 7 Management of Business Logistics, 7th Ed. 71 Inventory at Multiple Locations – The Square Root Law (SQL) 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, 7th Ed. 72 Inventory at Multiple Locations – The Square Root Law X2= (X1) * √(n /n ) 2 1 Where: n1 = number of existing facilities n2 = number of future facilities X1 = total inventory in existing facilities X2 = total inventory in future facilities Chapter 7 Management of Business Logistics, 7th Ed. 73 Square Root Law Example Current distribution 40,000 units Eight facilities shrinking to two Using the square root law: √(2/8) X2 = (40,000) * X2 = 20,000 units Chapter 7 Management of Business Logistics, 7th Ed. 74 Table 7-9 Example Impacts of Square Root Law on Logistics Inventories Warehouses 1 √n 1.0000 Total Av Inv 3,885 % Change --- 2 3 4 1.4142 1.7321 2.0000 5,494 6,729 7,770 141% 173% 200% 5 10 15 2.2361 3.1623 3.8730 8,687 12,285 15,047 224% 316% 387% 20 23 25 4.4721 4.7958 5.0000 17,374 18,632 19,425 447% 480% 500% Chapter 7 Management of Business Logistics, 7th Ed. 75 Four Directions for Replenishment Logistics Figure 7-17 Chapter 7 Management of Business Logistics, 7th Ed. 76 4. Quick Response (QR) Structure of QR Shorter, compressed time horizons. Real-time information available by SKU. Seamless, integrated logistics networks with rapid transportation, cross-docking and effective store receipt and distribution systems. Chapter 7 Management of Business Logistics, 7th Ed. 77 4: Quick Response (QR) (cont.) Structure of QR Partnership relationships present among supply chain members. Redesign of manufacturing processes to reduce lot sizes, changeover times and enhanced flexibility. Commitment to TQM. Chapter 7 Management of Business Logistics, 7th Ed. 78 Figure 7-18 Basic Elements of Quick Response (QR) Chapter 7 Management of Business Logistics, 7th Ed. 79 5. Efficient Consumer Response (ECR) Structure of ECR 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, 7th Ed. 80 Figure 7-19 Efficient Consumer Response: Broad Operating Capabilities Tailored to Each Unique Partner Chapter 7 Management of Business Logistics, 7th Ed. 81 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 A7-1 Sawtooth Model Modified for Inventory in Transit Chapter 7 Management of Business Logistics, 7th Ed. 83 Figure A7-2 EOQ Costs Considering Volume Transportation Rate Chapter 7 Management of Business Logistics, 7th Ed. 84 Table 7A-1 Annual Savings, Annual Cost, and Net Savings by Various Quantities Using Incentive Rates Chapter 7 Management of Business Logistics, 7th Ed. 85 Figure A7-3 Net Savings Function for Incentive Rate Chapter 7 Management of Business Logistics, 7th Ed. 86 End of Chapter 7 and 7A Slides Inventory Decision Making