Chapter 7: Inventory Decision Making

Fundamental Approaches to Managing InventoryBasic issues are simple

how much to order and when to orderwhere to store inventory and what items to order.

Traditionally, conflicts were usually presentas customer service levels increased, investment in inventory also increased.Recent emphasis is on increasing customer service and reducing inventory investment.

Fundamental Approaches to Managing InventoryFour factors might permit this apparent paradox, that is, the firm can achieve higher levels of customer service without actually increasing inventory:More responsive order processingAbility to strategically manage logistics dataMore capable and reliable transportationImprovements in the location of inventory

Figure 7-1 Relationship between Inventory and Customer Service Level

Key Differences among Approaches to Managing InventoryThree differences of approach:

Dependent versus Independent DemandPull versus PushSystemwide versus single-facility solutions

Each approach has models developed for approach solution to the inventory problem.

Key Differences among Approaches to Managing Inventory1. Dependent versus Independent DemandDependent 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.

Key Differences among Approaches to Managing InventoryOf 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.

Key Differences among Approaches to Managing Inventory2. Pull versus PushPull approach is a reactive system, relying on customer demand to pull product through a logistics system. MacDonalds is an example.Push approach is a proactive system, and uses inventory replenishment to anticipate future demand. Catering businesses are examples of push systems.

Key Differences among Approaches to Managing InventoryPull versus PushPull 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.

Key Differences among Approaches to Managing Inventory3. systemwide versus single-facility approachIs to estimate whether the selected approach would apply to the whole system, or is appropriate to a single facility

On the Line: American Cancer SocietyACS 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.

We now look at models of

Fixed order cost with condition of CertaintyFixed order cost with condition of Uncertainty

1. Fixed Order Quantity Approach (Condition of Certainty): Inventory CyclesIn 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.

Figure 7-2 Fixed Order Quantity Model under the Condition of Certainty

Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ ModelSimple EOQ Model AssumptionsContinuous, 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.

Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ ModelSimple EOQ Model VariablesR = annual rate of demandQ = quantity ordered (lot size in units)A = order or setup costV = value or cost of one unit in dollarsW = carrying cost per dollar value in percentS = VW = annual storage cost in $/unit per yeart = time in daysTAC = total annual costs in dollars per year

Figure 7-3 Inventory Carrying Cost

Figure 7-4 Order or Setup Cost

Figure 7-5 Inventory Costs

Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ ModelTAC = QVW + AR or TAC = QS + AR 2 Q 2 Q

First term is the average carrying cost

Second term is order or setup costs per year

Figure 7-6 Sawtooth Model

Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ ModelTAC = QVW + AR or TAC = QS + AR 2 Q 2 Q

Solving for Q gives the following expressions:

Q = 2 RA or Q = 2RA or Q = 2RA VW or S VW S

Fixed Order Quantity Approach (Condition of Certainty): Simple EOQ ModelWhere R = 3600 units V = $100; W = 25%; S (or VW)= $25; A = $200 per orderQ = 2 RA or Q = 2RA or Q = 2RA VW or S VW S 2*3600*$200 2*3600*$200$100*25%$25

Q = 240 units Q = 240 units

Figure 7-7 Sawtooth Models

Table 7-1 Total Costs for Various EOQ Amounts

Figure 7-8 Graphical Representation of the EOQ Example

1. Fixed Order Quantity Approach (Condition of Certainty)Summary and Evaluation of the Fixed Order Quantity Approach:EOQ is a popular inventory model.EOQ doesnt handle multiple locations as well as a single location.EOQ doesnt 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.

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.

Figure 7-9 2. Fixed Order Quantity Model under Conditions of Uncertainty

2. Fixed Order Quantity Approach (Condition of Uncertainty)Reorder Point A Special NoteWith uncertainty of demand, the reorder point becomes the average daily demand during lead time plus the safety stock.Based on rate of probabilityExamine Figure 7-9 again.

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.

Notes for the following tablesAssume k =10, each unit,v =$100, carrying cost,w =25%, A=200,R=3600 Table 7-1 illustrates the rate of probability of shortageTable 7-2 shows the units of shortageTable 7-3 combines Tables 7-1 and 7-2Table 7-4 computes all relevant values

Table 7-2 Probability Distribution of Demand during Lead Time

Table 7-3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points

Table 7-3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points

Note for Table 7-4e = expected excess per cycle =of values above diagonal line of Table 7.4g = expected shorts per cycle =of values below diagonal line of Table 7.4K = stockout cost in dollarsG =gk =expected stockout cost per cycleG (R/Q) = 5 = expected stockout per year

Refer to page 241 of text for calculation.

Fixed Order Quantity Approach (Condition of Certainty): Expanded EOQ ModelWhere 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

Fixed Order Quantity Approach (Condition of Certainty): Expanded EOQ ModelWhere R = 3600 units V = $100; W = 25%; A = $200 per order; G = 8; Q = 242; e = 10.8TAC = QVW + AR + eVW + GR 2 Q QTAC = (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)

Fixed Order Quantity Approach (Condition of Uncertainty): ConclusionsFollowing costs will rise to cover the uncertainty:Stockout costs.Inventory carrying costs of safety stockResults 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.

Figure 7-10 Area under the Normal Curve

Table 7-5 Reorder Point Alternatives and Stockout Possibilities

Fixed Order Interval ApproachA second basic approachInvolves ordering at fixed intervals and varying Q depending upon the remaining stock at the time the order is placed.Less monitoring than the basic modelExamine Figure 7-11.Amount ordered over each five weeks in the example varies each week.

Figure 7-11 Fixed Order Interval Model (with Safety Stock)

Summary and Evaluation of EOQ Approaches to Inventory ManagementFour basic inventory models:Fixed quantity/fixed intervalFixed quantity/irregular intervalIrregular quantity/fixed intervalIrregular quantity/irregular intervalWhere 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

Summary and Evaluation of EOQ Approaches to Inventory ManagementRelationship to ABC analysisA items suited to a fixed quantity/irregular interval approach.C items best suited to a irregular quantity/fixed interval approach.Importance of trade-offsFamiliarity with EOQ approaches assists the manager in trade-offs inherent in inventory management.

Summary and Evaluation of EOQ Approaches to Inventory ManagementNew conceptsJIT, 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.

Additional Approaches to Inventory ManagementFive 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)QR (Quick Response)ECR (Efficient Consumer Response)

1. JIT: Time-Based Approaches to Replenishment LogisticsDefinition 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.

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.

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.

1. JIT versus EOQ Approaches to Inventory ManagementSix 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.

1. JIT versus EOQ Approaches to Inventory Management4. 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.

Table 7-6 EOQ versus JIT Attitudes and Behaviors

1. JIT (cont.)JIT versus Traditional Inventory ManagementReduces excess inventoriesShorter, more frequent production runsMinimize waiting lines by delivering materials when and where neededShort, consistent lead times through proximate locationQuality stressed throughout supply chainWin-win relationships necessary to a healthy supply chain

2. JIT (cont.)Examples of JIT Successes:Apple Computers 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.

Note for Figure 7-12 (next)It shows JIT-based manufacturing use time-sequenced motor carrier pickup from suppliers in conjunction with rail-motor to meet JIT requirements.

Figure 7-12The Orderly Pickup Concept

2: MRP: Time-Based Approaches to Replenishment LogisticsA 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.

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.

2. MRP (cont.)Key elements of an MRP:Master production scheduleBill of materials fileInventory status fileMRP programOutputs and reports

Figure 7-13 An MRP System

Figure 7-14 Relationship of Parts to Finished Product: MRP Egg Timer Example

Table 7-7 Inventory Status File: MRP Egg Timer Example

Figure 7-15 Master Schedule: MRP Egg Timer Example

Time-Based Approaches to Replenishment Logistics: MRPPrincipal advantages of MRP:Maintain reasonable safety stock.Minimize or eliminate inventories.Identification of process problems.Production schedules based on actual demand.Coordination of materials ordering.Most suitable for batch or intermittent production schedules.

2. MRP (cont.)Principal shortcomings of MRP:Computer intensive.Difficult to make changes once operating.Ordering and transportation costs may rise.Not usually as sensitive to short-term fluctuations in demand.Frequently become quite complex.May not work exactly as intended.

3: Distribution Resource PlanningMRP 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.

3. Distribution Resource Planning (cont.)DRP develops a projection for each SKU (stock keep unit) and requires17:Forecast of demand for each SKU.Current inventory level for each SKU.Target safety stock.Recommended replenishment quantity.Lead time for replenishment.

Table 7-8 DRP Table for Chicken Noodle Soup

Figure 7-16 Combining DRP Tables

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.

Inventory at Multiple Locations The Square Root LawX2= (X1) * (n2/n1) Where: n1 = number of existing facilitiesn2 = number of future facilitiesX1 = total inventory in existing facilitiesX2 = total inventory in future facilities

Square Root Law ExampleCurrent distribution 40,000 unitsEight facilities shrinking to twoUsing the square root law: X2 = (40,000) * (2/8)X2 = 20,000 units

Table 7-9 Example Impacts of Square Root Law on Logistics Inventories

Figure 7-17 Four Directions for Replenishment Logistics

4. Quick Response (QR)Structure of QRShorter, 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.

4: Quick Response (QR) (cont.)Structure of QRPartnership relationships present among supply chain members.Redesign of manufacturing processes to reduce lot sizes, changeover times and enhanced flexibility.Commitment to TQM.

Figure 7-18Basic Elements of Quick Response (QR)

5. Efficient Consumer Response (ECR)Structure of ECRGrocery 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

Figure 7-19 Efficient Consumer Response: Broad Operating Capabilities Tailored to Each Unique Partner

Chapter 7: Summary and Review QuestionsStudents 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

Figure A7-2 EOQ Costs Considering Volume Transportation Rate

Table 7A-1 Annual Savings, Annual Cost, and Net Savings by Various Quantities Using Incentive Rates

Figure A7-3 Net Savings Function for Incentive Rate

End of Chapter 7 and 7A SlidesInventory Decision Making