2-1Inventory Management全球化趨勢下一般企業經常面對的問題全球化趨勢下一般企業經常面對的問題l高度需求變動高度需求變動l訂貨前置時間長訂貨前置時間長l不可靠的供應程序不可靠的供應程序l大量的儲存單位大量的儲存單位(SKUs)2-2Inventory Management案例案例l三工業的問題三工業的問題(前置時間前置時間)l手機的產品壽命週期：手機的產品壽命週期：200000元元 (產品產品壽週期壽週期需求變異需求變異)lIpad 對電子書的衝擊對電子書的衝擊 (競爭競爭需求變異需求變異)l新機推出後一個月新機推出後一個月IPhone跌跌2千；千；hTC跌跌5千；三星跌千；三星跌3千千l智慧型手機可能帶來衝擊智慧型手機可能帶來衝擊l電子書電子書l遊戲機遊戲機l隨身聽隨身聽l衛星導航衛星導航2-3Inventory ManagementWhy Is Inventory Important?1Distribution and inventory (logistics) costs are quite substantial Total U.S. Manufacturing Inventories ($m):l1992-01-31: $m 808,773 l1996-08-31: $m 1,000,774 l2006-05-31: $m 1,324,108 Inventory-Sales Ratio (U.S. Manufacturers):l1992-01-01: 1.56 l2006-05-01: 1.25 2-4Inventory ManagementlGMs production and distribution networkl20,000 supplier plantsl133 parts plantsl31 assembly plantsl11,000 dealerslFreight transportation costs: $4.1 billion (60% for material shipments) lGM inventory valued at $7.4 billion (70%WIP; Rest Finished Vehicles)lDecision tool to reduce:lcombined corporate cost of inventory and transportation. l26% annual cost reduction by adjusting: lShipment sizes (inventory policy) lRoutes (transportation strategy)Why Is Inventory Important?22-5Inventory ManagementInventorylWhere do we hold inventory?lSuppliers and manufacturerslwarehouses and distribution centerslretailerslTypes of InventorylWIP (work in process)lraw materialslfinished goods2-6Inventory ManagementThe reasons of holding inventorylUnexpected changes in customer demandlThe short life cycle of an increasing number of products.lThe presence of many competing products in the marketplace.lUncertainty in the quantity and quality of the supply, supplier costs and delivery times.lDelivery Lead Time, Capacity limitationslEconomies of scale (transportation cost)2-7Inventory Management問題討論問題討論l小米小米3上市上市，對智慧型手機市場的衝擊對智慧型手機市場的衝擊l3DS上市對掌上型遊戲機市場的衝擊上市對掌上型遊戲機市場的衝擊2-8Inventory ManagementGoals: Reduce Cost, Improve Service Example1lBy effectively managing inventory:lWal-Mart became the largest retail company utilizing efficient inventory managementlGM has reduced parts inventory and transportation costs by 26% annually2-9Inventory ManagementGoals: Reduce Cost, Improve Service Example2lBy not managing inventory successfullylIn 1994, “IBM continues to struggle with shortages in their ThinkPad line” (WSJ, Oct 7, 1994)lIn 1993, “Dell Computers predicts a loss; Stock plunges. Dell acknowledged that the company was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993)2-10Inventory ManagementInventory Management vs. Demand ForecastslUncertain demand makes demand forecast critical for inventory related decisions:lWhat to order?lWhen to order?lHow much is the optimal order quantity?lApproach includes a set of techniqueslINVENTORY POLICY!2-11Inventory ManagementSupply Chain Factors in Inventory Policy1lEstimation of customer demandlReplenishment lead timelThe number of different products being consideredlThe length of the planning horizonlService level requirements2-12Inventory ManagementSupply Chain Factors in Inventory Policy2lCostslOrder cost (or setup cost): lProduct cost lTransportation costlInventory holding cost (or inventory carrying cost):lState taxes, property taxes, and insurance on inventorieslMaintenance costslObsolescence costlOpportunity costs2-13Inventory Management2.2 Single Stage Inventory ControllSingle supply chain stagelVariety of techniqueslEconomic Lot Size ModellDemand UncertaintylSingle Period ModelslInitial InventorylMultiple Order OpportunitieslContinuous Review PolicylVariable Lead TimeslPeriodic Review PolicylService Level Optimization2-14Inventory ManagementExamplelBook Store Mug SaleslDemand is constant, at 20 units a weeklFixed order cost of $12.00, no lead timelHolding cost of 25% of inventory value annuallylMugs cost $1.00, sell for $5.00lQuestionlHow many, when to order?2-15Inventory Management2.2.1 Economic Lot Size Model (EOQ)(Ford W. Harris, 1915)TimeInventoryOrderSizeNote: No Stockouts Order when no inventory Order Size determines policyAvg. InvenCycle Time =T2-16Inventory ManagementAssumptionslD items per day: Constant demand ratelQ items per order: Order quantities are fixed, i.e., each time the warehouse places an order, it is for Q items.lK, fixed setup cost, incurred every time the warehouse places an order.lh, inventory carrying cost accrued per unit held in inventory per day that the unit is held (also known as, holding cost)lLead time = 0 (the time that elapses between the placement of an order and its receipt)lInitial inventory = 0lPlanning horizon is long (infinite).2-17Inventory ManagementDeriving EOQlTotal cost at every cycle:lCycle time T =Q/D lAverage total cost per unit time: 2-18Inventory ManagementEOQ:Total CostTotal CostOrder CostHolding Cost2-19Inventory ManagementEOQ: Optimal Order QuantitylSo for our problem (Mug sales), the optimal quantity is 3162-20Inventory ManagementEOQ: Important ObservationslTrade-off between set-up costs and holding costs when determining order quantity. In fact, we order so that these costs are equal per unit timelTotal Cost is not particularly sensitive to the optimal order quantity2-21Inventory ManagementSensitivity Analysisb.5.8.911.11.21.52Increase in cost25%2.5%0.5% 0.4%1.6% 8.9%25%Total inventory cost relatively insensitive to order quantitiesActual order quantity: Q Q is a multiple b of the optimal order quantity Q*. For a given b, the quantity ordered is Q = bQ* 2-22Inventory Management2.2.2 The Effect of Demand UncertaintylMost companies treat the world as if it were predictable:lProduction and inventory planning are based on forecasts of demand made far in advance of the selling seasonlCompanies are aware of demand uncertainty when they create a forecast, but they design their planning process as if the forecast truly represents realitylRecent technological advances have increased the level of demand uncertainty:lShort product life cycles lIncreasing product variety2-23Inventory Management問題問題liPhone 5S 與與 iPhone 5C的銷售量的銷售量(參考參考iPhone 4？)lNew hTC one 的銷售量的銷售量(參考蝴蝶機參考蝴蝶機？)2-24Inventory ManagementThree principles of all forecasting techniqueslThe forecast is always wronglIt is difficult to match supply and demandlThe longer the forecast horizon, the worse the forecastlIt is even more difficult if one needs to predict customer demand for a long period of timelAggregate forecasts are more accurate.lMore difficult to predict customer demand for individual SKUslMuch easier to predict demand across all SKUs within one product family2-25Inventory Management2.2.3. Single Period ModelsShort lifecycle products(例如，例如，ipad)lOne ordering opportunity onlylOrder quantity to be decided before demand occurslOrder Quantity Demand = Dispose excess inventorylOrder Quantity Lose sales/profits2-26Inventory ManagementSingle Period ModelslUsing historical datalidentify a variety of demand scenarios ldetermine probability each of these scenarios will occurlGiven a specific inventory policyldetermine the profit associated with a particular scenariolgiven a specific order quantity lweight each scenarios profit by the likelihood that it will occurldetermine the average, or expected profit for a particular ordering quantity. lOrder the quantity that maximizes the average profit.2-27Inventory ManagementSwimsuit productionlFashion items have short life cycles, high variety of competitors (智慧型手機？智慧型手機？)lSwimsuit productionlNew designs are completedlOne production opportunitylBased on past sales, knowledge of the industry, and economic conditions, the marketing department has a probabilistic forecastlThe forecast averages about 13,000, but there is a chance that demand will be greater or less than this.Example Swimsuit production2-28Inventory ManagementDemand ScenariosExample Swimsuit production11%28%11%22%18%10%2-29Inventory ManagementCostslProduction cost per unit (C): $80lSelling price per unit (S): $125lSalvage value per unit (V): $20lFixed production cost (F): $100,000lQ is production quantityExample Swimsuit production2-30Inventory ManagementTwo ScenarioslScenario One:lSuppose you make 10,000 swimsuits and demand ends up being 12,000 swimsuits.lProfit = 125(10,000) - 80(10,000) - 100,000 = $350,000lScenario Two:lSuppose you make 10,000 swimsuits and demand ends up being 8,000 swimsuits.lProfit = 125(8,000) - 80(10,000) - 100,000 + 20(2,000) = $ 140,000Example Swimsuit production2-31Inventory ManagementProbability of Profitability Scenarios with Production = 10,000 UnitslProbability of demand being 8000 units = 11%lProbability of profit of $140,000 = 11%lProbability of demand being 12000 units = 28%lProbability of profit of $350,000 = 28%lTotal profit = Weighted average of profit scenarios 2-32Inventory ManagementExpected profit of production quantity Q1lDi=the ith demandlPi=the profit of production quantity Q at demand Di2-33Inventory ManagementExpected profit of production quantity Q2lf(Pi)=the probability of profit P at demand Di When production quantity=QExpect Profit of Q: E(P)2-34Inventory ManagementSwimsuit production SolutionlFind order quantity that maximizes weighted average profit.lQuestion: Will this quantity be less than, equal to, or greater than average demand?Example Swimsuit production2-35Inventory ManagementOrder Quantity that Maximizes Expected ProfitFIGURE 2-6: Average profit as a function of production quantity2-36Inventory ManagementRelationship Between Optimal Quantity and Average DemandlCompare marginal profit of selling an additional unit and marginal cost of not selling an additional unitlMarginal profit/unit = Selling Price - Variable Ordering (or, Production) Cost lMarginal cost/unit =Variable Ordering (or, Production) Cost - Salvage Value lIf Marginal Profit Marginal Cost = Optimal Quantity Average DemandlIf Marginal Profit Optimal Quantity Marginal Profit= optimal production quantity profit achieved if we produce to increase inventory to 12,000 units lIf we produce, the most we can make on average is a profit of $371,000. lSame average profit with initial inventory of 8,245 units and not producing anything. lIf initial inventory produce to raise the inventory level to 12,000 units. lIf initial inventory is at least 8,245 units, we should not produce anything (s, S) policy or (min, max) policy Manufacturer Initial Inventory = 10,000 Example Swimsuit production2-48Inventory Management(s, S) PolicieslFor some starting inventory levels, it is better to not start productionlIf we start, we always produce to the same levellThus, we use an (s,S) policy. If the inventory level is below s, we produce up to S. ls is the reorder point, and S is the order-up-to levellThe difference between the two levels is driven by the fixed costs associated with ordering, transportation, or manufacturing2-49Inventory Management2.2.5. Multiple Order Opportunities1REASONSlTo balance annual inventory holding costs and annual fixed order costs. lTo satisfy demand occurring during lead time. lTo protect against uncertainty in demand.2-50Inventory Management2.2.5. Multiple Order Opportunities2lTWO POLICIESlContinuous review policy(持續檢視政策持續檢視政策)linventory is reviewed continuouslylan order is placed when the inventory reaches a particular level or reorder point. linventory can be continuously reviewed (computerized inventory systems are used)lPeriodic review policy(週期檢視政策週期檢視政策)linventory is reviewed at regular intervals lappropriate quantity is ordered after each review. lit is impossible or inconvenient to frequently review inventory and place orders if necessary.2-51Inventory Management2.2.6. Continuous Review Policy AssumptionslDaily demand is random and follows a normal distribution. lEvery time the distributor places an order from the manufacturer, the distributor pays a fixed cost, K, plus an amount proportional to the quantity ordered.lInventory holding cost is charged per item per unit time.lInventory level is continuously reviewed, and if an order is placed, the order arrives after the appropriate lead time.lIf a customer order arrives when there is no inventory on hand to fill the order (i.e., when the distributor is stocked out), the order is lost.(不考慮缺貨不考慮缺貨)lThe distributor specifies a required service level. 2-52Inventory ManagementThe (Q,R) Policyl(Q,R ) Policy: Whenever the inventory position drops below a certain level, R, we order to raise the inventory position to level Q.lThe reorder point (R) is a function of:lThe Lead TimelAverage demandlDemand variabilitylService level2-53Inventory Management NotationlAVG = average daily demandlSTD = standard deviation of daily demandlL = replenishment lead time in dayslh = holding cost of one unit for one daylK = fixed cost (setup cost)l = service level. This implies that the probability of stocking out is 1 - lAlso, the Inventory Position at any time is the actual inventory plus items already ordered, but not yet delivered.2-54Inventory Management Analysis1lThe reorder point - (R) has two components:l1. To account for average demand during lead time:l2. To account for deviations from average (we call this safety stock) where z is chosen from statistical tables to ensure that the probability of stock-outs during leadtime is 100%-SL.2-55Inventory Management Analysis2lreorder point - (R):lThe total order-up-to level is (S)(倉庫容倉庫容量量):lThe average inventory level is:2-56Inventory ManagementService Level & Safety Factor, zService Level (1-)90%91%92%93%94% 95%96%97%98%99%99.9%z1.291.341.411.481.561.651.751.882.052.333.08z is chosen from statistical tables to ensure that the probability of stock-outs during lead time is exactly 1 - 2-57Inventory ManagementInventory Level Over TimeInventory level before receiving an order =Inventory level after receiving an order =Average Inventory =FIGURE 2-9: Inventory level as a function of time in a (Q,R) policy2-58Inventory ManagementContinuous Review Policy Example1lA distributor of TV sets that orders from a manufacturer and sells to retailerslFixed ordering cost = $4,500lCost of a TV set to the distributor = $250lAnnual inventory holding cost = 18% of product costlReplenishment lead time = 2 weekslExpected service level = 97%(z=1.9)2-59Inventory ManagementMonthSeptOct Nov. Dec. Jan. Feb. Mar. Apr. May June July AugSales 200 152 100 221 287 176 151 198 246 309 98 156Continuous Review Policy Example2Average monthly demand = 191.17 Standard deviation of monthly demand = 66.53Average weekly demand = Average Monthly Demand/4.3 =44.58Standard deviation of weekly demand = Monthly standard deviation/4.3 =32.082-60Inventory ManagementParameterAverage weekly demandStandard deviation of weekly demandAverage demand during lead timeSafety stockReorder pointValue44.5832.0889.1686.20176Weekly holding cost = Optimal order quantity = Average inventory level = 679/2 + 86.20 = 426Continuous Review Policy Example32-61Inventory Management2.2.7.變動的前置時間與需求變動的前置時間與需求1l在許多情況下，運送至倉庫的運輸前置時間被假在許多情況下，運送至倉庫的運輸前置時間被假設是固定的，而且是預先知道，實則不然。在許設是固定的，而且是預先知道，實則不然。在許多實際情況下，多實際情況下，運送至倉庫的前置時間，必須假運送至倉庫的前置時間，必須假設為常態機率分配，平均前置時間以設為常態機率分配，平均前置時間以AVGL表示表示及標準差以及標準差以STDL表示表示。在此情況下，再訂購點。在此情況下，再訂購點R的計算如下：的計算如下：2-62Inventory Management2.2.7.變動的前置時間與需求變動的前置時間與需求2l其中其中AVG AVGL表示平均前置時間內的平均需表示平均前置時間內的平均需求，而求，而 l為平均前置時間內的平均需求標準差。為平均前置時間內的平均需求標準差。l因此，應維持之安全存貨為：因此，應維持之安全存貨為：2-63Inventory Management2.2.7.變動的前置時間與需求變動的前置時間與需求3Order Quantity =l如前述，訂購量上限為安全存貨加上如前述，訂購量上限為安全存貨加上Q和前和前置時間內平均需求的最大值，也就是：置時間內平均需求的最大值，也就是：2-64Inventory ManagementlInventory level is reviewed periodically at regular intervals lAn appropriate quantity is ordered after each review lTwo Cases:lShort Intervals (e.g. Daily)lDefine two inventory levels s and S lDuring each inventory review, if the inventory position falls below s, order enough to raise the inventory position to S. l(s, S) policy2.2.8. Periodic Review Policy12-65Inventory Management(s,S) policylCalculate the Q and R values as if this were a continuous review modellSet s equal to RlSet S equal to R+Q.2-66Inventory ManagementA View of (s, S) PolicyTimeInventory LevelSs0LeadTimeLeadTimeInventory Position2-67Inventory ManagementlTwo Cases:lLonger Intervals (e.g. Weekly or Monthly)lMay make sense to always order after an inventory level review. lDetermine a target inventory level, the base-stock levellDuring each review period, the inventory position is reviewed lOrder enough to raise the inventory position to the base-stock level. lBase-stock level policy2.2.8. Periodic Review Policy22-68Inventory ManagementBase-Stock Level Policy1 lDetermine a target inventory level, the base-stock levellEach review period, review the inventory position is reviewed and order enough to raise the inventory position to the base-stock levellAssume:r = length of the review periodL = lead time AVG = average daily demand STD = standard deviation of this daily demand. 2-69Inventory ManagementBase-Stock Level Policy2lEach review echelon, inventory position is raised to the base-stock level.lThe base-stock level includes three components:lAverage demand during (r +L) days (the time until the next order arriveslSafety stock during that timelAmount on hand at order time (A)2-70Inventory ManagementBase-Stock Level Policy3l安全存量為安全存量為 l基本存貨水準基本存貨水準(base-stock level) l而進貨的前一刻，前置時間內的需求已耗用，只剩安全而進貨的前一刻，前置時間內的需求已耗用，只剩安全存量存量l因此平均存貨水準等於：因此平均存貨水準等於：(訂購量訂購量=保護期間的預期需求保護期間的預期需求+安全存量安全存量-再訂購點時的現有數量再訂購點時的現有數量)2-71Inventory ManagementBase-Stock Level Policy 4FIGURE 2-10: Inventory level as a function of time in a periodic review policy2-72Inventory ManagementlAssume: ldistributor places an order for TVs every 3 weekslLead time is 2 weekslBase-stock level needs to cover 5 weekslAverage demand = 44.58 x 5 = 222.9lSafety stock = lBase-stock level = 223 + 136 = 359lAverage inventory level =lDistributor keeps 5 (= 203.17/44.58) weeks of supply.Base-Stock Level Policy Example 2-73Inventory ManagementlOptimal inventory policy assumes a specific service level target. lWhat is the appropriate level of service? lMay be determined by the downstream customerlRetailer may require the supplier, to maintain a specific service levellSupplier will use that target to manage its own inventorylFacility may have the flexibility to choose the appropriate level of service2.2.9. Service Level Optimization2-74Inventory ManagementService Level OptimizationFIGURE 2-11: Service level inventory versus inventory level as a function of lead time2-75Inventory ManagementTrade-OffslEverything else being equal:lthe higher the service level, the higher the inventory level. lfor the same inventory level, the longer the lead time to the facility, the lower the level of service provided by the facility. lthe lower the inventory level, the higher the impact of a unit of inventory on service level and hence on expected profit2-76Inventory ManagementRetail (多樣化產品多樣化產品) StrategylGiven a target service level across all products determine service level for each SKU so as to maximize expected profit. lEverything else being equal, service level will be higher for products with:lhigh profit marginlhigh volumellow variabilitylshort lead time2-77Inventory ManagementProfit Optimization and Service Level1FIGURE 2-12: Service level optimization by SKU2-78Inventory ManagementlTarget inventory level = 95% across all products. lService level 99% for many products with high profit margin, high volume and low variability. lService level 95% for products with low profit margin, low volume and high variability. Profit Optimization and Service Level22-79Inventory ManagementRisk Pooling Question1lConsider these two systems:Market TwoSupplierWarehouse OneWarehouse TwoMarket OneMarket TwoSupplierWarehouseMarket One2-80Inventory ManagementRisk Pooling Question2lFor the same service level, which system will require more inventory? Why?lFor the same total inventory level, which system will have better service? Why?lWhat are the factors that affect these answers? 2-81Inventory Management案例案例l北半球冬季的泳衣銷售為淡季北半球冬季的泳衣銷售為淡季 But 南半南半球為夏季球為夏季2-82Inventory Management2.3 Risk PoolinglDemand variability is reduced if one aggregates demand across locations. lMore likely that high demand from one customer will be offset by low demand from another. lReduction in variability allows a decrease in safety stock and therefore reduces average inventory. 2-83Inventory Management問題討論問題討論l零件自製零件自製 vs. 委外給專業製造商委外給專業製造商2-84Inventory ManagementDemand VariationlStandard deviation measures how much demand tends to vary around the averagelGives an absolute measure of the variabilitylCoefficient of variation is the ratio of standard deviation to average demandlGives a relative measure of the variability, relative to the average demand2-85Inventory Management變異係數變異係數 =標準差標準差平均需求平均需求2-86Inventory ManagementAcme Risk Pooling CaselElectronic equipment manufacturer and distributorl2 warehouses for distribution in Massachusetts and New Jersey (partitioning the northeast market into two regions)lCustomers (that is, retailers) receiving items from warehouses (each retailer is assigned a warehouse)lWarehouses receive material from ChicagolCurrent rule: 97 % service level (z=1.9)lEach warehouse operate to satisfy 97 % of demand (3 % probability of stock-out)lLead time for delivery is about one week2-87Inventory ManagementlReplace the 2 warehouses with a single warehouse (located some suitable place) and try to implement the same service level 97 %lDelivery lead times may increaselBut may decrease total inventory investment considerably.lh = holding cost of one unit for one week=0.27lk = fixed cost (setup cost) =60New Idea2-88Inventory ManagementHistorical DataPRODUCT AWeek12345678Massachusetts3345373855301858New Jersey4635414026481855Total79807878817836113PRODUCT BWeek12345678Massachusetts02300130New Jersey24003100Total263032302-89Inventory ManagementSummary of Historical DataStatisticsProductAverage DemandStandard Deviation of DemandCoefficient of VariationMassachusettsA39.313.20.34MassachusettsB1.1251.361.21New JerseyA38.612.00.31New JerseyB1.251.581.26TotalA77.920.710.27TotalB2.3751.90.812-90Inventory ManagementInventory LevelsProductAverage Demand During Lead Time(LAVG)Safety Stock(zSTDL(1/2)Reorder PointQ(2kAVG/h)1/2MassachusettsA39.325.0865132MassachusettsB1.1252.58425New JerseyA38.622.862131New JerseyB1.253524TotalA77.939.35118186TotalB2.3753.616332-91Inventory ManagementSavings in InventorylAverage inventory for Product A: lAt NJ warehouse is about 88 units (ss+Q/2=22.8+131/2=88)lAt MA warehouse is about 91 unitslIn the centralized warehouse is about 132 unitslAverage inventory reduced by about 26 percent lAverage inventory for Product B:lAt NJ warehouse is about 15 unitslAt MA warehouse is about 14 unitslIn the centralized warehouse is about 20 units lAverage inventory reduced by about 31 percent 2-92Inventory ManagementlThe higher the coefficient of variation, the greater the benefit from risk poolinglThe higher the variability, the higher the safety stocks kept by the warehouses. The variability of the demand aggregated by the single warehouse is lower Critical Points12-93Inventory ManagementlThe benefits from risk pooling depend on the behavior of the demand from one market relative to demand from anotherlrisk pooling benefits are higher in situations where demands observed at warehouses are negatively correlated lReallocation of items from one market to another easily accomplished in centralized systems. Not possible to do in decentralized systems where they serve different marketsCritical Points22-94Inventory Management2.4 Centralized versus Decentralized Systems The Trade-offslSafety stock: lower with centralizationlService level: higher service level for the same inventory investment with centralizationlOverhead costs: higher in decentralized systemlCustomer lead time: response times lower in the decentralized systemlTransportation costs: not clear. Consider outbound and inbound costs.2-95Inventory ManagementlInventory decisions are given by a single decision maker whose objective is to minimize the system-wide costlThe decision maker has access to inventory information at each of the retailers and at the warehouse2.5 Managing Inventory in the Supply Chain12-96Inventory ManagementManaging inventory in the supply chain2lEchelon inventory (階層存貨階層存貨)lThe inventory on hand at the echelon, plus all downstream inventory (downstream means closer to the customer)lEchelon inventory position (階層存貨狀態階層存貨狀態)lThe echelon inventory at the echelon, plus those items ordered by the echelon that have not yet arrived minus all items that are backordered.2-97Inventory ManagementEchelon InventoryFIGURE 2-13: A serial supply chain2-98Inventory ManagementReorder Point with Echelon Inventory (distributor)lLe = echelon lead time, llead time between the retailer and the distributor plus the lead time between the distributor and its supplier, the wholesaler.lAVG = average demand at the retailer lSTD = standard deviation of demand at the retailerlReorder point 2-99Inventory Management4-Stage Supply Chain ExamplelAverage weekly demand faced by the retailer is 45lStandard deviation of demand is 32 lAt each stage, management is attempting to maintain a service level of 97% (z=1.88) lLead time between each of the stages, and between the manufacturer and its suppliers is 1 week 2-100Inventory ManagementCosts and Order QuantitiesK (ordering cost)D (weekly demand)H (holding cost)Q (order quantities)retailer250451.2137distributor20045.9141wholesaler20545.8152manufacturer50045.72552-101Inventory ManagementReorder Points at Each StagelFor the retailer, R=1*45+1.88*32*1 = 105lFor the distributor, R=2*45+1.88*32*2 = 175lFor the wholesaler, R=3*45+1.88*32*3 = 239lFor the manufacturer, R=4*45+1.88*32*4 = 300lAt each echelon, when the echelon inventory position falls below the reorder point for that echelon, the appropriate Q is ordered.2-102Inventory ManagementMore than One Facility at Each StagelFollow the same approach (two stage)lEchelon inventory at the warehouse is the inventory at the warehouse, plus all of the inventory in transit to and in stock at each of the retailers. lSimilarly, the echelon inventory position at the warehouse is the echelon inventory at the warehouse, plus those items ordered by the warehouse that have not yet arrived minus all items that are backordered. 2-103Inventory ManagementWarehouse Echelon InventoryFIGURE 2-14: The warehouse echelon inventory2-104Inventory ManagementReorder Point with Echelon InventoryThe reorder point of warehouse isWhere Le=echelon lead time, defined as the lead time between the retailers and the warehouse plus the lead time between the warehouse and its supplier AVG=average demand across all retailers STD=standard deviation of demand across all retailers2-105Inventory Management2.6 Practical Issues1lPeriodic inventory review. lTo identify slow-moving and obsolete products and allows management to continuously reduce inventory levels.lTight management of usage rates, lead times, and safety stock. lReduce safety stock levels. lIntroduce or enhance cycle counting practice. lReplaces the annual physical inventory countlPart of inventory is counted every day, and each item is counted several times per year.2-106Inventory Management2.6 Practical Issues2lABC approach. lClass A: a high-frequency periodic review policy (e.g., a weekly review)lClass C: the firm either keeps no inventory of expensive Class C products or keeps a high inventory of inexpensive Class C products.lShift more inventory or inventory ownership to suppliers.lQuantitative approaches. FOCUS: not reducing costs but reducing inventory levels. (JIT) Significant effort in industry to increase inventory turnover2-107Inventory ManagementInventory Turnover RatiolInventory turnover ratio = annual sales/avg. inventory levellIncrease in inventory turnover leads tolDecrease in average inventory levelslHigher level of liquiditylSmaller risk of obsolescencelReduced investment in inventorylIncreases the risk of lost sales2-108Inventory ManagementInventory Turnover Ratios for Different Manufacturers IndustryUpper quartileMedianLower quartileElectronic components and accessories8.14.93.3Electronic computers22.77.02.7Household audio and video equipment6.33.92.5Paper Mills11.78.05.5Industrial chemicals14.16.44.2Bakery products39.723.012.6Books: Publishing and printing7.22.81.52-109Inventory ManagementFactors that Drive Reduction in Inventory lTop management emphasis on inventory reduction (19%)lReduce the Number of SKUs in the warehouse (10%)lImproved forecasting (7%)lUse of sophisticated inventory management software (6%)lCoordination among supply chain members (6%)lOthers2-110Inventory Management2.7 ForecastinglGeneral Overview:lJudgment methodslMarket research methodslTime-series methodslCausal methods2-111Inventory ManagementJudgment Methods1lAssemble the opinion of expertslSales-force composite combines salespeoples estimatesl優點優點l銷售員直接與顧客接觸，較能知道顧客對於未來的銷售員直接與顧客接觸，較能知道顧客對於未來的考量與計畫。考量與計畫。l缺點缺點l銷售員銷售員無法區分顧客想做與實際會做無法區分顧客想做與實際會做的事。的事。l銷售員易銷售員易過度受到最近經驗的影響過度受到最近經驗的影響。2-112Inventory ManagementJudgment Methods2lPanels of experts internal, external, bothlDelphi methodlEach member surveyedlOpinions are compiledlEach member is given the opportunity to change his opinion2-113Inventory ManagementMarket Research MethodslParticularly valuable for developing forecasts of newly introduced productslMarket testinglFocus groups assembled.lResponses tested.lExtrapolations to rest of market made.lMarket surveyslData gathered from potential customerslInterviews, phone-surveys, written surveys, etc.2-114Inventory ManagementTime Series MethodslPast data is used to estimate future datalExamples includelMoving averages average of some previous demand points.lExponential Smoothing more recent points receive more weightlMethods for data with trends:lRegression analysis fits line to datalHolts method combines exponential smoothing concepts with the ability to follow a trendlMethods for data with seasonalitylSeasonal decomposition methods (seasonal patterns removed)lWinters method: advanced approach based on exponential smoothinglComplex methods (not clear that these work better)2-115Inventory Management時間數列預測法時間數列預測法l趨勢趨勢 - 資料中資料中漸進而長期漸進而長期的移動的移動l季節變動季節變動 - 資料中資料中短期而規則短期而規則性的變動性的變動l循環循環 - 在在一年以上一年以上的時間內，呈的時間內，呈波狀波狀的變的變動動l不規則的變動不規則的變動 - 由於不尋常的情況所產生由於不尋常的情況所產生的的l隨機變動隨機變動 - 偶然發生偶然發生2-116Inventory Management趨勢、季節變動、循環變動、隨機變動與不規則變動趨勢、季節變動、循環變動、隨機變動與不規則變動趨勢不規則變動循環季節變動9089882-117Inventory Management平均法平均法l天真預測法天真預測法(naive forecasts)l移動平均法移動平均法(moving average method)l加權移動平均法加權移動平均法(weighted moving average method)l指數平滑化法指數平滑化法(exponential smoothing method)2-118Inventory Management天真預測法天真預測法嗯嗯, 請給我一分鐘想想請給我一分鐘想想. 上週我們已銷售上週我們已銷售250個輪胎個輪胎. 所以所以下週我下週我們將要銷售們將要銷售.2-119Inventory Management問題問題l倘若前一期的需求為極端值倘若前一期的需求為極端值2-120Inventory Management移動平均法移動平均法(Moving Average)MAn =nDii = 1n2-121Inventory Management問題問題l與本期較近之期間的需求，其參考價值應與本期較近之期間的需求，其參考價值應較高較高? ?2-122Inventory Management加權加權移動平均移動平均(Weighted Moving Average)法法2-123Inventory Management指數平滑指數平滑法法(Exponential Smoothing)Ft = Ft-1 + (Dt-1 - Ft-1)Ft：第：第t期的預測需求期的預測需求Dt：第：第t期的實際需求期的實際需求：平滑係數：平滑係數 =Dt-1 +(1- )Ft-12-124Inventory Management選取平選取平滑化指數滑化指數.2.052-125Inventory Management平滑係數的選擇平滑係數的選擇l目的目的l在在反應真實變動反應真實變動與與平滑隨機變動平滑隨機變動之利益間取得之利益間取得平衡。平衡。l選擇情境選擇情境l平均值傾向穩定時，使用較低的平均值傾向穩定時，使用較低的值值。l平均值容易受變動影響時，使用較大的平均值容易受變動影響時，使用較大的值。值。2-126Inventory Management範例範例1根據下表計算第六期之預測值根據下表計算第六期之預測值期數期數抱怨數抱怨數160265355458564l天真預測法天真預測法l三期移動平均三期移動平均l權重為權重為0.50(最近最近)0.3與與0.2的加權平的加權平均法均法l平滑常數為平滑常數為0.40的的指數平滑法指數平滑法(以第一以第一期之實際值作為第期之實際值作為第二期之預測值二期之預測值)2-127Inventory Management範例範例2l天真預測法天真預測法l64l三期移動平均三期移動平均lMA3=(55+58+64)/3=59lWA=(0.5 64)+(0.3 58)+(0.2 55)2-128Inventory Management範例範例3期數期數 抱怨數抱怨數 預測值預測值 計算計算160公式：公式：Ft=Ft-1+(Dt-1-Ft-1)265603556260+0.4(65-60)=6245859.262+0.4(55-62)=59.256458.7259.2+0.4(58-59.2)=58.72660.8358.72+0.4(64-58.72)=60.832-129Inventory Management趨勢環境下之預測方法趨勢環境下之預測方法l雙指數平滑法雙指數平滑法(double exponential smoothing method)l迴歸分析法迴歸分析法(regression analysis)l又稱最小平方法又稱最小平方法(least square method)2-130Inventory Management雙指數平滑法雙指數平滑法lFITt+1 = Ft+1 + Tt lFt+1 = FITt + (At FITt)l Tt = Tt-1 + (FITt FITt-1) Tt-1)l =Tt-1 + (Ft FITt-1)l其中其中Ft+1=第第t+1期之不含趨勢預測期之不含趨勢預測Tt=第第t期之趨勢預測值期之趨勢預測值 FITt=第第t期之含趨勢預測值期之含趨勢預測值 =平均平滑常數平均平滑常數 =趨勢平滑常數趨勢平滑常數 與與皆介於皆介於0與與1之間。之間。2-131Inventory Management趨勢方程式趨勢方程式Yt = a + b t0 1 2 3 4 5 tY2-132Inventory Management計算計算 a 與與 b2-133Inventory Management線型趨勢方程式範例線型趨勢方程式範例12-134Inventory Management線型趨勢方程式範例線型趨勢方程式範例2y = 143.5 + 6.3t b = 5 (2499) - 15(812)5(55) - 225 = 12495-12180275-225 = 6.3a = 812 - 6.3(15)5 = 143.5 2-135Inventory Management季節性因素處理季節性因素處理l若一時間數列明顯含有若一時間數列明顯含有季節性因素季節性因素，必，必須先計算各季之須先計算各季之季節指數季節指數，再利用該各，再利用該各季節指數來對資料進行季節指數來對資料進行去除季節性去除季節性，然，然後才可用一後才可用一預測預測方法對去除季節性之資方法對去除季節性之資料，做正常之分析與預測。料，做正常之分析與預測。最後最後計算出計算出預測值必須再乘以季節指數，使之變為預測值必須再乘以季節指數，使之變為含季節性之預測值含季節性之預測值。2-136Inventory Management考慮季節性考慮季節性之指數平滑法之指數平滑法l季節指數季節指數(簡單平均簡單平均)It當季平均需求當季平均需求總平均需求總平均需求=Ft=At-1It-1(1-)Ft-1It-1+ItFt=At-1+(1-)Ft-1ItIt-12-137Inventory ManagementTM 12.3b考慮季節性之預測範例考慮季節性之預測範例Suppose the projected demand for year 3 is 1320 units.quarterquarterquarterquarter(1320/4)=3302-138Inventory ManagementCausal MethodslForecasts are generated based on data other than the data being predictedlExamples include:lInflation rateslGNPlUnemployment rateslWeatherlSales of other products2-139Inventory Management多元技術多元技術(multiple techniques)的使用的使用l複合預測法複合預測法(combination forecasts)l使用不同的預測方法或資料進行預測，取其平使用不同的預測方法或資料進行預測，取其平均值作為預測值。均值作為預測值。l焦點預測法焦點預測法(focus forecasts)l同時使用多種預測技術，採用最近且預測效果同時使用多種預測技術，採用最近且預測效果最佳的方法作為本期之預測方法。最佳的方法作為本期之預測方法。2-140Inventory Management預測的準確性預測的準確性l l誤差誤差 = 實際值與預測值之間的差額實際值與預測值之間的差額l l平均絕對誤差平均絕對誤差(mean absolute deviation，MAD)l l均方誤差均方誤差(mean squared error，MSE)l l平均絕對百分比誤差平均絕對百分比誤差(mean absolute percent error，MAPE)2-141Inventory Management平均絕對平均絕對誤誤差差、均方均方誤誤差差與與平均絕對百平均絕對百分比誤差分比誤差MSE = Actual forecast)-12n(MAD = Actual forecastnMAPE =ActualtforecasttnActualt100%2-142Inventory Management預測的控制預測的控制l l預測方法適用與否之判斷預測方法適用與否之判斷預測誤差是否預測誤差是否是隨機的是隨機的。l l方法方法l l追蹤信號追蹤信號追蹤信號追蹤信號(tracking signal)(tracking signal)l l管制圖管制圖管制圖管制圖2-143Inventory Management追蹤信號追蹤信號1l其範圍通常從其範圍通常從3到到8l一般採用一般採用4追蹤信號追蹤信號t= (實際值實際值i-預測值預測值i)MADt i=1t2-144Inventory Management追蹤信號追蹤信號2MADt= MADt-1+(|實際值實際值-預測值預測值|t-MADt-1)2-145Inventory Management管制圖管制圖l管制中心線管制中心線(center line, CL)=E(e)=0l管制上限管制上限(upper control limit, UCL)=E(e)+ze=z(MSE)1/2l管制下限管制下限(lower control limit, LCL)=E(e)-ze=-z(MSE)1/22-146Inventory ManagementSelecting the Appropriate Approach (Chambers, Mullick, and Smith, CMS)lWhat is the purpose of the forecast?lGross or detailed estimates?lWhat are the dynamics of the system being forecast?lIs it sensitive to economic data?lIs it seasonal? trending?lHow important is the past in estimating the future?2-147Inventory ManagementProduct life cycle vs. forecast techniqueslTesting and intro: market research methods, judgment methodslRapid growth: time series methods (with trend)lMature: time series, causal methods (particularly for long-range planning)lIt is typically effective to combine approaches. (Georgoff and Murdick)2-148Inventory ManagementSUMMARYlMatching supply with demand a major challengelForecast demand is always wronglLonger the forecast horizon, less accurate the forecastlAggregate demand more accurate than disaggregated demandlNeed the most appropriate techniquelNeed the most appropriate inventory policy