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1、全球化趨勢下一般企業經常面對的問題,高度需求變動訂貨前置時間長不可靠的供應程序大量的儲存單位(SKUs),案例,三工業的問題(前置時間)手機的產品壽命週期：200000元(產品壽週期需求變異)Ipad 對電子書的衝擊(競爭需求變異)新機推出後一個月IPhone跌2千；hTC跌5千；三星跌3千智慧型手機可能帶來衝擊電子書遊戲機隨身聽衛星導航,Why Is Inventory Important?1,Distribution and inventory(logistics)costs are quite substantial Total U.S.Manufacturing Inventories
2、($m):1992-01-31:$m 808,773 1996-08-31:$m 1,000,774 2006-05-31:$m 1,324,108 Inventory-Sales Ratio(U.S.Manufacturers):1992-01-01:1.56 2006-05-01:1.25,GMs production and distribution network20,000 supplier plants133 parts plants31 assembly plants11,000 dealersFreight transportation costs:$4.1 billion(6
3、0%for material shipments)GM inventory valued at$7.4 billion(70%WIP;Rest Finished Vehicles)Decision tool to reduce:combined corporate cost of inventory and transportation.26%annual cost reduction by adjusting:Shipment sizes(inventory policy)Routes(transportation strategy),Why Is Inventory Important?2
4、,Inventory,Where do we hold inventory?Suppliers and manufacturerswarehouses and distribution centersretailersTypes of InventoryWIP(work in process)raw materialsfinished goods,The reasons of holding inventory,Unexpected changes in customer demandThe short life cycle of an increasing number of product
5、s.The presence of many competing products in the marketplace.Uncertainty in the quantity and quality of the supply,supplier costs and delivery times.Delivery Lead Time,Capacity limitationsEconomies of scale(transportation cost),問題討論,小米3上市，對智慧型手機市場的衝擊3DS上市對掌上型遊戲機市場的衝擊,Goals:Reduce Cost,Improve Servic
6、e Example1,By effectively managing inventory:Wal-Mart became the largest retail company utilizing efficient inventory managementGM has reduced parts inventory and transportation costs by 26%annually,Goals:Reduce Cost,Improve Service Example2,By not managing inventory successfullyIn 1994,“IBM continu
7、es to struggle with shortages in their ThinkPad line”(WSJ,Oct 7,1994)In 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),Inventory Management vs.Demand Forecasts,Uncert
8、ain demand makes demand forecast critical for inventory related decisions:What to order?When to order?How much is the optimal order quantity?Approach includes a set of techniquesINVENTORY POLICY!,Supply Chain Factors in Inventory Policy1,Estimation of customer demandReplenishment lead timeThe number
9、 of different products being consideredThe length of the planning horizonService level requirements,Supply Chain Factors in Inventory Policy2,CostsOrder cost(or setup cost):Product cost Transportation costInventory holding cost(or inventory carrying cost):State taxes,property taxes,and insurance on
10、inventoriesMaintenance costsObsolescence costOpportunity costs,2.2 Single Stage Inventory Control,Single supply chain stageVariety of techniquesEconomic Lot Size ModelDemand UncertaintySingle Period ModelsInitial InventoryMultiple Order OpportunitiesContinuous Review PolicyVariable Lead TimesPeriodi
11、c Review PolicyService Level Optimization,Example,Book Store Mug SalesDemand is constant,at 20 units a weekFixed order cost of$12.00,no lead timeHolding cost of 25%of inventory value annuallyMugs cost$1.00,sell for$5.00QuestionHow many,when to order?,2.2.1 Economic Lot Size Model(EOQ)(Ford W.Harris,
12、1915),Time,Inventory,OrderSize,Note:No Stockouts Order when no inventory Order Size determines policy,Avg.Inven,Cycle Time=T,Assumptions,D items per day:Constant demand rateQ items per order:Order quantities are fixed,i.e.,each time the warehouse places an order,it is for Q items.K,fixed setup cost,
13、incurred every time the warehouse places an order.h,inventory carrying cost accrued per unit held in inventory per day that the unit is held(also known as,holding cost)Lead time=0(the time that elapses between the placement of an order and its receipt)Initial inventory=0Planning horizon is long(infi
14、nite).,Deriving EOQ,Total cost at every cycle:Cycle time T=Q/D Average total cost per unit time:,EOQ:Total Cost,Total Cost,Order Cost,Holding Cost,EOQ:Optimal Order Quantity,So for our problem(Mug sales),the optimal quantity is 316,EOQ:Important Observations,Trade-off between set-up costs and holdin
15、g costs when determining order quantity.In fact,we order so that these costs are equal per unit timeTotal Cost is not particularly sensitive to the optimal order quantity,Sensitivity Analysis,Total inventory cost relatively insensitive to order quantitiesActual order quantity:Q Q is a multiple b of
16、the optimal order quantity Q*.For a given b,the quantity ordered is Q=bQ*,2.2.2 The Effect of Demand Uncertainty,Most companies treat the world as if it were predictable:Production and inventory planning are based on forecasts of demand made far in advance of the selling seasonCompanies are aware of
17、 demand uncertainty when they create a forecast,but they design their planning process as if the forecast truly represents realityRecent technological advances have increased the level of demand uncertainty:Short product life cycles Increasing product variety,問題,iPhone 5S 與 iPhone 5C的銷售量(參考iPhone 4？
18、)New hTC one 的銷售量(參考蝴蝶機？),Three principles of all forecasting techniques,The forecast is always wrongIt is difficult to match supply and demandThe longer the forecast horizon,the worse the forecastIt is even more difficult if one needs to predict customer demand for a long period of timeAggregate fo
19、recasts are more accurate.More difficult to predict customer demand for individual SKUsMuch easier to predict demand across all SKUs within one product family,2.2.3.Single Period Models,Short lifecycle products(例如，ipad)One ordering opportunity onlyOrder quantity to be decided before demand occursOrd
20、er Quantity Demand=Dispose excess inventoryOrder Quantity Lose sales/profits,Single Period Models,Using historical dataidentify a variety of demand scenarios determine probability each of these scenarios will occurGiven a specific inventory policydetermine the profit associated with a particular sce
21、nariogiven a specific order quantity weight each scenarios profit by the likelihood that it will occurdetermine the average,or expected profit for a particular ordering quantity.Order the quantity that maximizes the average profit.,Swimsuit production,Fashion items have short life cycles,high variet
22、y of competitors(智慧型手機？)Swimsuit productionNew designs are completedOne production opportunityBased on past sales,knowledge of the industry,and economic conditions,the marketing department has a probabilistic forecastThe forecast averages about 13,000,but there is a chance that demand will be greate
23、r or less than this.,Example Swimsuit production,Demand Scenarios,Example Swimsuit production,11%,28%,11%,22%,18%,10%,Costs,Production cost per unit(C):$80Selling price per unit(S):$125Salvage value per unit(V):$20Fixed production cost(F):$100,000Q is production quantity,Example Swimsuit production,
24、Two Scenarios,Scenario One:Suppose you make 10,000 swimsuits and demand ends up being 12,000 swimsuits.Profit=125(10,000)-80(10,000)-100,000=$350,000Scenario Two:Suppose you make 10,000 swimsuits and demand ends up being 8,000 swimsuits.Profit=125(8,000)-80(10,000)-100,000+20(2,000)=$140,000,Example
25、 Swimsuit production,Probability of Profitability Scenarios with Production=10,000 Units,Probability of demand being 8000 units=11%Probability of profit of$140,000=11%Probability of demand being 12000 units=28%Probability of profit of$350,000=28%Total profit=Weighted average of profit scenarios,Expe
26、cted profit of production quantity Q1,Di=the ith demandPi=the profit of production quantity Q at demand Di,Expected profit of production quantity Q2,f(Pi)=the probability of profit P at demand Di When production quantity=QExpect Profit of Q:E(P),Swimsuit production Solution,Find order quantity that
27、maximizes weighted average profit.Question:Will this quantity be less than,equal to,or greater than average demand?,Example Swimsuit production,Order Quantity that Maximizes Expected Profit,FIGURE 2-6:Average profit as a function of production quantity,Relationship Between Optimal Quantity and Avera
28、ge Demand,Compare marginal profit of selling an additional unit and marginal cost of not selling an additional unitMarginal profit/unit=Selling Price-Variable Ordering(or,Production)Cost Marginal cost/unit=Variable Ordering(or,Production)Cost-Salvage Value If Marginal Profit Marginal Cost=Optimal Qu
29、antity Average DemandIf Marginal Profit Optimal Quantity Average Demand,For the Swimsuit Example,Average demand=13,000 units.Optimal production quantity=12,000 units.Marginal profit=125-80=$45Marginal cost=80-20=$60.Thus,Marginal Cost Marginal Profit=optimal production quantity average demand.,Risk-
30、Reward Trade-offs,Optimal production quantity maximizes average profit is about 12,000($371000)Producing 9,000 units or producing 16,000 units will lead to about the same average profit of$294,000.If we had to choose between producing 9,000 units and 16,000 units,which one should we choose?,Swimsuit
31、 production Expected Profit,Example Swimsuit production,9000,Risk-Reward Tradeoffs1,FIGURE 2-7:A frequency histogram of profit,Risk-Reward Tradeoffs2,Production Quantity=9000 unitsProfit is:either$200,000 with probability of about 11%or$305,000 with probability of about 89%Production quantity=16,000
32、 units.Distribution of profit is not symmetrical.Losses of$220,000 about 11%of the time Profits of at least$410,000 about 50%of the timeWith the same average profit,increasing the production quantity:Increases the possible riskIncreases the possible reward,Key Insights from this Model,The optimal or
33、der quantity is not necessarily equal to average forecast demandThe optimal quantity depends on the relationship between marginal profit and marginal costAs order quantity increases,average profit first increases and then decreasesAs production quantity increases,risk increases.In other words,the pr
34、obability of large gains and of large losses increases,Example Swimsuit production,2.2.4.What If the Manufacturer Has an Initial Inventory?,Trade-off between:Using on-hand inventory to meet demand and avoid paying fixed production cost:need sufficient inventory stockPaying the fixed cost of producti
35、on and not have as much inventory,Initial Inventory Solution,FIGURE 2-8:Profit and the impact of initial inventory,Example Swimsuit production,225000,Manufacturer Initial Inventory=5,000,If nothing is produced,average profit=225,000(from the figure)+5,000 x 80=625,000(125 5000=625000)If the manufact
36、urer decides to produceProduction should increase inventory from 5,000 units to 12,000 units.Average profit=371,000(from the figure)+5,000 80=771,000,Example Swimsuit production,Trade-off between Produced and not Produced,Example Swimsuit production,Let X is the trade-off point,No need to produce an
37、ything average profit profit achieved if we produce to increase inventory to 12,000 units If we produce,the most we can make on average is a profit of$371,000.Same average profit with initial inventory of 8,245 units and not producing anything.If initial inventory produce to raise the inventory leve
38、l to 12,000 units.If 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 production,(s,S)Policies,For some starting inventory levels,it is better to not start productionIf we start,we always prod
39、uce to the same levelThus,we use an(s,S)policy.If the inventory level is below s,we produce up to S.s is the reorder point,and S is the order-up-to levelThe difference between the two levels is driven by the fixed costs associated with ordering,transportation,or manufacturing,2.2.5.Multiple Order Op
40、portunities1,REASONSTo balance annual inventory holding costs and annual fixed order costs.To satisfy demand occurring during lead time.To protect against uncertainty in demand.,2.2.5.Multiple Order Opportunities2,TWO POLICIESContinuous review policy(持續檢視政策)inventory is reviewed continuouslyan order
41、 is placed when the inventory reaches a particular level or reorder point.inventory can be continuously reviewed(computerized inventory systems are used)Periodic review policy(週期檢視政策)inventory is reviewed at regular intervals appropriate quantity is ordered after each review.it is impossible or inco
42、nvenient to frequently review inventory and place orders if necessary.,2.2.6.Continuous Review Policy Assumptions,Daily demand is random and follows a normal distribution.Every time the distributor places an order from the manufacturer,the distributor pays a fixed cost,K,plus an amount proportional
43、to the quantity ordered.Inventory holding cost is charged per item per unit time.Inventory level is continuously reviewed,and if an order is placed,the order arrives after the appropriate lead time.If a customer order arrives when there is no inventory on hand to fill the order(i.e.,when the distrib
44、utor is stocked out),the order is lost.(不考慮缺貨)The distributor specifies a required service level.,The(Q,R)Policy,(Q,R)Policy:Whenever the inventory position drops below a certain level,R,we order to raise the inventory position to level Q.The reorder point(R)is a function of:The Lead TimeAverage dem
45、andDemand variabilityService level,Notation,AVG=average daily demandSTD=standard deviation of daily demandL=replenishment lead time in daysh=holding cost of one unit for one dayK=fixed cost(setup cost)=service level.This implies that the probability of stocking out is 1-Also,the Inventory Position a
46、t any time is the actual inventory plus items already ordered,but not yet delivered.,Analysis1,The reorder point-(R)has two components:1.To account for average demand during lead time:2.To account for deviations from average(we call this safety stock)where z is chosen from statistical tables to ensu
47、re that the probability of stock-outs during leadtime is 100%-SL.,Analysis2,reorder point-(R):The total order-up-to level is(S)(倉庫容量):The average inventory level is:,Service Level&Safety Factor,z,z is chosen from statistical tables to ensure that the probability of stock-outs during lead time is exa
48、ctly 1-,Inventory Level Over Time,Inventory 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)policy,Continuous Review Policy Example1,A distributor of TV sets that orders from a manufacturer and se
49、lls to retailersFixed ordering cost=$4,500Cost of a TV set to the distributor=$250Annual inventory holding cost=18%of product costReplenishment lead time=2 weeksExpected service level=97%(z=1.9),Continuous Review Policy Example2,Average monthly demand=191.17 Standard deviation of monthly demand=66.5
50、3Average weekly demand=Average Monthly Demand/4.3=44.58Standard deviation of weekly demand=Monthly standard deviation/4.3=32.08,Weekly holding cost=,Optimal order quantity=,Average inventory level=679/2+86.20=426,Continuous Review Policy Example3,2.2.7.變動的前置時間與需求1,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，
