固定订购量系统与定期订购系统的比较

1、Operations ManagementCh 17 Inventory ControluInventory System DefineduInventory CostsuIndependent vs. Dependent DemanduSingle-Period Inventory Model uMulti-Period Inventory Models: Basic Fixed-Order Quantity ModelsuMulti-Period Inventory Models: Basic Fixed-Time Period ModeluMiscellaneous Systems an

2、d IssuesOBJECTIVES Inventory SystemInventory is the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-processAn inventory system is the set of policies and controls that monitor levels of inventory and dete

3、rmines what levels should be maintained, when stock should be replenished, and how large orders should bePurposes of Inventory1. To maintain independence of operations2. To meet variation in product demand3. To allow flexibility in production scheduling4. To provide a safeguard for variation in raw

4、material delivery time5. To take advantage of economic purchase-order sizeInventory CostsuHolding (or carrying) costsnCosts for storage, handling, insurance, etcuSetup (or production change) costsnCosts for arranging specific equipment setups, etcuOrdering costsnCosts of someone placing an order, et

5、cuShortage costsnCosts of canceling an order, etcIndependent vs. Dependent DemandE(1)Independent Demand (Demand for the final end-product or demand not related to other items)Dependent Demand(Derived demand items for component parts, subassemblies, raw materials, etc)FinishedproductComponent partsIn

6、ventory Systemsu Single-Period Inventory ModelnOne time purchasing decision (Example: vendor selling t-shirts at a football game)nSeeks to balance the costs of inventory overstock and under stocku Multi-Period Inventory ModelsnFixed-Order Quantity ModelsnEvent triggered (Example: running out of stoc

7、k)nFixed-Time Period Models nTime triggered (Example: Monthly sales call by sales representative)Single-Period Inventory ModeluouCCCPsold be unit will y that theProbabilitestimatedunder demand ofunit per Cost Cestimatedover demand ofunit per Cost C:WhereuoPThis model states that we should continue t

8、o increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+CuSingle Period Model Exampleu Our college basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,40

9、0 shirts with a standard deviation of 350. We make $10 on every shirt we sell at the game, but lose $5 on every shirt not sold. How many shirts should we make for the game?Cu = $10 and Co = $5; P $10 / ($10 + $5) = .667Z.667 = .432 (use NORMSDIST(.667) or Appendix E) therefore we need 2,400 + .432(3

10、50) = 2,551 shirts圖17.4固定訂購量系統與定期訂購系統的比較閒置狀態等待需求需求發生：從庫存中取出需求單位或缺貨計算庫存狀態：狀態=在庫+在途-缺貨目前狀態訂購點發出剛好Q單位的訂單閒置狀態等待需求需求發生：從庫存中取出需求單位或缺貨檢視時間到了嗎？計算庫存狀態：狀態=在庫+在途-缺貨計算使庫存回到需要水準所要訂購的數量發出一個需要數目的訂單固定訂購量系統（Q模式）否是定期訂購系統（P模式）否是Multi-Period Models:Fixed-Order Quantity Model Model Assumptions (Part 1)uDemand for the pr

11、oduct is constant and uniform throughout the perioduLead time (time from ordering to receipt) is constantuPrice per unit of product is constant Multi-Period Models:Fixed-Order Quantity Model Model Assumptions (Part 2)uInventory holding cost is based on average inventoryuOrdering or setup costs are c

12、onstantuAll demands for the product will be satisfied (No back orders are allowed) Basic Fixed-Order Quantity Model and Reorder Point BehaviorR = Reorder pointQ = Economic order quantityL = Lead timeLLQQQRTimeNumberof unitson hand1. You receive an order quantity Q.2. Your start using them up over ti

13、me.3. When you reach down to a level of inventory of R, you place your next Q sized order.4. The cycle then repeats.Cost Minimization GoalOrdering CostsHoldingCostsOrder Quantity (Q)COSTAnnual Cost ofItems (DC)Total CostQOPTBy adding the item, holding, and ordering costs together, we determine the t

14、otal cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costsBasic Fixed-Order Quantity (EOQ) Model FormulaH 2Q + S QD + DC = TCTotal Annual =Cost AnnualPurchaseCostAnnualOrderingCostAnnualHoldingCost+TC=Total annual costD =DemandC =Cost per unitQ =Order qu

15、antityS =Cost of placing an order or setup costR =Reorder pointL =Lead timeH=Annual holding and storage cost per unit of inventoryDeriving the EOQUsing calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the o

16、ptimized (cost minimized) value of Qopt Q = 2DSH = 2(Annual Demand)(Order or Setup Cost)Annual Holding CostOPT Reorder point, R = d L_d = average daily demand (constant) L = Lead time (constant)_We also need a reorder point to tell us when to place an orderEOQ Example (1) Problem DataAnnual Demand =

17、 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50Lead time = 7 daysCost per unit = $15Given the information below, what are the EOQ and reorder point?EOQ Example (1) SolutionQ = 2DSH = 2(1,000 )(10)2.50 = 89.443 units

18、 or OPT90 unitsd = 1,000 units / year365 days / year = 2.74 units / day Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _20 unitsIn summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of

19、90 units.EOQ Example (2) Problem DataAnnual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = $15Determine the economic order quantity and the reorder point gi

20、ven the followingEOQ Example (2) SolutionQ=2DSH=2(10,000 )(10)1.50= 365.148 units, or OPT366 unitsd =10,000 units / year365 days / year= 27.397 units / dayR = d L = 27.397 units / day (10 days) = 273.97 or _274 unitsPlace an order for 366 units. When in the course of using the inventory you are left

21、 with only 274 units, place the next order of 366 units.Fixed-Time Period Model with Safety Stock Formulaorder)on items (includes levelinventory current = I timelead and review over the demand ofdeviation standard = yprobabilit service specified afor deviations standard ofnumber the= zdemanddaily av

22、erageforecast = ddaysin timelead = Lreviewsbetween days ofnumber the= Tordered be toquantitiy = q:WhereI - Z+ L)+(Td = qL+TL+Tq = Average demand + Safety stock Inventory currently on handMulti-Period Models: Fixed-Time Period Model: Determining the Value of T+LT+Ldi 1T+LdT+Ld2 = Since each day is in

23、dependent and is constant, = (T+ L)i2The standard deviation of a sequence of random events equals the square root of the sum of the variancesExample of the Fixed-Time Period ModelAverage daily demand for a product is 20 units. The review period is 30 days, and lead time is 10 days. Management has se

24、t a policy of satisfying 96 percent of demand from items in stock. At the beginning of the review period there are 200 units in inventory. The daily demand standard deviation is 4 units. Given the information below, how many units should be ordered?Example of the Fixed-Time Period Model: Solution (P

25、art 1) T+Ld22 = (T+ L)= 30+10 4= 25.298The value for “z” is found by using the Excel NORMSINV function, or as we will do here, using Appendix D. By adding 0.5 to all the values in Appendix D and finding the value in the table that comes closest to the service probability, the “z” value can be read b

26、y adding the column heading label to the row label. So, by adding 0.5 to the value from Appendix D of 0.4599, we have a probability of 0.9599, which is given by a z = 1.75Example of the Fixed-Time Period Model: Solution (Part 2) or 644.272, = 200 - 44.272 800 = q200- 298)(1.75)(25. + 10)+20(30 = qI

27、- Z+ L)+(Td = qL+Tunits 645So, to satisfy 96 percent of the demand, you should place an order of 645 units at this review periodMiscellaneous Systems: Bin SystemsTwo-Bin SystemFullEmptyOrder One Bin ofInventoryOne-Bin SystemPeriodic CheckOrder Enough toRefill BinABC Classification Systemu Items kept in inventory are not of equal importance in terms of:ndollars investednprofit potentialnsales or usage volumenstock-out penalties 030603060ABC% of $ Value% of UseSo, identify inventory items based on percentage of total dollar value, where “A” items are roughly t