2Learning ObjectivesDefine the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management.Discuss the nature and importance of service inventoriesDiscuss periodic and perpetual review systems.Discuss the objectives of inventory management.Describe the A-B-C approach and explain how it is useful.
3Learning ObjectivesDescribe the basic EOQ model and its assumptions and solve typical problems.Describe the economic production quantity model and solve typical problems.Describe the quantity discount model and solve typical problems.Describe reorder point models and solve typical problems.Describe situations in which the single-period model would be appropriate, and solve typical problems.
4Independent demand is uncertain. Dependent demand is certain. InventoryIndependent DemandAB(4)C(2)D(2)E(1)D(3)F(2)Dependent DemandIndependent demand is uncertain. Dependent demand is certain.Inventory: a stock or store of goods
5Inventory ModelsIndependent demand: finished goods, items that are ready to be soldE.g. a computerDependent demand: components of finished productsE.g. parts that make up the computer
6Types of Inventories Raw materials and purchased parts Partially completed goods called work-in-process (WIP)Finished-goods inventories(manufacturing firms) or merchandise (retail stores)
7Types of Inventories Replacement parts, tools, and supplies Goods-in-transit to warehouses or customers
8Functions of Inventory To meet anticipated demandTo smooth production requirementsTo decouple operationsTo protect against stockouts
9Functions of Inventory To take advantage of order cyclesTo help hedge against price increasesTo permit operationsTo take advantage of quantity discounts
10Objectives of Inventory Control To achieve satisfactory levels of customer service while keeping inventory costs within reasonable boundsLevel of customer serviceCosts of ordering and carrying inventoryInventory turnover is the ratio of the annual cost of goods sold to the average inventory investment.
11Effective Inventory Management A system to keep track of inventoryA reliable forecast of demandKnowledge of lead timesReasonable estimates ofHolding costsOrdering costsShortage costsA classification system
12Inventory Counting Systems Periodic SystemPhysical count of items made at periodic intervalsPerpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item
13Inventory Counting Systems Two-bin system: Two containers of inventory; reorder when the first is emptyUniversal Product Code (UPC): Bar code printed on a label that has information about the item to which it is attachedRadio Frequency Identification(RFID) Tags
14Key Inventory TermsLead time: time interval between ordering and receiving the orderHolding (carrying) costs: cost to carry an item in inventory for a length of time, usually a yearOrdering costs: costs of ordering and receiving inventoryShortage costs: costs when demand exceeds supply of inventory
15ABC Classification System Figure 12.1Classifying inventory according to some measure of importance and allocating control efforts accordingly.A - very importantB - moderately importantC - least importantAnnual$ valueof itemsABCHighLowPercentage of Items
16Cycle Counting A physical count of items in inventory Cycle counting managementHow much accuracy is needed?When should cycle counting be performed?Who should do it?
17Economic Order Quantity Models Economic order quantity (EOQ) modelThe order size that minimizes total annual costEconomic production modelQuantity discount model
18Assumptions of EOQ Model Only one product is involvedAnnual demand requirements knownDemand is even throughout the yearLead time does not varyEach order is received in a single deliveryThere are no quantity discounts
19Profile of Inventory Level Over Time The Inventory CycleFigure 12.2Profile of Inventory Level Over TimeQuantityon handQReceiveorderPlaceLead timeReorderpointUsagerateTime
20Total Cost Annual carrying cost Annual ordering cost Total cost = + Q 2HDS+TC =Q = Order quantity in unitsH = Holding (carrying) cost per unitD = Demand, usually in units per yearS = Ordering cost
21Cost Minimization Goal Figure 12.4CThe Total-Cost Curve is U-ShapedAnnual CostOrdering CostsOrder Quantity (Q)QO(optimal order quantity)
22Deriving the EOQUsing calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
23Minimum Total CostThe total cost curve reaches its minimum where the carrying and ordering costs are equal.Q2HDS=Q
24Economic Production Quantity (EPQ) Production done in batches or lotsCapacity to produce a part exceeds the part’s usage or demand rateAssumptions of EPQ are similar to EOQ except orders are received incrementally during production
25Economic Production Quantity Assumptions Only one item is involvedAnnual demand is knownUsage rate is constantUsage occurs continuallyProduction rate is constantLead time does not varyNo quantity discounts
26Economic Run Size Q0 = Order quantity in units H = Holding (carrying) cost per unitD = Demand, usually in units per yearS = Ordering costp = Production or delivery rateu = Usage rate
27Total Costs with Purchasing Cost AnnualcarryingcostPurchasingTC =+Q2HDSorderingPD
28Total Costs with PD Figure 12.7 Cost EOQTC with PDTC without PDPDQuantityAdding purchasing cost doesn’t change EOQ
29Total Cost with Constant Carrying Costs OCEOQQuantityTotal CostTCaTCcTCbDecreasingPriceCC a,b,cFigure 12.9A
30When to Reorder with EOQ Ordering Reorder Point: When the quantity on hand of an item drops to this amount, the item is reorderedSafety Stock: Stock that is held in excess of expected demand due to variable demand rate and/or lead timeService Level: Probability that demand will not exceed supply during lead time
31Determinants of the Reorder Point The rate of demandThe lead timeDemand and/or lead time variabilityStockout risk (safety stock)
32Reorder PointIf demand and lead time are both constant, the reorder point is simplyROP = d X LTWhered = Demand rate (units per day or week)LT = Lead times in days or weeks
33Safety Stock Figure 12.12 Quantity Maximum probable demand LTTimeExpected demandduring lead timeMaximum probable demandROPQuantitySafety stockSafety stock reduces risk ofstockout during lead time
34Reorder Point Figure 12.13 The ROP based on a normal Risk ofa stockoutService levelProbability ofno stockoutExpecteddemandSafetystockzQuantityz-scaleThe ROP based on a normaldistribution of lead time demand
35Fixed-Order-Interval Model Orders are placed at fixed time intervalsOrder quantity for next interval?Suppliers might encourage fixed intervalsMay require only periodic checks of inventory levelsRisk of stockoutFill rate: the percentage of demand filled by the stock on hand
36Fixed-Interval Benefits Tight control of inventory itemsItems from same supplier may yield savings in:OrderingPackingShipping costsMay be practical when inventories cannot be closely monitored
37Fixed-Interval Disadvantages Requires a larger safety stock for given risk of stockoutIncreases carrying costCosts of periodic reviews
38Single Period ModelSingle period model: model for ordering of perishables and other items with limited useful livesShortage cost: unrealized profits per unit (generally)Excess cost: difference between purchase cost and salvage value of items left over at the end of a period
39Single Period Model Continuous stocking levels Identifies optimal stocking levelsOptimal stocking level balances unit shortage and excess costDiscrete stocking levelsService levels are discrete rather than continuousDesired service level is matched or exceeded
40Optimal Stocking Level Figure 12.16Service level =CsCs + CeCs = Shortage cost per unit Ce = Excess cost per unitCeCsService LevelQuantitySoBalance point
41Example 15 Ce = $0.20 per unit Cs = $0.60 per unit Service level = Cs/(Cs+Ce) = .6/(.6+.2)Service level = .75Service Level = 75%QuantityCeCsStockout risk = 1.00 – 0.75 = 0.25
42Operations Strategy Too much inventory Wise strategy Tends to hide problemsEasier to live with problems than to eliminate themCostly to maintainWise strategyReduce lot sizesReduce safety stockAccurate and up-to-date inventory records