2 C 11 Inventory Management Pencils, papers, clips, advertisements-flyer, visiting cards, nuts, bolts, trucks, needles, airplanesRaw materials, semi-finished goods, finished goodsWhat is the worth?Let top management see the money withheld
3 Inventory- a stock or store of goods Independent DemandB(4)E(1)D(2)C(2)F(2)D(3)ADependent DemandIndependent demand is uncertain. Dependent demand is certain.
4 Inventory 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
5 Types of Inventories Raw materials & purchased parts Partially completed goods called work in progressFinished-goods inventoriesmanufacturing firmsretail stores (merchandise )Replacement parts, tools, & suppliesGoods-in-transit to warehouses or customers
6 Functions of Inventory To meet anticipated demandAnticipation stockTo smooth production requirementsSeasonal demand (e.g. Potato case!)To decouple operationsBuffer for continuous operationTo protect against stock-outsDelayed delivery, abrupt demandSafety stocks
7 Functions of Inventory … To take advantage of order cyclesPurchasing, Producing in Batches (Lots)Cycle stock for periodicTo help hedge against price increasesOil priceTo permit operationsIntermediate Stocks (WIP)Pipeline inventoryTo take advantage of quantity discounts
8 Objective 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 turnoverRatio of average cost of goods sold to average inventory investment.Days of inventory on hand
9 Effective Inventory Management A system to keep track of inventory (and S.O.)A reliable forecast of demandKnowledge of lead times (and variability)Reasonable estimates ofHolding costsOrdering costsShortage costsA classification system
10 Inventory Counting Systems Periodic SystemPhysical count of items made at periodic intervalsSmall Retailers- checks and orders replenishmentPerpetual Inventory SystemKeeps track of removals from inventory continuously, thus monitoring current levels of each itemReorder point QAlso requires periodic countingErrors, pilferage, spoliageCost?
11 Inventory Counting Systems … Two-Bin System - Two containers of inventory; reorder when the first is empty2nd cart has enough inventory for the lead timeOrder cardUniversal Bar Code - Bar code printed on a label that has information about the item to which it is attached
12 Key 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
13 The Inventory Cycle- Figure 12.2 Profile of Inventory Level Over Time QUsagerateQuantityon handReorderpointTimeReceiveorderPlaceorderReceiveorderPlaceorderReceiveorderLead time
14 ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly.A - very importantB - mod. importantC - least importantAnnual$ valueof itemsABCHighLowPercentage of ItemsExample 1- P 549
15 Cycle 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?
16 Economic Order Quantity Models Economic order quantity (EOQ) modelThe order size that minimizes total annual costEconomic production modelQuantity discount model
17 Total Cost* Annual carrying cost Annual ordering cost Total cost* = + Q2HDS+TC =
18 Cost Minimization Goal- Figure 12.4C The Total-Cost Curve is U-ShapedAnnual CostOrdering CostsOrder Quantity (Q)QO(optimal order quantity)Minimum Total Cost
19 Only one product is involved Annual demand requirements knownDemand is even throughout the yearLead time does not varyEach order is received in a single deliveryThere are no quantity discountsAssumptions of EOQ Model
20 Deriving the EOQUsing calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.Minimum Total CostThe total cost curve reaches its minimum where the carrying and ordering costs are equal.Q2HDS=
21 Economic Production Quantity (EPQ) Production done in batches or lotsCapacity to produce a part exceeds the part’s usage or demand rateSimilar to EOQOrders are received incrementally during productionAssumptionsOnly one item is involvedAnnual demand is knownUsage rate is constantUsage occurs continuallyProduction rate is constantLead time does not varyNo quantity discounts
22 Economic Run Size We do not buy the product. We produce it. Total demand / year is DDemand / day or consumption rate is uProduction rate is p / day
24 EPQ: Incremental Replenishment (Production and Consumption) p-uDemand / day or consumption rate is uProduction rate is p / dayu × ( number of working days ) = D = Total demand per year
25 EPQ: Ordering Cost and Carrying Cost State Imax in terms of Q!
26 EPQ : Production & Consumption; rate & time How much do we produce each time? QHow long does it take to produce Q? d1What is our production rate per day? pHow long does it take to consume Q? d1 +d2What is our consumption rate per day ? up-uuI maxd1d2
27 Example- What is the optimal production size? A toy manufacturerUses parts for one of its products.Consumption rate is uniform throughout the year.Working days are 240 / year.The firm can produce at a rate of 800 parts / dayCarrying cost is $1 / part / yearSetup cost for production run is $45 / setup
28 What is Run Time, What is Cycle Time Q0 using formula = 2400u = /240 = 200 units/dayp-uuI maxd1d2
31 Reorder Point- ROP Reorder Point When the quantity on hand of an item drops to this amount, the item is reorderedIf setup time takes 2 days, at which level of inventory we should start setup?2(200) = 400200 ?
32 Yet Another ExampleA company has a yearly demand of 120,000 boxes of its product. The product can be produced at a rate of 2000 boxes per day. The shop operates 240 days per year. Assume that demand is uniform throughout the year. Setup cost is $8000 for a run, and holding cost is $10 per box per year.a) What is the demand rate per dayb) What is the Economic Production Quantity (EPQ)c) What is the run timed) What is the maximum inventorye) What is the total cost of the system
33 Yet Another Example … =16000 What is the demand rate per day Demand per year is 120,000 there are 240 days per yearDemand per day = /240 = 500u = D/240 = 500b) What is the Economic Production Quantity (EPQ)=16000
34 Yet Another Example … c) What is the run time We produce unitsOur production rate is 2000 per dayIt takes 16000/2000 = 8 daysd1 = EPQ/p = 8 daysd) What is the maximum inventoryWe produce for 8 days. Each day we produce 2000 units and we consume 500 units of it. Therefore we add to our inventory at rate of 1500 per day for 8 days. That isImax = 8(1500) = 12000Imax = pd1 = 8(1500) = 12000
35 Yet Another Example …e) What is the total cost of the system
36 Including the Purchasing Cost AnnualcarryingcostPurchasingTC =+Q2HDSorderingPDIncluding the Purchasing Cost
37 Total Costs with Vs. Quantity Ordered EOQTC with PDTC without PDPDQuantityAdding Purchasing cost doesn’t change EOQ
38 Total Cost with Constant Carrying Costs OCEOQQuantityTotal CostTCaTCcTCbDecreasingPriceCC a,b,c
39 Total Cost with Variable Carrying Costs Do the MathEx 5, 6Total Cost with Variable Carrying Costs
40 ROP with EOQ Ordering Safety Stock Service Level When to ReorderSafety StockStock that is held in excess of expected demand due to variable demand rate and/or lead time.Service LevelProbability that demand will not exceed supply during lead time.
41 Determinants of the Reorder Point The rate of demandThe lead timeDemand and/or lead time variabilityStockout risk (safety stock)
42 Safety Stock- Figure 12.12 Quantity Maximum probable demand LTTimeExpected demandduring lead timeMaximum probable demandROPQuantitySafety stockSafety stock reduces risk ofstockout during lead time
43 Reorder Point- Figure 12.13 The ROP based on a normal See also: Fig 11.14The ROP based on a normalDistribution of lead time demandService levelRisk ofa stockoutProbability ofno stockoutROPQuantityExpecteddemandSafetystockzz-scaleROPs = Exp. Demand + z. σdLT
44 Shortage and Service Level Service level determines ROPE(n) = E(z) z σdLTE(n) = Expected number of short/cycleE(z) = Standardized number of units-short from table 11.3σdLT = Standard deviation of lead timeExample Page 568
45 Fixed-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
47 Fixed-Interval tradeoffs BenefitsTight control of inventory itemsItems from same supplier may yield savings in:OrderingPackingShipping costsMay be practical when inventories cannot be closely monitoredDisadvantagesRequires a larger safety stockIncreases carrying costCosts of periodic reviews
48 Single Period Model Model for ordering items with limited useful lives PerishablesShortage cost is generally the unrealized profits per unitExcess cost is the difference between purchase cost and salvage value of items left over at the end of a periodContinuous stocking levelsIdentifies optimal stocking levelsOptimal stocking level balances unit shortage and excess costDiscrete stocking levelsService levels are discrete rather than continuousDesired service level is equaled or exceeded
49 Optimal Stocking Level Service level =CsCs + CeCs = Shortage cost per unit Ce = Excess cost per unitService LevelSoQuantityCeCsBalance point
50 Example 15 Stockout risk = 1.00 – 0.75 = 0.25 Ce = $0.20 per unit Cs = $0.60 per unitService level = Cs/(Cs+Ce) = .6/(.6+.2)Service level = .75Service Level = 75%QuantityCeCsStockout risk = 1.00 – 0.75 = 0.25
51 Operations Strategy Too much inventory Wise strategy Tends to hide problemsEasier to live with problems than to eliminate themCostly to maintainWise strategyReduce lot sizesReduce safety stock
53 Learning ObjectivesDefine the term inventory and 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.
54 Learning 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.