Chpt13 Inventory Handout

13-1Inventory ManagementCHAPTER13-2Inventory ManagementInventoryInventory A stock or store of goods Independent demand items Items that are ready to be sold or used 13InventoryManagementHomework problems # 3,4,8, 14,15,17, 24,26,36,37 on pp. 589-595.13-3Inventory ManagementIndependent vs. Dependent DemandIndependent Demandl When item’s demand is influenced by market conditions and isnot related to (i.e., is “independent” of) production decision forany other item.l Wholesale and retail merchandise (finished goods), serviceindustry inventory, end-item and replacement-part inventories,spare-parts, MRO (maintenance, repair, and operating) supplies.l Demand must be forecasted.13-4Inventory ManagementInventory: a stock or store of goods13-5Inventory ManagementTypes of Inventories Raw materials and purchased partsWork-in-processFinished goods inventories or merchandiseMaintenance and repairs (MRO) inventory, tools andsuppliesGoods-in-transit to warehouses or customers (pipelineinventory) e.g., DeLLDependent DemandAC(2)B(4)Dependent Demandl When item’s demand derives from (i.e., “depend” on) theproduction decisions for its parents.l All intermediate and purchased items in manufacturing.l Demand must be derived.D(2)13-6Independent DemandE(1)D(3)F(2)Inventory ManagementFunctions of Inventory Inventories serve a number of functions such as:1.2.3.4.5.To meet anticipated customer demandTo smooth production requirementsTo decouple operationsTo protect against stockoutsTo take advantage of order cycles7.To hedge against price increasesTo permit operations8.To take advantage of quantity discounts6.

13-7Inventory Management13-8Inventory Management Inventory ManagementEffective Inventory ManagementManagement has two basic functions concerninginventory:1.2.Establish a system for tracking items in inventoryMake decisions about How much to order? When to order? A system to keep track of inventory A reliable forecast of demand Knowledge of lead times Reasonable estimates of Holding costs 13-9Inventory ManagementPeriodic System Shortage costsForecasts Physical count of items in inventory made atperiodic intervalsInventories are necessary to satisfy customer demands, so it is importantto have a reliable estimates of the amount and timing of demand Lead time Point-of-sale (POS) systems System that keeps track of removals frominventory continuously, thus monitoring currentlevels of each item Two-bin system A classification systemDemand Forecast and Lead TimePerpetual (continuous) Inventory System Ordering costs13-10 Inventory ManagementInventory Tracking/Reviewing/Counting Systems Time interval between ordering and receiving the orderA system that electronically records actual salesSuch demand information is very useful for enhancing forecasting andinventory managementTwo containers of inventory; reorderwhen the first is empty13-11 Inventory Management13-12 Inventory ManagementABC Classification System A-B-C approach Classifying inventory according to some measure of importance,and allocating control efforts accordingly A items (very important) B items (moderately important) C items (least important) 50 to 60 percent of the numberof items in inventory but onlyabout 10 to 15 percent of theannual dollar valueHighAnnual valueof items Cycle counting Cycle counting management 10 to 20 percent of the number of items in inventory andabout 60 to 70 percent of the annual dollar value Who should do it?ACLowFewManyVolume of ItemsA physical count of items in inventoryHow much accuracy is needed? A items: 0.2 percent B items: 1 percent C items: 5 percentWhen should cycle counting be performed? BCycle Counting

13-13 Inventory ManagementHow Much to Order: EOQ Modelsorder quantity model Economicproduction model Skipdiscount model13-15 Inventory ManagementKey Inventory Terms Basic EOQ Model Economic Quantity 13-14 Inventory ManagementLead time: time interval between ordering andreceiving the orderHolding (carrying) costs: cost to carry an item ininventory for a length of time, usually a yearOrdering costs: costs of ordering and receivinginventoryShortage costs: costs when demand exceeds supplyThe basic EOQ model is used to find a fixed orderquantity that will minimize total annual inventory costsAssumptions Only one product is involved (at a time) Annual demand requirements are known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery (no partial delivery) There are no quantity discounts13-16 Inventory ManagementThe Inventory CycleProfile of Inventory Level Over TimeQUsagerateQuantityon TimeReceiveorderPlaceorderLead timeWhen order quantity is Q , how much is average inventory?13-17 Inventory ManagementLarge vs. Small orders13-18 Inventory ManagementTotal CostAnnualAnnualTotal cost carrying orderingcostcostTC QH2 DSQ

13-19 Inventory Management13-20 Inventory ManagementCost Minimization GoalDeriving the EOQAnnual CostThe Total-Cost Curve is U-ShapedUsing calculus, we take the derivative of the totalcost function and set the derivative (slope) equal tozero and solve for Q.QH2QOPT 2DS2(Annual Demand)(Or der or Setup Cost) HAnnual Holding CostOrdering Costs D SQQ O(optimal order quantity)Order Quantity (Q)How to find the optimal order quantity?13-21 Inventory ManagementMinimum Total CostThe total cost curve reaches its minimum wherethe carrying and ordering costs are equal.13-22 Inventory Management 13-23 Inventory ManagementEOQ SensitivityEOQ SensitivityWhat happens to optimal order quantity (and cycleinventory) if the demand rate increase?What happens to lot sizes if setup/ordering costsdecrease?What happens if interest rates drop?How critical are errors in estimating D, H, and S?Conclusion: EOQ is robust, insensitive to parameterestimation errors!13-24 Inventory ManagementEconomic Production Quantity (EPQ) Production done in batches or lotsCapacity to produce a part exceeds the part’susage or demand rateAssumptions of EPQ are similar to EOQ exceptorders are received incrementally duringproduction

13-25 Inventory ManagementEOQ with Quantity Discounts Total Costs with Quantity DiscountsObjectives: 13-26 Inventory ManagementConsider tradeoffs between discount benefits and increasesin holding costsThe introduction of quantity discounts will cause theoptimum order quantity to be unchanged or greater.Types of Discounts: AnnualAnnualTC carrying ordering PurchasingcostcostcostTC All-units:Increment:13-27 Inventory ManagementTotal Costs with constant PDQH2 DSQ PD13-28 Inventory ManagementTotal Costs with Variable PDconstant13-29 Inventory ManagementEOQ with Quantity Discounts Two-Step Procedure Step 1. Beginning with lowest price, calculate the EOQfor each price level until a feasible EOQ is found. It isfeasible if it lies in the range corresponding to its price.Step 2. If the first feasible EOQ found is for the lowestprice level, this quantity is best. Otherwise, calculatethe total cost for the first feasible EOQ and for the pricebreak quantity at each lower price level. The quantitywith the lowest total cost is optimal.13-30 Inventory ManagementQuantity Discounts ExampleExample. Assume that the following quantity discount schedule isprovided by a supplier:Order size0 49Discount0%Unit cost 30.0050 99100 or more5%10% 28.50 27.00If annual demand is 120 units, ordering cost is 20 per order, andannual unit inventory holding cost is 25%, what order quantitywould minimize total inventory costs?

13-31 Inventory ManagementWhen to Reorder with EOQ Ordering Reorder Point - When the quantity on hand of anitem drops to this amount, the item is reorderedSafety Stock - Stock that is held in excess ofexpected demand due to variable demand rateand/or lead time.Service Level - Probability that demand will notexceed supply during lead time.13-33 Inventory ManagementDeterminants of the Reorder PointThe rate of demandThe lead time Demand and/or lead time variability Stockout risk (safety stock) Example:13-34 Inventory ManagementSafety StockFigure 13.1213-35 Inventory Management13-32 Inventory ManagementReorder PointReorder PointThe ROP is based on a Normaldistribution of lead time demandFigure 13.1313-36 Inventory ManagementFigure 13.14Reorder Point ModelsuVariable demand and constant lead timeROP 𝑑 LT Z 𝜎 𝐿𝑇duConstant demand and variable lead timeROP 𝑑 𝐿𝑇 Z d 𝜎LTuVariable demand and variable lead time&ROP 𝑑 𝐿𝑇 Z 𝐿𝑇 𝜎𝑑& 𝑑 𝜎𝐿𝑇 &

13-37 Inventory ManagementReorder Point ExampleThe injection molding department of a company uses 40 ponds ofa powder a day. Inventory is reordered when the amount on handis 240 pounds. Lead time averages five days. It is normallydistributed and has a standard deviation of two days.a). What is the probability of a stockout during lead time?13-38 Inventory ManagementFixed-order-interval (FOI) model Orders are placed at fixed time intervalsReasons for using the FOI model: Supplier’s policy may encourage its use May require only periodic checks of inventory levele.g., grocery stores, small shopsb). What reorder point would provide a 5% stockout? 13-39 Inventory ManagementFixed-Interval Benefits 13-40 Inventory ManagementFixed-order-interval Model (Figure 13-15)Tight control of inventory itemsItems from same supplier can be combined and mayyield savings in: Ordering Packing Shipping costsMay be practical when inventories cannot be closelymonitoredNote:13-41 Inventory ManagementFixed-order-interval Model Compare P and Q systems in terms of order quantity,reorder point, order interval (time between order)order quantityreorder point13-42 Inventory ManagementFixed-Interval Benefits order intervalQ systemP system Grouping orders from the same supplier canproduce savings in shipping costsSome circumstances do not lend themselves tocontinuously monitoring inventory positionWhen both demand and lead time are constant, P and Qsystems function identically. Tight control of inventory itemsItems from same supplier may yield savings in: Ordering Packing Shipping costsMay be practical when inventories cannot beclosely monitored

13-43 Inventory ManagementFixed-Interval Disadvantages13-44 Inventory ManagementFixed-order-interval order quantityAmount to order(target Inventory) Requires a larger safety stock Increases carrying cost Costs of periodic reviews ? WhereOI order (review) intervalA inventory on hand at reorder time13-45 Inventory Management13-46 Inventory ManagementFOI ExampleSingle Period Model Single period model: model for ordering of perishablesand other items with limited useful lives Shortage cost: generally the unrealized profits per unit Excess cost: difference between purchase cost andsalvage value of items left over at the end of a periodCs Ce 13-47 Inventory Management13-48 Inventory ManagementSingle Period Model ExampleStocking LevelsCe CsService levelQuantitySoBalance PointService level S o OptimumStocking QuantityCsC s CewhereCs shortage cost per unitSoCe excess cost per unitOptimal stocking point Great Farmer’s Market buys organic mixed salad for 2.00 perpound and sells it for 4.20 per pound. At the end of each week,any remaining mixed salad is sold to a producer of canned soupfor 0.6 per pound. Weekly demand can be approximately by anormal distribution with a mean of 100 pounds and a standarddeviation of 10 pounds. What is the optimal stocking level?

13-49 Inventory Management13-50 Inventory ManagementOperations StrategyAreas under the standard normal curve, from - to z- 0 Too much inventory Tends to hide problems Easier to live with problems than to eliminatethem Costly to maintainWise strategy Reduce lot sizes Reduce safety stock

13-13 Inventory Management Economic order quantity model Economic production model Quantity discount model How Much to Order: EOQ Models Skip 13-14 Inventory Management Basic EOQ Model The basic EOQ model is used to find a fixed order quantity that will minimize total annual inventory costs