2Learning ObjectivesDiscuss the role of information technology in managing inventories.Describe the functions and costs of an inventory system.Determine the order quantity.Determine the reorder point and safety stock for inventory systems with uncertain demand.Design a continuous or periodic review inventory-control system.Conduct an ABC analysis of inventory items.Determine the order quantity for the single-period inventory case.Describe the rationale behind the retail discounting model.
3Role of Inventory in Services Decoupling inventoriesSeasonal inventoriesSpeculative inventoriesCyclical inventoriesIn-transit inventoriesSafety stocks
4Considerations in Inventory Systems Type of customer demandPlanning time horizonReplenishment lead timeConstraints and relevant costs
5Relevant Inventory Costs Ordering costsReceiving and inspections costsHolding or carrying costsShortage costs
6Inventory Management Questions What should be the order quantity (Q)?When should an order be placed, called a reorder point (ROP)?How much safety stock (SS) should be maintained?
7Inventory Models Economic Order Quantity (EOQ) Special Inventory Models With Quantity Discounts Planned ShortagesDemand Uncertainty - Safety StocksInventory Control Systems Continuous-Review (Q,r) Periodic-Review (order-up-to)Single Period Inventory Model
8Inventory Levels For EOQ Model Units on HandQQTimeD
10EOQ FormulaNotation D = demand in units per year H = holding cost in dollars/unit/year S = cost of placing an order in dollars Q = order quantity in unitsTotal Annual Cost for Purchase LotsEOQ
11Annual Costs for Quantity Discount Model 22,000210002000020001000C = $20.00C = $19.50C = $18.75Annual Cost, $Order quantity, Q
12Inventory Levels For Planned Shortages Model Q-KQTIME-KT1T2T
13Formulas for Special Models Quantity Discount Total Cost ModelModel with Planned Shortages
14Values for Q* and K* as A Function of Backorder Cost B Q* K* Inventory LevelsundefinedQ*
15Demand During Lead Time Example +++=u=3u=3u=3u=3ROPs sFour Days Lead TimeDemand During Lead time
16Safety Stock (SS)Demand During Lead Time (LT) has Normal Distribution with - -SS with r% service levelReorder Point
17Continuous Review System (Q,r) Amount used during first lead timeInventory on handEOQReorder point, ROPOrder quantity, EOQd3Average lead time usage, dLd1d2EOQSafety stock, SSFirst leadtime, LT1LT2LT3TimeOrder 1 placedOrder 2 placedOrder 3 placedShipment 1 receivedShipment 2 receivedShipment 3 received
18Periodic Review System (order-up-to) Inventory on HandReview periodRPRPRPTarget inventory level, TILFirst order quantity, Q1Q2Q3d3Amount used duringfirst lead timed1d2Safety stock, SSFirst lead time, LT1LT2LT3TimeOrder 1 placedOrder 2 placedOrder 3 placedShipment 1 receivedShipment 2 receivedShipment 3 received
19Inventory Control Systems Continuous Review SystemPeriodic Review System
21Inventory Items Listed in Descending Order of Dollar Volume Monthly Percent ofUnit cost Sales Dollar Dollar Percent ofInventory Item ($) (units) Volume ($) Volume SKUs ClassComputers , AEntertainment center ,000Television sets ,000Refrigerators , BMonitors ,000Stereos ,000Cameras ,000Software , CComputer disks ,000CDs ,000Totals ,
22Single Period Inventory Model Newsvendor Problem Example D = newspapers demandedp(D) = probability of demandQ = newspapers stockedP = selling price of newspaper, $10C = cost of newspaper, $4S = salvage value of newspaper, $2Cu = unit contribution: P-C = $6Co = unit loss: C-S = $2
23Single Period Inventory Model Expected Value Analysis Stock Qp(D) DExpected Profit $ $ $ $ $35.33
24Single Period Inventory Model Incremental Analysis E (revenue on last sale) E (loss on last sale)P ( revenue) (unit revenue) P (loss) (unit loss)(Critical Fractile)where:Cu = unit contribution from newspaper sale ( opportunity cost of underestimating demand)Co = unit loss from not selling newspaper (cost of overestimating demand)D = demandQ = newspaper stocked
25Critical fractile for the newsvendor problem P(D<Q)(Co applies)P(D>Q)(Cu applies)0.722
26Retail Discounting Model S = current selling priceD = discount priceP = profit margin on cost (% markup as decimal)Y = average number of years to sell entire stock of “dogs” at current price (total years to clear stock divided by 2)N = inventory turns (number of times stock turns in one year)Loss per item = Gain from revenueS – D = D(PNY)
27Topics for DiscussionDiscuss the functions of inventory for different organizations in the supply chain.How would one find values for inventory costs?How can information technology create a competitive advantage through inventory management?How valid are the assumptions for the EOQ model?How is a service level determined for inventory items?What inventory model would apply to service capacity such as seats on an aircraft?
28Interactive ExerciseThe class engages in an estimation of the cost of a 12-ounce serving of Coke in various situations (e.g., supermarket, convenience store, fast-food restaurant, sit-down restaurant, and ballpark). What explains the differences?