Presentation on theme: "OPSM 501: Operations Management"— Presentation transcript:
1OPSM 501: Operations Management Koç University Graduate School of BusinessMBA ProgramOPSM 501: Operations ManagementWeek 11:The Newsvendor Problem-ways to avoid mismatchZeynep Aksin
2Hammer 3/2 timeline and economics Each suit sells for p = $180TEC charges c = $110 per suitDiscounted suits sell for v = $90The “too much/too little problem”:Order too much and inventory is left over at the end of the seasonOrder too little and sales are lost.Marketing’s forecast for sales is 3200 units.
3The demand-supply mismatch cost Definition – the demand supply mismatch cost includes the cost of left over inventory (the “too much” cost) plus the opportunity cost of lost sales (the “too little” cost):The maximum profit is the profit without any mismatch costs, i.e., every unit is sold and there are no lost sales:The mismatch cost can also be evaluated withMismatch cost = Maximum profit – Expected profit
4Revisit Example 3: Manufacturing cost=60TL, Selling price=80TL, Discounted price (at the end of the season)=50TLMarket research gave the following probability distribution for demand.Find the optimal q, expected number of units sold for this orders size, and expected profit, for this order size.Demand ProbabilityP(D<=n-1)0.10.30.50.70.80.9Cu=20 Co=10P(D<=n-1)<=20/30=0.66<=0.66q=800For q=800:E(units sold)=710E(profit)=13,300Max profit=20*770=15400
5When is the mismatch cost high? Hammer 3/2’s mismatch cost as a percentage of the maximum profit is $31,680/$223,440 = 14.2%Mismatch cost as a percent of the maximum profit increases as …(1) the coefficient of variability of demand increases(2) the critical ratio decreases
6Options to reduce the mismatch cost Make to orderReactive CapacityUnlimitedLimited
8Assemble-to-Order Model SuppliersConfigurationAssembly
9Unlimited, but expensive reactive capacity TEC charges a premium of 20% per unit ($132 vs. $110) in the second order.There are no restrictions imposed on the 2nd order quantity.O’Neill forecast of total season sales is nearly perfect after observing initial season sales.How many units should O’Neill order in October?12-9
10Revisit Example 2: Finding Cu and Co A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290.The demand for winter has a normal distribution with mean 32,500 and std dev 6750.How much should they order from China??
11Example 2: Finding Cu and Co A textile company in UK orders coats from China. They buy a coat from 250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at a discount price of 225€. When the demand is more than what they have in stock, they have an option of having emergency delivery of coats from Ireland, at a price of 290.The demand for winter has a normal distribution with mean 32,500 and std dev 6750.How much should they order from China??Cu=75-35=40Co=25F(z)=40/(40+25)=40/65=0.61z=0.28 q= *6750=34390
12Apply Newsvendor logic even with a 2nd order option The “too much cost” remains the same:Co = c – v = 110 – 90 =20.The “too little cost” changes:If the 1st order is too low, we cover the difference with the 2nd order.Hence, the 2nd order option prevents lost sales.So the cost of ordering too little per unit is no longer the gross margin, it is the premium we pay for units in the 2nd order.Cu = 132 – 110 = 22Critical ratio:Corresponding z-statistic F(0.05)=0.5199, F(0.06)=0.5239, so z = 0.06.
13Profit improvement due to the 2nd order option With a single ordering opportunity:Optimal order quantity = 4101 unitsExpected profit = $191,760Mismatch cost as % of revenue = 4.9%The maximum profit is unchanged = $223,440With a second order option:Optimal order quantity = 3263 unitsReduction in mismatch cost = 38% (19,774 vs 31,680)Mismatch cost as % of revenue = 3.1%
14Limited reactive capacity Units in the 2nd order are no more expensive than in the 1st orderBut there is limited capacity for a 2nd order
15Sample of wetsuits1st order must be at least 10,200 suits so that there is enough capacity for the 2nd order.Also a minimum order quantity-order onceWhat should we produce in the 1st order?
16Profit and mismatch with only 1 ordering opportunity Use the Newsvendor model to evaluate the optimal order quantity, expected profit, maximum profit and mismatch costA suits produced in the 1st order earns the Newsvendor profit but a suit produced in the 2nd order earns the maximum profit.12-16
17Produce “safer” products early, produce “risky” products with reactive capacity Sort items by their mismatch cost to order quantity ratio.Fill the 1st order up to the minimum quantity (10,200) with the items that have the lowest mismatch – quantity ratioThe mismatch cost is reduced by 66%!12-17
18Push-Pull Supply Chains The Supply Chain Time LinePush-Pull BoundaryPUSH STRATEGYPULL STRATEGYCustomersSuppliersLow UncertaintyHigh Uncertainty
19A new Supply Chain Paradigm A shift from a Push System...Production decisions are based on forecast…to a Push-Pull SystemParts inventory is replenished based on forecastsAssembly is based on accurate customer demand
20Demand Forecast The three principles of all forecasting techniques: Forecasts are always wrongThe longer the forecast horizon the worst is the forecastAggregate forecasts are more accurateThe Risk Pooling Concept
21Business models in the Book Industry From Push Systems...Barnes and Noble...To Pull SystemsAmazon.com,And, finally to Push-Pull SystemsAmazon.com, 1999-presentAround 40 warehouses
22Business models in the Grocery Industry From Push Systems...Supermarket supply chain...To Pull SystemsPeapod,Stock outs 8% to 10%And, finally to Push-Pull SystemsPeapod, 1999-presentDedicated warehousesStock outs less than 2%