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OPSM 501: Operations Management Week 11: The Newsvendor Problem-ways to avoid mismatch Koç University Graduate School of Business MBA Program Zeynep Aksin zaksin@ku.edu.tr

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Hammer 3/2 timeline and economics Economics: Each suit sells for p = $180 TEC charges c = $110 per suit Discounted suits sell for v = $90 The too much/too little problem: –Order too much and inventory is left over at the end of the season –Order too little and sales are lost. Marketings forecast for sales is 3200 units.

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The 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 with Mismatch cost = Maximum profit – Expected profit

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Revisit Example 3: Manufacturing cost=60TL, Selling price=80TL, Discounted price (at the end of the season)=50TL Market 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 Probability 5000.10 6000.2 7000.2 8000.2 9000.10 10000.10 11000.10 P(D<=n-1) 0 0.1 0.3 0.5 0.7 0.8 0.9 Cu=20 Co=10 P(D<=n-1)<=20/30=0.66 <=0.66 q=800 For q=800: E(units sold)=710 E(profit)=13,300 Max profit=20*770=15400

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When is the mismatch cost high? Hammer 3/2s 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

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Options to reduce the mismatch cost Make to order Reactive Capacity –Unlimited –Limited

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7 Make-to-Stock Model Configuration Assembly Suppliers

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8 Assemble-to-Order Model Configuration Assembly Suppliers

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Unlimited, 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 2 nd order quantity. ONeill forecast of total season sales is nearly perfect after observing initial season sales. How many units should ONeill order in October? 12-9

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Revisit Example 2: Finding C u and C o 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??

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Example 2: Finding C u and C o 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=40 Co=25 F(z)=40/(40+25)=40/65=0.61 z=0.28 q=32500+0.28*6750=34390

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Apply Newsvendor logic even with a 2 nd order option The too much cost remains the same: –C o = c – v = 110 – 90 =20. The too little cost changes: –If the 1 st order is too low, we cover the difference with the 2 nd order. –Hence, the 2 nd 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 2 nd order. C u = 132 – 110 = 22 Critical ratio: Corresponding z-statistic (0.05)=0.5199, (0.06)=0.5239, so z = 0.06.

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Profit improvement due to the 2 nd order option With a single ordering opportunity: –Optimal order quantity = 4101 units –Expected profit = $191,760 –Mismatch cost as % of revenue = 4.9% The maximum profit is unchanged = $223,440 With a second order option: –Optimal order quantity = 3263 units –Reduction in mismatch cost = 38% (19,774 vs 31,680) –Mismatch cost as % of revenue = 3.1%

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Limited reactive capacity Units in the 2 nd order are no more expensive than in the 1 st order But there is limited capacity for a 2 nd order

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Sample of wetsuits 1 st order must be at least 10,200 suits so that there is enough capacity for the 2 nd order. Also a minimum order quantity-order once What should we produce in the 1 st order?

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Profit and mismatch with only 1 ordering opportunity Use the Newsvendor model to evaluate the optimal order quantity, expected profit, maximum profit and mismatch cost A suits produced in the 1 st order earns the Newsvendor profit but a suit produced in the 2 nd order earns the maximum profit. 12-16

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Produce safer products early, produce risky products with reactive capacity Sort items by their mismatch cost to order quantity ratio. Fill the 1 st order up to the minimum quantity (10,200) with the items that have the lowest mismatch – quantity ratio The mismatch cost is reduced by 66%! 12-17

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18 Push-Pull Supply Chains Push-Pull Boundary PUSH STRATEGYPULL STRATEGY Low Uncertainty High Uncertainty The Supply Chain Time Line Customers Suppliers

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19 A new Supply Chain Paradigm A shift from a Push System... –Production decisions are based on forecast …to a Push-Pull System –Parts inventory is replenished based on forecasts –Assembly is based on accurate customer demand

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20 Demand Forecast The three principles of all forecasting techniques: –Forecasts are always wrong –The longer the forecast horizon the worst is the forecast –Aggregate forecasts are more accurate The Risk Pooling Concept

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21 Business models in the Book Industry From Push Systems... –Barnes and Noble...To Pull Systems –Amazon.com, 1996-1999 And, finally to Push-Pull Systems –Amazon.com, 1999-present Around 40 warehouses

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22 Business models in the Grocery Industry From Push Systems... –Supermarket supply chain...To Pull Systems –Peapod, 1989-1999 Stock outs 8% to 10% And, finally to Push-Pull Systems –Peapod, 1999-present Dedicated warehouses Stock outs less than 2%

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23 Locating the Push-Pull Boundary

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24 Organizational Skills Needed Raw Material Customers Pull Push Low Uncertainty Long Lead Times Cost Minimization Resource Allocation High Uncertainty Short Cycle Times Service Level Responsiveness

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25 Speculative Production capacity Reactive Production capacity Initial forecast Later orders Low Risk: Push High Risk: Push-Pull ONeill: quick response (reactive capacity)

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Announcement Read the HP case for next week We will analyze it in-class Bring your laptops!

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