Koç University Graduate School of Business MBA Program OPSM 501: Operations Management Week 11: The Newsvendor Problem-ways to avoid mismatch Zeynep Aksin email@example.com
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. • Marketing’s forecast for sales is 3200 units.
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
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 • 500 0.10 • 600 0.2 • 700 0.2 • 800 0.2 • 900 0.10 • 1000 0.10 • 1100 0.10 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
When 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
Options to reduce the mismatch cost • Make to order • Reactive Capacity • Unlimited • Limited
Make-to-Stock Model Suppliers Configuration Assembly
Assemble-to-Order Model Suppliers Configuration Assembly
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 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
Revisit 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??
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?? Cu=75-35=40 Co=25 F(z)=40/(40+25)=40/65=0.61z=0.28 q=32500+0.28*6750=34390
Apply 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 = 22 • Critical ratio: • Corresponding z-statistic F(0.05)=0.5199, F(0.06)=0.5239, so z = 0.06.
Profit improvement due to the 2nd 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%
Limited reactive capacity • Units in the 2nd order are no more expensive than in the 1st order • But there is limited capacity for a 2nd order
Sample of wetsuits • 1st order must be at least 10,200 suits so that there is enough capacity for the 2nd order. • Also a minimum order quantity-order once • What should we produce in the 1st order?
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 1st order earns the Newsvendor profit but a suit produced in the 2nd order earns the maximum profit. 12-16
Produce “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 ratio • The mismatch cost is reduced by 66%! 12-17
PUSH STRATEGY PULL STRATEGY High Uncertainty Low Uncertainty Push-Pull Boundary Push-Pull Supply Chains The Supply Chain Time Line Customers Suppliers
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
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
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
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%
Organizational Skills Needed Raw Material Customers Push Pull High Uncertainty Short Cycle Times Service Level Responsiveness Low Uncertainty Long Lead Times Cost Minimization Resource Allocation
O’Neill: quick response (reactive capacity) High Risk: Push-Pull Low Risk: Push Speculative Production capacity Reactive Production capacity Later orders Initial forecast
Announcement • Read the HP case for next week • We will analyze it in-class • Bring your laptops!