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**Chapter 12 Assemble-to-Order, Make-to-Order, and Quick Response with Reactive Capacity**

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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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**When is the mismatch cost cost high?**

Mismatch cost as a percent of the maximum profit where f(z) = density function of the Normal distribution (In Excel f(z)=normdist(z,0,1,0)) Hammer 3/2’s mismatch cost as a percentage of the maximum profit is The mismatch cost is high when (f(z) / F(z)) and (s / m) are high.

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**Low critical ratios - high mismatch costs**

The mismatch cost is high when (f(z) / F(z)) is high … … (f(z) / F(z)) is high when the critical ratio is low:

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**High demand uncertainty - high mismatch costs**

The mismatch cost is high when the coefficient of variation, s/m, is high. The coefficient of variation is the right measure of demand uncertainty: The probability demand is within 20% of the forecast demand depends on the coefficient of variation (COV) and not the standard deviation:

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**Find your product’s mismatch cost (as % of maximum profit) …**

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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 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?

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**Apply Newsvendor logic even with a 2nd order option**

“Too much cost” “Too little cost” Critical ratio: Corresponding z-statistic Order quantity

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**Profit improvement due to the 2nd order option**

With a single ordering opportunity: Optimal order quantity Expected profit Mismatch cost as % of revenue The maximum profit is unchanged With a second order option: Reduction in mismatch cost

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**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

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

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12.12 Office Supply Company has a spare parts warehouse in Alaska to support its office equipment maintenance needs. Once every six months, a major replenishment shipment is received. If the inventory of any given part runs out before the next replenishment, then emergency air shipments are used to resupply the part as needed. Orders are placed on March 17 and September 17, and orders are received on April 17 and October 17 respectively. OSC must determine replenishment quantities for its spare parts. As an example, historical data show that total demand for part 1AA-66 over a six month interval is Poisson with mean 6.5. The cost of inventorying the unneeded part for six months is $5 (which includes both physical and financial holding costs and is charged based on inventory at the end of the six month period.) The variable production cost for 1AA-66 is $37 per part. The cost of a regular, semiannual shipment is $32 per part and the cost of an emergency shipment is $50 per part. It is March 17, and there are currently three 1AA-66 parts in inventory. How many parts should arrive on April 17?

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12.6 Marisol is considering a “Pick Your Minutes” calling plan where she would specify a quantity of minutes, say x, per month that she would buy at 5 cents per. If her usage is less than x, she loses the minutes and if her usage is over x, she pays 40 cents per. The same rates apply whether the call is local or long distance. Once she signs the contract, she cannot change the number of minutes specified for a year. Marisol estimates that her monthly needs are best approximated by the normal distribution, with a mean of 250 minutes and a standard deviation of 24 minutes. Sure she does. If she chooses the “Pick Your Minutes” plan, for how many should she contract? Instead she chooses to contract for 240 minutes. How much does she expect to pay at 40 cents per minute? A friend advises her to contract for 280 minutes to limit her 40 cents per minute outlay. Under this contract, how many minutes does she expect to waste? If she contracts for 260 minutes, what’s her expected cell phone bill?

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Simulation Chapter 16 of Quantitative Methods for Business, by Anderson, Sweeney and Williams Read sections 16.1, 16.2, 16.3, 16.4, and Appendix 16.1.

Simulation Chapter 16 of Quantitative Methods for Business, by Anderson, Sweeney and Williams Read sections 16.1, 16.2, 16.3, 16.4, and Appendix 16.1.

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