Question

Problem: Taco Fast Food Chain’s Case

Martin Oritz, a purchasing manager of the True Taco fast food chain, was contacted by a salesperson of a food service company. The salesperson pointed out that the higher breakage rate was common in the shipment of most taco shells. Martin was aware of this fact, and noted that the chain usually experienced a 10% to 15% breakage rate. The salesperson then explained that his company recently had designed a new shipping container that reduced the breakage rate to less than 5%, and he produced the results of an independent test to support his claim. Martin asked about the price of the shipment. The salesperson said that his company charged $25 for a case of 500 taco shells. It is $1.25 more than True Taco currently was paying. But the salesperson claimed that the lower breakage rate more than compensated for the higher cost, offering a lower cost per usable taco shell than the current supplier. Martin, however, felt that he should try the new product on a limited basis and develop his own evidence. He decided to order a dozen cases and compare the breakage rate in these 12 cases with the next shipment of 18 cases from the current supplier. For each case received, Marin carefully counted the number of usable shells. The results of the usable shells are shown in the below table.

New Supplier	Current Supplier
468	444
474	449
474	443
479	440
482	439
478	448
467	441
469	434
484	427
470	446
463	452
468	442
	450
	444
	433
	441
	436
	429

Part 1

1. Run @RISK’s distribution fitting procedure on the given datasets using the Binomial distribution for both the new and the current supplier data respectively.

2. Show the correct @RISK –Fit Results window with the Binomial distribution that fits the data using the “Discrete Probability Distribution” graph and the “Cumulative Ascending” graph for both the new and the current supplier data respectively.

3. Find the Median (50th percentile), the 5th and the 95th percentile values, using the fit of the Binomial distribution, for both the new and the current supplier data respectively.

Part 2

The objective is to find the lowest expected cost per usable taco shell.

1. Use the probability of the median (50th percentile) assigned 63% as well as the 5th and 95th percentile probabilities assigned 18.5% each to construct a Decision Tree to compute the expected value for the two suppliers.

Note that your tree should include the following considerations if any.

Your resultant tree should have only TWO decision strategies that you can see their curves in the Cumulative Chart.

We use the negative sign (-) for the cost, the expenses, cash outflow, etc.

We use the positive sign (+) for the revenue, profit, cash inflow, etc.

In the model setting, under the calculation tab, you need to use payoff formula, which is the cost per case divided by the number of usable taco shells in a case.

2. Generate the risk profile for the decision tree. The risk profile only includes the Cumulative Chart.

3. Explain which optimal decision strategy should be chosen using the concepts of EMV and stochastic dominance.

Answer 1

a) cdf

New supplier:

     

                

                 = 468 + 474 +...........+ 468

                 = 5209.

Current supplier:

      F(x) = 444 + 449 +...............+429

             = 7938

Median:

For new supplier:

    There are 11 values.

      Median = 478

For current supplier, there are 18 values,

Median = 436.5

      

       = 1.

       

       = 19.