Hamptonshire Express Case Essay

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1. a. The simulation indicates that 584 is the optimum stocking quantity. Daily profit at this stocking quantity is $331.4346.
b. Using the newsvendor model, Cu = 1 - 0.2 = 0.8 and Co = .2. Cu /(Cu + Co) = .8.
Using the spreadsheet, we found Q* = NORM.INV(.8,500,100) = 584.16. The simulation and newsvendor model give the same optimal stocking quantity.

2. a. According to the simulation spreadsheet, 4 hours of investment in creation maximizes daily profit at $371.33.
b. Sheen would choose an effort level where the marginal benefit gained by the effort is equal to her marginal cost of expending the effort. To calculate the effort level, h, we equalize marginal cost and marginal benefit. Here (.8 * 50) / (2√h) = 10. Solving gives h = 4,
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4. a. The optimal stocking quantity is 409 according to the spreadsheet in the simulation, which is a decrease from 516 in problem #3 because in the event that the Express stocks out, Ralph still makes a profit from 40% of customers who will buy the Private. Therefore, because he makes more profit off of the Private, his risk decreases because of cost of understocking of the Express.
b. For problems #1 and #2 there were no profitable alternatives to understocking, whereas in problem #3, Ralph has a profitable alternative for understocking since 40% of customers will buy the Private. The different critical ratios from each problem produce a different optimal stocking quantity.
c. This decreases his optimal stocking quantity because Ralph is allocating $0.03 to the cost of each newspaper, making his cost of understocking now 1-.83-40%*.4=.01. Co=.83 Critical ratio 0.01/.83= 0.012 According to the data, the optimal stocking quantity is Q*=NORMINV(.012,500,100).

5. a. A lower buy-back price means a lower stocking quantity, because it affects the cost of overstocking. Ralph wants to stock a lower quantity in order to lower his risk of overstocking. The optimal buy-back price is $0.75, which gives a stocking quantity of 659 and channel profits of $369.80.
b. The optimal transfer price is $0.99, giving a buy-back price of $0.988, and channel profits of $372.62. However, this is an unrealistic scenario because Ralph’s profits are negative at -$24 and

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