Hamptonshire Express

Problem #1

One of the ways to find the optimal ordering quantity is to use sensitivity analysis in "Hamptonshire Express: Problem 1" model by substituting numbers into the model to examine the relationships between ordering quantity and profit. Since the daily demand of Express is normally distributed, we entered different numbers for the stocking quantities from 200 (μ-3×σ=200 ), and incrementing the quantities with 50 each time up to 800 (μ+3×σ=800) to see how profit would change in relation to stocking quantities. We can therefore plot a graph show in Exhibit 1. As show in the graph, the optimal stocking quantity occurs between 550 and 600. We then examined each numbers in the range to see which one maximizes the profit, which is $331.44 with the optimal ordering quantity to be 584.

Another way to acquire the optimal stocking quantity is to use the add-in Solver function provided in Excel. By changing the stocking quantity, solver can find the optimal number where the profit is maximized. Since it is more efficient to use Solver in excel than sensitivity analysis. We will use Solver, if applicable, as the mean to find the optimized configuration for each question in this paper.

We substitute the numbers into the newsvendor formula: where Cu is the marginal benefit (price of one newspaper - printing cost/ copy = 0.8) and Co is the marginal cost (printing cost/ copy = 0.2). We can therefore find the optimal stocking quantity, 584 which is consistent with the number derived from "Hamptonshire Express: Problem 1".

Problem #2

By trying different values for h (from 0 to 15) in the spreadsheet "Hamptonshire Express： Problem #2", we can get that when Sheen invests 4 hours daily in the creation of the profile section, she can get the highest expected profit $371.33 and the optimal stocking quantity is 685. Exhibit 2 shows the relationship between the number of hours invested in the profile and Sheen's expected return. We can also easily and quickly get the answer by using the tool "Solver" in Excel. The optimal stocking quantity 685 is calculated based on the newsvendor formula. The detailed method can be found in Exhibit 3.

In economic view, marginal cost of effort refers to the cost of spending one more hour and marginal benefit refers to the gain of spending one more hour. If MC > MB, spending one extra hour would cause Sheen's profit to decrease. If MC < MB, spending one extra hour would cause Sheen's profit to increase, so Sheen should spend more hours to increase her profit until MC = MB in order to maximize her profit. The marginal cost of effort is $10 per hour and the marginal benefit of her effort is , so 10 = , then we get h = 4, which is Sheen's choice of optimal effort level.

The optimal profit in Problem #2 is larger than the one in Problem #1. The reason is that the time Sheen invests in creating the profile section increase. The increase of hours invested directly increases average daily demand. On the other hand, fixed and variable costs stay same, so the profit rises.

Problem #3:

When Armentrout runs the retailing part for Sheen, they brought out a channel profits accounted from individual's profits. Based on the Hamptonshire Express Problem 3 model, we use Excel Solver tool by constraining the working hours creating the profile section that Sheen has spent by 4 and maximizing the stocking quantity as the outcome, then we get that stocking quantity to be 516 papers in which their channel profits are $322.(Exhibit 4)

The optimal stocking quantity in this problem is less than the one identified in Problem #2 due to one more party as a retailer (Armentrout) involved. He would purchase at transfer price ($0.8/copy) and benefit less than his supplier (Sheen).Further, Armentrout has to carry a higher risk of loss once he does not sell out his inventory. However, this result is consistent with the Newsvendor formula, the same consequence is shown in Exhibit 5.

Sheen's optimal effort is 2.25 hours, which means that her profit meet the maximum value of $262 at that level while it starts to reduce after 2.25 hours (Exhibit 6). However, Armentrout's profits will keep going to increase as the more effort level Sheen spends on. This optimal effort is less than the answer in Problem 2 since the increase in demand cannot sufficiently cover the opportunity