Hamptonshire Express
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Problem #1
Using the simulation spreadsheet, the optimal stocking quantity would be 585 newspapers with an expected profit per day of $331.43.
Using the newsvendor model
Critical fractal = $1-$0.2$1= .8
z=.85
Q* = + z= 500 + .85(100) = 585 newspapers
Problem #2
The optimal amount of time that Sheen should spend in creating the profile section should be 4 hours with the optimal stocking quantity of 685 newspapers and an expected profit/day of $371.33.
Sheen’s choice of effort level is determined by weighing the cost of her time to the expected profit of newspaper sales of the expected demand. Because her marginal benefit of effort is equal to .8(50)2hso as h increases the marginal benefit decreases by twices the square root of h.
The optimal profit of this scenario where the demand is correlated with the amount of effort Sheen puts in has a higher expected profit than the scenario where the demand is normalized because this scenario’s demand is a power function [E(D) = 500 + 50h] showing that the output (marginal benefit) increases at a slower rate than the input (effort) increases.
Problem #3
Using the solver, the optimal stocking quantity would be 516 papers maximizing Ralph’s profit/day at $62.14.
In this case, a new person has been added and also demand is forecasted differently. Before, it was based upon number of hours spent but now it’s on Ralph’s estimate based on reading before placing the print order.
Using Newsvendor model:
Critical fractile = $0.2 – $0$1 – $0= .2
z = -0.84
Q* = + z= 600 + -.84(100) = 516 papers so yes, it’s consistent
Yes, in this case Sheen’s optimal effort is 2.25 hours. Profits are now being split between Sheen and Ralph, and Ralph will forecast demand differently if Sheen is putting in different amount of hours.
Increasing the transfer price from $0.80 to $0.90 would maximize Sheen’s profits putting her effort level just over 3 hours and Ralph’s stocking decision at 459 papers. If the transfer price goes below $.80, Ralph would make more profit because he would be stocking more but Sheen would be putting in much less effort because she’d be making less.
Integrated manufacturers share similar goals and therefore will work together to reach them. In this case, Sheen puts for maximum effort in order to achieve a maximum profit. In the case of the differentiated channel, both parties have separate goals and will only work to maximize their own rewards