Problem Solution Essay on Stocking and Effort Levels

Problem #1

How many newspapers should Sheen stock? Use the simulation in the spreadsheet Hamptonshire Express: Problem #1 to identify the optimal stocking quantity. What is the profit at this stocking quantity?

Optimal Stocking Quantity: 584

Expected profit at Optimal Stocking Quantity: $331.43 B. Verify that the value derived in part (a) is consistent with the optimal stocking quantity in the Newsvendor model

= mean = 500

= Standard Deviation = 100

= Overage Cost = $0.20$0 = $0.20

= Shortage Cost = $0.20$1.00 = $0.80

= 1.8 = .2 ïƒ corresponding zvalue = .84

∗

Problem #2

How many hours should Sheen invest daily in the creation of the profile section?

The optimal amount of hours Sheen should invest results in optimal profit/day at 4 hours With optimal stocking quantity: 685

And expected profit/day: $371.33

What explains Sheen's choice of effort level h?

Since the marginal cost of her effort is $10/hour and the marginal benefit of her effort is equal to:

8 * 50 = 10 ïƒ h = 4

2√

The hours invested will be optimized when marginal cost = marginal benefit, in this case, h = 4. C. Compare the optimal profit under this scenario with the optimal profit derived in Problem #1.

Optimal Profit in #1 = $331.43 @ 584 units = $0.5675/unit Optimal Profit in #2 = $371.33 @ 685 units = $0.5421/unit

Although the optimal profit is increased from scenario 1 to scenario 2 by $39.90 the per-unit profit is down by 0.0254/unit produced, however since overall profit is up, the added hours invested are still optimal.

Problem #3

Assuming h=4 what would Armentrout's stocking quantity be?

Armentrout's optimal stocking quantity is 516

Why does the optimal stocking quantity differ from the optimal stocking quantity identified in Problem #2? Is the result here consistent with the newsvendor formula?

The optimal stocking quantities differ because there is a new player involved and new costs associated with overages and shortages. These results are still consistent with the newsvendor formula since the new model looks like:

= mean = 600

= Standard Deviation = 100

= Overage Cost = $0.80

= Shortage Cost = $1.00$0.80 = $0.20

= 1.8 = .2 ïƒ corresponding zvalue = .85 .

∗

Now try varying h¦ How does her optimal effort in this question differ from the answer in question 2? Why?

In Question 2, Sheen's profit is maximized at optimal effort = 4. In Question 3, Sheen's profit is optimal when h = 2 because her profits are being shared with Armentrout and the amount of hours Sheen invests determines the number of copies that Armentrout will purchase depending on his demand.

How would change the transfer price from the current value of $0.80 per newspaper impact Sheen's effort level and Armentrout's shocking decision?

Transfer Price Increase from $0.80 to $0.90 =

Sheens Effort = 2.25 to 3.063

Armentrouts Stocking Decision = 491 to 459

Sheens are incentivized to put in more effort and therefore reap more profit but Armentrout's stock will decline and make less profit if the transfer price is increased.

Transfer Price Decrease from $0.80 to $0.70 =

Sheens Effort = 2.25 to 1.563

Armentrouts Stocking Decision = 491 to 510

If the transfer price is decreased, Sheens is incentivized to put in less effort because she is making less profit and Armentrout's stock will increase since his costs are lower allowing him to make a higher profit.

What conclusion can you draw about stocking and effort levels in a differentiated channel vis an integrated firm that manufactures and retails its product?

Stocking and effort levels are optimized throughout the chain in an integrated firm that manufactures and retails its products because there is a direct benefit and because incentives are aligned between manufacturing and retailing. They want to put forth the optimal effort to produce the maximum amount of units that will optimize profits.

Optimal Profit in Problem #2 @ h=4: $371.33 @ 685 Units with fill rate 98%

In a differentiated firm when there is an added level, in this case, a level to retail, the manufacturing, and retailing parties do not share the same goals, therefore stocking and effort

levels are not optimized. Supplier only wants to produce as much as retail will buy at the minimum effort level and retail only wants to buy as much as will make them an optimal profit, I because stocking excess will incur losses.

Optimal Profit in Problem #3 @ h=4 @ 516 Units with fill rate of only 86%