The Problem: Every fall, Rob Cummins of the fashion wear producer Cummings Wear, faces the task of committing to specific production quantities for each summer item the company will offer in the coming years line. Commitments are needed immediately in order to reserve space in production facilities located throughout Asia. Actual demand for these products will not become known for at least 6 months and, therefore, Rob faces a lot of uncertainty in his commitments.

The wholesale price is estimated at $110, and production and distribution costs (the order cost per unit) for a typical swimwear runs about 80 percent of the wholesale price. All swimwear not sold during the regular season is expected to be sold for a salvage value between 10 and 20 percent of the wholesale price. Since no other information is known for the salvage value, a uniform distribution with minimum of 10 percent and a maximum of 20 percent would be the best distribution to use in this case.

Rob has asked six of his most knowledgeable people to make forecasts of demand for the various models of swimwear. Forecasts for one product are given in the following Table I. However, experience suggests that given several forecasts, the best approach is to calculate an average value to use in the decision process, and that the actual standard deviation of the demand is twice that of the standard deviation in the sample forecasts given in Table I. Therefore, any modeling attempt would have to consider these recommendations.

Table I	Units
forecast 1	900
forecast 2	1,000
forecast 3	900
forecast 4	1,300
forecast 5	800
forecast 6	1,200

Rob is concerned with the impact on profit by ordering too much or too little, and asked you to evaluate the contribution to profit for an order of swimwear equal to the average forecast.

Consider the following in developing your model:

• The demand follows a Normal distribution with mean and standard deviation calculated from the forecast in table I and recommendations from past experience.
• Since demand cannot be negative, truncate the demand to disregard any negative value
• Regular sales are calculated as the smaller of the demand and the quantity ordered
• Leftover units are calculated as the difference between the order quantity and demand, or zero if demand exceeds the order quantity
• Salvage revenue is leftover unit times salvage value
• Contribution to profit is the sum of regular and salvage revenues, less cost.
• (see a suggested model layout at the end of this case)

In preparing your report, provide Rob with the following information:

1. Generate the demand distribution and confirm whether it matches the specifications.
2. Find the best (maximum) and worst (minimum) values for the contribution to profit.
3. Find the expected contribution to profit and its probability distribution.
4. Calculate the 95% confidence interval for the expected contribution to profit. Interpret.
5. Find the risk of having a loss.
6. Generate the probability distribution for the leftover units. Find the average number of leftover units that could not be sold in the regular season and corresponding salvage revenue.
7. What is the probability of having 500 or more leftover units?
8. Prepare a brief and formal analysis (no slangs, proper sentence structure, correct grammar etc) addressing Robs concern for ordering an order size equal to the average forecast. Use results in 1 through 7 to support your analysis. Extend the analysis to include whether you would recommend a different order size to maximize the contribution to profit. (for item 8, a report with 200 to 250 words should be sufficient)

Important guidelines:

a. For the simulation, set the number of trials at 5000

b. For parts 1 through 7, it is best to have the question and the answer below it. For example,

1. .

2. Find and report the best (maximum) and worst (minimum) values for the contribution to profit.

Maximum profit is $ 10,500

Minimum profit is $(2400)

3. Find and report the expected (mean) contribution to profit and its probability distribution.

The expected profit is $ 7,500

c. If the item asks for a chart or graph, cut and paste from Excel output.

d. Do not write in the report See Solution in Excel. That will lower score in the item by half.

e. The following layout is a suggestion for the model:

Data
Wholesale Price per Unit
Salvage price (markdown price)
Production Cost
Quantity to order
Demand for the period
Model
Sales during regular season (units)
Unsold units during regular season (units)
Regular revenue (at wholesale price)
Salvage revenue (at salvage price)
Results
Total revenue
Total cost
Contribution to profit

f. As a suggestion, using the following layout in the spreadsheet may facilitate model development:

Model