Simulation Case Problem $1$

Egress, Inc., is a small company that designs, produces, and sells ski jackets and other coats. The creative design team has labored for weeks over its new design for the coming winter season. It is now time to decide how many ski jackets to produce in this production run. Because of the lead times involved, no other production runs will be possible during the season. Predicting ski jacket sales months in advance of the selling season can be quite tricky. Egress has been in operation for only three years, and its ski jacket designs were quite successful in two of those years. Based on realized sales from the last three years, current economic conditions, and professional judgment, $12$ Egress employees have independently estimated demand for their new design for the upcoming season as: $14000,16000,13000,8000,14000,5000,14000,11000,15500,8000,10500$ and $15000.$

To assist in the decision on the number of units for the production run, management has gathered the data as below. Note that S is the price Egress charges retailers. Any ski jackets that do not sell during the season can be sold by Egress to discounters for V per jacket. The fixed cost of plant and equipment is F$.$ This cost is incurred regardless of the size of the production run.

Variable production cost per unit $($C$)$:

$$80$

Selling price per unit $($S$)$:

$$100$

Salvage value per unit $($V$)$:

$$30$

Fixed production cost $($F$)$:

$$100,000$

Analyze this problem and develop a presentation for your analysis to answer the following questions:

$1.$

Egress management believes that a normal distribution is a reasonable model for the unknown demand in the coming year. What mean and standard deviation should Egress use for the demand distribution?

$2.$

Use a spreadsheet model to simulate $1000$ possible outcomes for demand in the coming year. Based on these scenarios, what is the expected profit if Egress produces $7800$ ski jackets? What is the expected profit if Egress produces $12,000$ ski jackets? What is the standard deviation of profit in these two cases?

$3.$

Based on the same $1000$ scenarios, how many ski jackets should Egress produce to maximize expected profit? Call this quantity $.$

$4.$

Should $$ equal mean demand or not? Provide an argument that includes a comparison of the marginal revenue of producing one more ski jacket versus the marginal cost.

$5.$

Create a histogram of profit at the production level $.$ Create a histogram of profit when the production level $$ equals mean demand. What is the probability of a loss greater than $$100,000$ in each case?