Reference no: EM133675598

Assignment:

The GoGo Bunny is a hot toy this Christmas, and the manufacturer has decided to ration supply among the retailer stores. Production cost is $10 per unit. The manufacturer first classify all retail stores into two segments. The first segment consists of discount retail channels that are willing to commit orders three months before Christmas but are more price sensitive. Expected demand of this segment is 4500-60p where p is the price charged. The second segment consists of high-service retail channels. These retailers are willing to pay a higher price if it can commit orders when the holiday season starts in late November. Expected demand of this segment under a price p is 2000-20p.

Assume the manufacturer plans to adopt differential pricing to maximize its expected revenue.

• What price should the manufacturer charge each segment if there is no capacity constraint? Show your calculation steps.
• Now assume the total production capacity at the manufacturer is 1250 units. What price should the manufacturer charge each segment?

Solve this problem using an optimization model.

(i) Write down the optimization model formulation. Clearly define your decision variables, and write down the objective function and the constraints.

(ii) Then solve it with Excel Solver.

(c) Let's continue to assume the total production capacity at the manufacturer is 1250 units. Given that the discount segment orders before the high-service segment, the manufacturer decides to reserve part of the capacity for the high-service segment.

Further market survey indicates the following about the demand distribution from the two segments.

• It is estimated that the demand from the high-service segment follows a normal distribution, and has a standard deviation of 200.
• Demand in the discount segment is likely to skew towards higher values (negatively skewed). There is high probability that there is enough demand from the discount segment to use up the entire available capacity.
• With this information, how much capacity would you recommend the manufacturer to reserve for the high-serive segment? Assume the manufacturer adopts the optimal prices calculated in question (b) above. Show your calculation steps. Use Excel to find the z-score that corresponds to the optimal service level you calculated.