Optimal Production Schedule and Pricing Strategy

Submit via NYU Brightspace your report and Excel files by Session 8. Watch for specific instructions from the TA.

This assignment is to be done in groups of up to four. For each problem, please provide justification (analysis) for your answers. Your report should also include screenshots of your spreadsheet model and the results.

1. Sailco must determine how many sailboats to produce during each of the next four quarters. At the beginning of the first quarter, Sailco has an inventory of 10 sailboats.

Sailco must meet demand on time. The demand during each of the next four quarters is as follows:

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
    40         60        70       30

For simplicity, assume that sailboats made during a quarter can be used to meet demand for that quarter. During each quarter, Sailco can produce up to 50 sailboats with regulartime employees, at a labor cost of $400 per sailboat. By having employees work overtime during a quarter, Sailco can produce up to 20 additional sailboats with overtime labor at a cost of $450 per sailboat.

At the end of each quarter (after production has occurred and the current quarter’s demand has been satisfied,), a holding cost of $20 per sailboat is incurred. Sailco has limited storage space and can hold up to 20 sailboats at the end of each quarter.

a) Formulate a dynamic program to find a production schedule to minimize the sum of production and inventory holding costs during the next four quarters.

Implement your dynamic program in an Excel spreadsheet. You may assume (and this can be verified) that the production quantity in each period is a multiple of 10 units.

Before formulating the dynamic program, answer the following questions, which will help you reduce the number of alternatives (production quantity) in each stage (quarter):

• Is it OK to produce 25 sailboats in the first quarter? And what is the minimum possible production quantity in the first quarter?
• Would it be optimal to use overtime production in the first quarter, and why?
• Would it be optimal to produce more than 60 units in Quarter 2?
• Would it be optimal to produce fewer than 50 units in Quarter 3?

 

Decision Making Under Uncertainty 2 Prof. Juran
• Would it be optimal to produce more than 30 units in Quarter 4?
b) What is the optimal production schedule if the holding cost is $30 per sailboat per quarter?

 

2. Refer to the case “Pricing Strategies for Power-Pro’s MBA Laptop Bag”.
a) Formulate a dynamic program to find the optimal price of the laptop bags for the first week of the sales season. We assume Sarah’s objective is to maximize the expected revenues over the 9-week sales season.
b) How do you interpret the solution of the dynamic program? Focus on the solution for Week 2 only.
Make sure that you identify and briefly explain the following elements of your dynamic program: states, stages, value-to-go function, recursive equation.