EMIS 3360 Project

EMIS 3360 Fall 2001

Project Part

The assignment for the project is to work in groups of 3 or 4 people to formulate and solve an LP model for the Moon Megasystems problem
and perform sensitivity analysis on the solution.

Due Date

The project reports are due at the start of class on Tuesday, December 4, at which time each group will give a 10-minute presentation on their project.

Organize into groups of 3 or 4 people. No extra credit will be given for working alone.
Every member of the group is required to understand every part of the project.
It is your responsibility to ascertain that everybody in the group does a fair share of the work and understands every part of the project.

Problem Description

Moon Megasystems sells three types of computer systems called Phobos, Deimos and Io. The retail value and assembly times for each of the systems are shown in the table below.

System	Retail Value	Assembly Time in Hours
Phobos	$4,949	1.5
Deimos	$4,607	2.0
Io	$8,320	2.5

In anticipation of the holiday buying season, the sales department has received numerous orders for new systems. In order to satisfy all the orders, the following number of systems should be shipped by the end of each of the days listed below.

	Number of Systems
Due Date	Phobos	Deimos	Io
November 5, 2001	47	4	0
November 6, 2001	108	25	286
November 7, 2001	128	11	66
November 8, 2001	15	26	152
November 9, 2001	148	0	27
November 10, 2001	58	44	117
November 11, 2001	71	0	0
November 12, 2001	97	105	0
November 13, 2001	68	15	41
November 14, 2001	144	145	126
November 15, 2001	67	100	3
November 16, 2001	0	90	92
November 17, 2001	86	219	12
November 18, 2001	83	29	8

Once a system is assembled, it may either be shipped that day or stored in a warehouse and shipped at a later date. The cost for storing a system in a warehouse for 1 day is 1% of the system's retail value. Any number of systems may be warehoused at any time, but for insurance purposes, the total retail value of all warehoused systems cannot exceed $2,000,000 on any given day.

Moon Megasystems currently employs 45 full-time factory workers who work 8 hours a day, Monday through Friday and are paid $20 an hour. Full-time works may work up to 4 hours of overtime per day for which they are paid $30 per hour. The company also has 30 part-time workers who work 8 hours a day on Saturday and Sunday and are paid $15 an hour. Part-time workers do not work overtime.

In order to avoid a potential loss of goodwill with its customers, the marketing and sales divisions of Moon Megasystems are demanding that all ordered systems be assembled and shipped by the end of the day on November 18^th.

Your Assignment

Working in teams of 3 or 4, your assignment is to:

Formulate and solve an appropriate operations research model that can be used to help Moon Megasystems find a minimum cost production plan that will allow the company to meet all its demand for November by the end of business on the 18^th.

Write a short report on your solution using the suggested outline for the Senior Design Project. The reports are due at the start of class on December 4th at which time each group will give a short presentation of their report.

Formulation

Define all the variables clearly and state the units used.
Justify briefly all the constraints and the objective function.
Some aspects of the problem description are open to interpretation; make any reasonable assumption whenever needed, but be sure to state clearly and discuss any assumption you make.
You are required to solve your formulation and perform sensitivity analysis.

Solving the Problem

Present the optimal solution clearly in non-technical terms. It is advisable to use tables, summaries and graphs when applicable. It should be presented in a way that is understandable to management personnel that have no training in Operations Research. Mathematical formulations and output from CPLEX or other LP solvers should be included in an appendix.

Sensitivity Analysis and Integer Programming Solution

1) Chose five "what-if" questions to answer about your optimal solution from from Part I of the project using sensitivity analysis.

2) Justify or explain why you chose these question.

3) Your analysis should use the topics covered in class while discussing sensitivity analysis. Include a variety of question types, e.g., change in objective function coefficient, change of right hand side of a non-binding constraint, change in the right hand side of a binding constraint, etc ...

4) Solve your original problem as an integer programming problem and compare the solution to the you found with using linear programming

5) A large portion of your grade will be based on the way in which you present your results. The main text of the report should be a non-technical description of the sensitivity analysis in plain English that can be understood by a reader who understands what the diet problem is, but does know anything about linear programming. The report should also contain an appendix in which you justify your results using the methods and notation used in class. This part of the report should be written for someone who has a background in linear programming.