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MIE262: Operations Research I, Lab project D.M. Aleman

Lab project: WARP Shoe Company


1 Introduction 1

2 Problem statement 1

3 Questions 2

4 Assignment 3

5 Database tables 3

6 Helpful hints 4

1 Introduction

The WARP Shoe Company is one of the oldest shoe companies in Canada. Over the past

three years, the WARP management found it helpful and sometimes profitable to consult

with students from the department of Industrial Engineering of the University of Toronto.

Please make yourselves familiar with the information on the company’s website:


All information needed on the WARP Shoe Company, including the database, can be found



The management of WARP Shoe Company would like to thank you in advance for your

effort and help.

2 Problem statement

At the beginning of year 2006, one of the major market competitors of WARP went bankrupt.

Thus, WARP market analysts predict that for the month of February the demand for all

types of shoes will double. Assume that closing inventory of January 2006 was zero for all

types of shoes. Assume also that all sales happen at the end of the month.

The management of WARP wants to know what is the most profitable production plan.

You are advised to take the following considerations into account:


MIE262: Operations Research I, Lab project D.M. Aleman

• The budget for raw materials is $10,000,000.

• Sales price on shoes remains the same as in the Product Master Table.

• Not meeting the demand for any type of shoe means loss of new potential customers,

and hence has been evaluated at a cost of $10/pair. Demand for each month from

1997-2003 can be found in the Product_Demand table.

• It has been decided that during February 2006 the WARP shoe production plant,

including all machines, will work up to 12 hours a day, 28 days a month. The cost of

operation of each machine is given in the Machine_Master table. Assume that setup

times and costs are negligible. The amount of time (s) each shoe requires from each

machine is given in the Machine_Assign table.

• Workers are paid on an hourly basis at the rate of $25/hour. Each machine has to be

operated by one worker.

• The total warehouse capacity can be obtained from the Warehouse_Master table.

• Transportation costs can be ignored.

• The manufacturing sequence can be ignored.

3 Questions

If you had to use the LP relaxation method (see Hint 2 in Section 6), answer all questions

for the LP relaxation solution unless the question specifically states otherwise.

1. How should you estimate the demand for the month of February?

2. How many variables and constraints do you have?

3. If you had to relax your integer program to an LP, how many constraints were violated

after rounding the LP solution to the closest integer solution?

4. Which constraints are binding, and what is the real-world interpretation of those binding


5. Assume that some additional warehouse space is available at the price of $10/box of

shoes. Is it economical to buy it? What is the optimal amount of space to buy in this


6. Imagine that machines were available for only 8 hours per day. How would your solution

change? Which constraints are binding now? Does the new solution seem realistic to


7. If in addition there were a $7,000,000 budget available to buy raw materials, what

would you do? Change your formulation and solve again.


MIE262: Operations Research I, Lab project D.M. Aleman

4 Assignment

Complete the following:

• Formulation of the problem (decision variables, objective function, constraints)

• Gurobi solution report

• Answers to the questions in Section 3.

• Explanation of obtained results

To solve this problem, you will need to obtain data from the database. The relevant database

contents are described in Section 5.

5 Database tables

Table Description Contents

Product_Master Basic product info Product name

Sales price

Product_Demand How much was sold by each store per month Year


Store number


Machine_Master Basic machine info Machine name

Setup cost per month

Operating cost per


Setup time (min)


Machine_Assign The processing time of each shoe on each


Product number

Machine number

Average duration (s)

Step number

RM_Master Basic raw material info Raw material name


Available quantity


BOM Bill of materials (raw material required per


Product number

Raw material number

Quantity required


MIE262: Operations Research I, Lab project D.M. Aleman

6 Helpful hints

1. It might be helpful to construct (or consider) the following tables:

• Shoe type and profit from selling of one pair

• Machine number, product number, and average processing time required

2. If the computational time for solving your integer model is more than 10 minutes, relax

your model to an LP by removing the integer requirements for the variables. After

solving the relaxed LP model, round the values of the relaxed variables to the closest

integer (round up if the decimal part is ≥ 0.5, and round down otherwise). This LP

relaxation method is a common workaround to get decent solutions to IPs quickly.

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