ENGRI 115
Engineering Applications of OR
Fall 2007
Linear Programming Formulations
Lab 9
Name:
Objectives:
•
Practice in formulating linear programming problems
•
Introduce the idea of linear relaxation
•
Demonstrate the relationship between an integer program and its linear relaxation
Key Ideas:
•
Objective function
•
Constraints
•
Optimal solution
•
Redundant constraint
•
Fractional solution
•
Integer solution
•
Linear relaxation
Reading Assignment:
•
Chapter 3 of Winston, especially the sections on a workscheduling problem and production process
models
Part #1  A Workscheduling problem
[Adapted from Hillier & Lieberman] A new company is being set up to take telephone orders. The phone lines
are staffed around the clock. People are hired to work in 8hour shifts, starting at 6AM, 8AM, 12PM, 4PM,
or 10PM. From survey data, the management has concluded that there are minimum staffing requirements
at certain times of the day, as given in the table below.
Time period
Minimum Staff Size
6AM8AM
48
8AM10AM
79
10AMNoon
65
Noon2PM
87
2PM4PM
64
4PM6PM
87
6PM8PM
64
8PM10PM
73
10PMMidnight
82
Midnight6AM
43
1
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A person is paid differently, depending on their assigned shift, where the daily salary is $170, $160, $175,
$180, $195, for the five shifts, respectively. The management would like to decide the number of people to
be hired for each shift so as to minimize the total salary costs. The first part of this lab is aimed at helping
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 Spring '05
 TROTTER
 Operations Research, Linear Programming, Optimization, optimal solution, Linear Programming Formulations

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