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# lab9 - ENGRI 115 Engineering Applications of OR Fall 2007...

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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 work-scheduling problem and production process models Part #1 - A Work-scheduling 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 8-hour 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 6AM-8AM 48 8AM-10AM 79 10AM-Noon 65 Noon-2PM 87 2PM-4PM 64 4PM-6PM 87 6PM-8PM 64 8PM-10PM 73 10PM-Midnight 82 Midnight-6AM 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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lab9 - ENGRI 115 Engineering Applications of OR Fall 2007...

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