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4120_lecture6-F2010

# 4120_lecture6-F2010 - Computational Methods for Management...

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Computational Methods for Management and Economics Carla Gomes Lecture 6 Reading: 3.4 and 3.5 of textbook

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Main Categories of LP problems: Cost-benefit-trade-off problems (contd.)
Work-scheduling problem

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Overview Work-scheduling problem The model Practical enhancements or modifications Two non-linear objectives that can be made linear A non-linear constraint that can be made linear These slides are adapted from James Orlin’s
A Work-Scheduling Problem (from Intro Math Programming A post office requires different numbers of full-time employees on different days of the week. Union rules state that each full-time employee must work five consecutive days and then receive two days off. For example, an employee who works on Monday to Friday must be off on Saturday and Sunday. The post office wants to meet its daily requirements using only full-time employees, and minimizing number of employees.

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Scheduling Postal Workers Each postal worker works for 5 consecutive days, followed by 2 days off, repeated weekly. Day Mon Tues Wed Thurs Fri Sat Sun Demand 17 13 15 19 14 16 11 Minimize the number of postal workers (for the time being, we will permit fractional workers on each day.)
Day Mon Tues Wed Thurs Fri Sat Sun Demand 17 13 15 19 14 16 11 Minimize z = x 1 + x 2 + x 3 + x 4 + x 5 + x 6 + x 7 subject to x 1 17 x 2 13 x 3 15 x 4 19 x 5 14 x 6 16 x 7 11 x j 0 for j = 1 to 7 Decision variables –Let x 1 be the number of workers who work on Monday –Let x 2 be the number of workers who work on Tuesday … –Let x 3 , x 4 , …, x 7 be defined similarly. What’s wrong with this formulation?

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Answer Objective function is not number of full- time post office employees each employee is counted five times; • The variables x 1 , x 2 , x 3 , etc are interrelated but that is not captured in our formulation (for example some people who are working on Monday are also working on Tuesday)
LP Formulation Select the decision variables

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4120_lecture6-F2010 - Computational Methods for Management...

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