# 02_LP2 - More Linear Programming Models 1 MIT and James...

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MIT and James Orlin © 2003 1 More Linear Programming Models

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MIT and James Orlin © 2003 2 Overview Applications personnel scheduling production and inventory management Goals get practice in recognizing and modeling linear constraints (and non-linear constraints) use of models in practice
MIT and James Orlin © 2003 3 Overview 5 in 7 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

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MIT and James Orlin © 2003 4 Overview 5 in 7 scheduling problem The model
MIT and James Orlin © 2003 5 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.)

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MIT and James Orlin © 2003 6 Formulating as an LP Select the decision variables Let x 1 be the number of workers who start working on Monday, and work till Friday Let x 2 be the number of workers who start on Tuesday … Let x 3 , x 4 , …, x 7 be defined similarly.
MIT and James Orlin © 2003 7 Minimize z = x 1 + x 2 + x 3 + x 4 + x 5 + x 6 + x 7 subject to x 1 + x 4 + x 5 + x 6 + x 7 17 Day  Mon  Tues  Wed  Thurs  Fri  Sat  Sun  Demand  17  13  15  19  14  16  11    x 1 + x 2 + x 5 + x 6 + x 7 13 x 1 + x 2 + x 3 + x 6 + x 7 15 x 1 + x 2 + x 3 + x 4 + x 7 19 x 1 + x 2 + x 3 + x 4 + x 5 14 x 2 + x 3 + x 4 + x 5 + x 6 16 x 3 + x 4 + x 5 + x 6 + x 7 11 x j 0 for j = 1 to 7

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MIT and James Orlin © 2003 8 On the selection of decision variables Would it be possible to have y j be the number of workers on day j?
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