Lecture on 1-17
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SA305 Spring 2014
Work Scheduling Problems
Another very standard problem to model with a linear program is scheduling problems. How do
you assign workers to a certain demand on schedules? We begin with an example.
Example 1.1. A base needs guards at all times. We decide to split each day into 2 shifts: day
shift 6am-6pm and night shift 6pm-6am. Then each guard will work either day or night shift and
work 5 days in a row and have 2 days off. If we need 10 guards on weekdays, 15 on weekends, 20
on weekend days and 25 on weekend nights then what is the minimum number of guards we need?
Write a linear program that determines the minimum total number of employees needed.
First attempt
Define the following decision variables:
x1 = number of employees
x2 = number of employees
..
.
x13 = number of employees
x14 = number of employees
who work on Monday day
who work on Monday night
who work on Sunday day
who work on Sunday night
Then our linear program might look like:
max x1 + · · · + x14
s.t.
x1 ≥ 10
x2 ≥ 15
..
.
x14 ≥ 25
xi ≥ 0
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Second attempt
Define the following decision variables:
y1 = number of employees who start
y2 = number of employees who start
y3 = number of employees who start
..
.
y14 = number of employees who start
work on Monday day and work though Friday
work on Monday night and work though Friday
work on Tuesday day and work though Saturday
work on Sunday night and work through Thursday
Key Vocab:
Key Ideas:
creation of the model is delicate
integer solutions
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