Formulate an optimization model to minimize labor expenses. You must solve the optimizati either the IBM ILOG CPLEX Optimization Studio or the Microsoft Excel Solver.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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Please formulate the problem as AN OPTIMIZATION MODEL only and I will finish the rest.

Health Center is planning to open its facilities 24 hours a day and wants to determine an optimal schedule. for their nurses. A nurse's work schedule is 8 hours in a row and can only start at the beginning of each shift. The personnel requirement for each shift is shown in Table 1.

Table 1 – Personnel Requirement

Table 1 - Personnel Requirement
Required
Nurses
Shift
Time
8:00am-12:00pm
12:00pm-4:00pm
4:00pm-8:00pm
8:00pm-12:00am
12:00am-4:00am
1
50
2
56
3
60
4
42
32
4:00am-8:00am
24
Each nurse is paid $100 per hour in the daytime (from 8:00am to 8:00 pm) and $125 at night (from 8:00pm to
8:00am on the following day). Consider that each nurse can also work overtime hours. If a nurse works
overtime hours, then she/he will work 4 consecutive hours beyond her/his normal work time, and be paid an
additional 50% for each of the 4 hours. Furthermore, no more than 25% of the nurses can work overtime hours
at each shift. Formulate an optimization model to minimize labor expenses. You must solve the optimization
problem using either the IBM IL0G CPLEX Optimization Studio or the Microsoft Excel Solver.
Transcribed Image Text:Table 1 - Personnel Requirement Required Nurses Shift Time 8:00am-12:00pm 12:00pm-4:00pm 4:00pm-8:00pm 8:00pm-12:00am 12:00am-4:00am 1 50 2 56 3 60 4 42 32 4:00am-8:00am 24 Each nurse is paid $100 per hour in the daytime (from 8:00am to 8:00 pm) and $125 at night (from 8:00pm to 8:00am on the following day). Consider that each nurse can also work overtime hours. If a nurse works overtime hours, then she/he will work 4 consecutive hours beyond her/his normal work time, and be paid an additional 50% for each of the 4 hours. Furthermore, no more than 25% of the nurses can work overtime hours at each shift. Formulate an optimization model to minimize labor expenses. You must solve the optimization problem using either the IBM IL0G CPLEX Optimization Studio or the Microsoft Excel Solver.
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