Question: A warehouse has a 24 hour operations and its workers can start their work at midnight (00.00 H), or at 4:00 am or at 8:00

A warehouse has a 24 hour operations and its workers can start their work at midnight (00.00 H), or at 4:00 am or at 8:00 am or at noon (12:00), or at 4:00 pm or at 8:00 pm and continue working for 8 consecutive hours. (E.g, if a worker starts at 4:00 am, then she will leave the warehouse at noon, and a worker who starts working at 12:00 noon will leave work at 8:00 pm) Assume that workers do work 7 days a week and are paid the same amount regardless of their work start time. The following table is the warehouse’s minimum need of employees at different time periods of the day in order to operate effeciently.

Time Interval	Employee Required
00:00 - 04:00	4
04:00 - 08:00	12
08:00 - 12:00	8
12:00 - 16:00	4
16:00 -20:00	6
20:00 – 00:00	6

a. Define the decision variables

b. Write down the mathematical model to optimize (minimizes) the number of workers.

c. Company realize that part-time (PT) employees are also an option. A PT employee works only 4 intervals and is paid 25% more than the regular hourly wage. Does this option will change your work force? How would you update the model to accommodate this new option and still minimize your total employee costs?

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