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Linear programming for Florida theme park

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Have you ever run a company? Do you know that companies face staffing schedule optimization problems everyday? The following problem relates to a conventional staffing optimization problem. You will find that when you know about optimization, your company could identify significant cost-savings strategies. In this example, you'll learn how to minimize staffing requirement for a Theme Park and how you can prove to you boss that you can save him almost 5 million dollars per year.

Maintenance at a major theme park in central Florida is an ongoing process that occurs 24 hours a day. Because it is a long drive from most residential areas to the park, employees do not like to work shifts of fewer than eight hours. These 8-hour shifts start every four hours throughout the day. The number of maintenance workers needed at different times throughout the day varies. The following table summarizes the minimum number of employees needed in each 4-hour time period (see attached table). The maintenance supervisor wants to determine the minimum number of employees to schedule that meets the minimum staffing requirements.
a) Formulate an LP model for this problem.
b) Create a spreadsheet model for this problem and solve using Excel Solver
c) What is the optimal solution?

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