The Post Office wants to establish a weekly schedule that can be reused for the future. The Post Office hires both full-time and part-time employees that work 5-day shifts. In other words, if an employee starts on Monday, his or her shift will end on Friday. Likewise, if an employee starts on Wednesday, then his or her shift will end on Sunday. Suppose that each fill-time employee work eight hours per day and part-time employees work four hours per day. The Post Office has determined the number of hours per day that they will need to meet in order to meet their performance goals.
Starting day of 5-day shift
Day Mon Tues Wed Thurs Fri Sat Sun
Hours required 136 104 120 152 112 128 88
The Post Office can meet is daily labor requirements by using both full-time and part-time employees. During each week, a full-time works eight hours a day for five consecutive days, and a part-time employee works four hours a day for five consecutive days. A full-time employ costs the post off $15 per hour, whereas a part-time employee (which reduced fringe benefits) costs the post office only $10 dollars an hour. Union requirements limit part-time labor to 25% of the total weekly labor hours available.
Develop an integer-programming model using Solver to determine the Post Office’s weekly schedule that minimizes total cost and meets the work requirements.
Ensure that you use the recommended settings for Solver. Do not be alarmed that it might take Solver some time to determine the optimal schedule for this problem. If you use the recommended settings for Solver, you will not have to wait any more than 100 seconds for Solver to determine a solution.
