Epsilon Airlines services predominately the eastern and southeastern United States. The vast majority of Epsilon's customers make reservations through Epsilon's website, but a small percentage of customers make reservations via phone. Epsilon employs call-center personnel to handle these reservations along with any problems with the website reservation system and for the rebooking of flights for customers if their plans change or their travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon's management teams. Having too many emplooyees on hand is a waste of money, but having too few results in very poor customer service and potential loss of customers.

Epsilon analysts have estimated the minimum number of call-center employees needed by day of week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows:

Day Minimum Number of Employees Needed

Monday 75

Tuesday 50

Wednesday 45

Thursday 60

Friday 90

Saturday 75

Sunday 45

The call-center employees work five consecutive days and then have two consecutive days off. An employee may start work any day of the week. Each call-center employee receives the same salary. Assume that the schedule cycles and ignore start-up and stopping of the schedule. Develop a model that will minimize the total number of call-center employees needed to meet the minimum requirements. Find the optimal solution. Give the number of call-center employees that exceed the minimum required.

Need to define decision variables and constraints