Epsilon Airlines services predominantly 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 phones. Epsilon employs call center personnel to handle these reservations and to deal with website reservation system problems and for the rebooking of flights for customers whose plans have changed or whose travel is disrupted. Staffing the call center appropriately is a challenge for Epsilon's management team. Having too many employees on hand is a waste of money, but having too few results in very poor customer service and the potential loss of customers.

Epsilon analysts have estimated the minimum number of call center employees needed by day of the 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 45

Tuesday 50

Wednesday 80

Thursday 60

Friday 50

Saturday 90

Sunday 80

The call center employees work for five consecutive days and then have two consecutive days off. An employee may start work on 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.

Let X_i = the number of call center employees who start work on day I

(i = 1 = Monday, i = 2 = Tuesday...)

MinX₁ +X₂ +X₃ +X₄ +X₅ +X₆ +X₇

s.t.

X1 + X4+X5+X6+X7 < or > or = ___________

X1 +X2+ X5+X6+X7 < or > or = _________

X1 +X2+X3+ X6+X7 < or > or = _________

X1 + X2+ X3+ X4+ X7 < or > or = _________

X1 + X2+ X3+ X4+ X5 < or > or = _________

X2 +X3+X4+X5+X6 < or > or = _________

X3 +X4+X5+X6+X7 < or > or = _________

X₁, X₂, X₃, X₄, X₅, X₆, X₇

Find the optimal solution.

X₁ = _________

X₂ = _________

X₃ = _________

X₄ = _________

X₅ = _________

X₆ = _________

X₇ = _________

Total Number of Employees= _________

Give the number of call center employees that exceed the minimum required.

Excess employees:

Monday = _________

Tuesday = _________

Wednesday = _________

Thursday = _________

Friday = _________

Saturday = _________

Sunday = _________