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Epsilon Airlines services predominately the eastern and southeastern United States. A vast majority of Epsilon’s customers...

Epsilon Airlines services predominately the eastern and southeastern United States. A 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 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 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. Use a software package LINGO or Excel Solver. If your answer is zero, enter "0".

Let Xi = the number of call center employees who start work on day i (i = 1 = Monday, i = 2 = Tuesday…)

Min X1______ + X2______ + X3______ + X4______ + X5______ + X6______ + X7______ ≥ ______
s.t.
X1______ + X2______ + X3______ + X4______ + X5______ + X6______ + X7______ ≥ ______
X1______ + X2______ + X2______ + X2______ + X5______ + X6______ + X7______ ≥ ______
X1______ + X2______ + X3______ + X4______ + X5______ + X6______ + X7______ ≥ ______
X1______ + X2______ + X3______ + X4______ + X5______ + X6______ + X7______ ≥ ______
X1______ + X2______ + X3______ + X4______ + X5______ + X6______ + X7______ ≥ ______
X1______ + X2______ + X3______ + X4______ + X5______ + X6______ + X7______ ≥ ______
X1______ + X2______ + X3______ + X4______ + X5______ + X6______ + X7______ ≥ ______
X1, X2, X3, X4, X5, X6, X7 ≥ 0

Solution:

X1 = ______
X2 = ______
X3 = ______
X4 = ______
X5 = ______
X6 = ______
X7 = ______

Number of excess employees:

Monday = ______
Tuesday = ______
Wednesday = ______
Thursday = ______
Friday = ______
Saturday = ______
Sunday = ______

Total Number of Employees = ______

Solutions

Expert Solution

milcah answered 1 year ago
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