# 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. Ebsilon 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’s 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:                                           Minimum Number of Day                                      Employees Needed Monday                                            75Tuesday                                            50Wednesday                                       45Thursday                                           60Friday                                                90Saturday                                            75Sunday                                              45The call center employs 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. Find the optimal solution. Give the number of call center employees that exceed the minimum required.a. What is optimal total number of employees?b. Which days have excess employees?Choice of answers: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday

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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. Ebsilon 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’s 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:
Minimum Number of
Day                                      Employees Needed
Monday                                            75
Tuesday                                            50
Wednesday                                       45
Thursday                                           60
Friday                                                90
Saturday                                            75
Sunday                                              45
The call center employs 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. Find the optimal solution. Give the number of call center employees that exceed the minimum required.
a. What is optimal total number of employees?
b. Which days have excess employees?
Choice of answers: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday

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Step 1

The call centre employs work for five consecutive days and then have two consecutive days off. An employee may start work on any day of the week.

Let X1, X2, X3, X4, X5, X6, X7 are the number of call centre employees who start work on day Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.

The decision variable is   X1, X2, X3, X4, X5, X6 and X7 and the total number of call centre employees has to be minimized.

Step 2

The objective function is:

Minimize Z = X1 + X2 + X3 + X4 + X5 + X6 + X7

Constraints:

Monday: X1 + 0 X2 + 0 X3 + X4 + X5 + X6 + X7   75

Tuesday: X1 + X2 + 0 X3 + 0 X4 + X5 + X6 + X7   50

Wednesday: X1 + X2 + X3 + 0 X4 + 0 X5 + X6 + X7   45

Thursday: X1 + X2 + X3 + X4 + 0 X5 + 0 X6 + X7   60

Friday: X1 + X2 + X3 + X4 + X5 + 0 X6 + 0 X7   90

Saturday: 0 X1 + X2 + X3 + X4 + X5 + X6 + 0 X7   75

Sunday: 0 X1 + 0 X2 + X3 + X4 + X5 + X6 + X7   45

X1, X2, X3, X4X5, X6 and X7   0 (Non-negativity constraint).

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