Answered Essay:

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 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:

Minimum Number of
Day Employees Needed
Monday 85
Tuesday 80
Wednesday 50
Thursday 75
Friday 45
Saturday 60
Sunday 50

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 and determine the total number of call-center employees under the optimal solution. Use Excel Solver.

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 + X4 + X5 + X6 + X7
X1 + X2 + X5 + X6 + X7
X1 + X2 + X3 + X6 + X7
X1 + X2 + X3 + X4 + X7
X1 + X2 + X3 + X4 + X5
X2 + X3 + X4 + X5 + X6
X3 + X4 + X5 + X6 + X7
X1, X2, X3, X4, X5, X6, X7 ≥ 0

Total Number of Employees Under the Optimal Solution= ?

There are similar problems on chegg of the same questions but with different numbers. At the end you cannot see the two cutoff boxes but one has an option for ≥, ≤, or =. The other box next to it is where you place your answer in regards to that.

Expert Answer

 

Formulation:

Min X1 + X2 + X3 + X4 + X5 + X6 + X7
s.t.
Requirement for Monday X1 + X4 + X5 + X6 + X7 >= 85
Requirement for Tuesday X1 + X2 + X5 + X6 + X7 >= 80
Requirement for Wednesday X1 + X2 + X3 + X6 + X7 >= 50
Requirement for Thursday X1 + X2 + X3 + X4 + X7 >= 75
Requirement for Friday X1 + X2 + X3 + X4 + X5 >= 45
Requirement for Saturday X2 + X3 + X4 + X5 + X6 >= 60
Requirement for Sunday X3 + X4 + X5 + X6 + X7 >= 50
X1, X2, X3, X4, X5, X6, X7 ≥ 0

Excel Spreadsheet Model and Solver Solution:

Optimal Solution:

Total number of employees under the optimal solution = 100 employees

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