A linear programming computer package is needed.
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 given in the following table.
Day Minimum Number of
Employees Needed
Monday 65
Tuesday 40
Wednesday 35
Thursday 50
Friday 75
Saturday 65
Sunday 40
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. (Let
Xi
= the number of call-center employees who start work on day i where
i = 1 = Monday,
i = 2 = Tuesday,
etc).
Min X1+X2+X3+X4+X5+X6+X7
Correct: Your answer is correct.
s.t.
Monday X1+X4+X5+X6+X7≥65
Correct: Your answer is correct.
Tuesday X1+X2+X5+X6+X7≥40
Correct: Your answer is correct.
Wednesday X1+X2+X3+X6+X7≥35
Correct: Your answer is correct.
Thursday X1+X2+X3+X4+X7≥50
Correct: Your answer is correct.
Friday X1+X2+X3+X4+X5≥75
Correct: Your answer is correct.
Saturday X2+X3+X4+X5+X6≥65
Correct: Your answer is correct.
Sunday X3+X4+X5+X6+X7≥40
Correct: Your answer is correct.
X1, X2, X3, X4, X5, X6, X7 ≥ 0
Find the optimal solution.
(X1, X2, X3, X4, X5, X6, X7) =
