Question

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: Minimum Number of Day Employees Needed Monday 70 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 a software package LINGO or Excel Solver. If your answer is zero, enter "O" Let Xi-the number of call center employees who start work on day i (i = 1 = Monday, i-2 = Tuesday )

Answer 1

Let the number of employees joining the duty on monday, be x_1, on tuesday be x_2, on wednesday be x_3, on thursday be x_4, on friday be x_5, on saturday be x_6 and sunday be x_7. thus the objective function is: x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 and we have to minimie the objective function .now, minimum no.of employees needed on monday = 70 an employee who join duty on thursday will work for 5 days i.e, thursday, friday, saturday sunday and monday . the applicable variables for these days are x_4, x_5, x_6, x_7 andx_1. thus x_1 + x_4 + x_5 + x_6 + x_7 > = 70 employees requirement for tuesday is 80.thus constaint will be: x_1 + x_2 + x_5 + x_6 + x_7 > = 80 employees requirement for tuesday is 50.thus constaint will be: x_1 + x_2 + x_3 + x_6 + x_7 = 50 employees requirement for tuesday is 75.thus constaint will be: x_1 + x_2 + x_3 + x_4 + x_6 > = 75 employees requirement for tuesday is 45.thus constaint will be: x_1 + x_2 + x
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