Question

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

DayEmployees Needed

Monday55

Tuesday80

Wednesday50

Thursday75

Friday45

Saturday60

Sunday50

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…)

MinX1+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 Unde

Answer 1

All the inequalities in the constraints are of greater than equal to type. So we introduce surplus variables and artificial variables, as required, to put the LPP in the standard form. It is then solved using Simplex method (Big M) to obtain the optimal solution. All tables are computed in Excel and screenshots of the same are attached.