Epsilon Airlines services predominately the eastern andsoutheastern United States. The vast majority of Epsilon’scustomers make reservations through Epsilon’s website, but a smallpercentage of customers make reservations via phone. Epsilonemploys call-center personnel to handle these reservations alongwith any problems with the website reservation system and for therebooking of flights for customers if their plans change or theirtravel is disrupted. Staffing the call center appropriately is achallenge for Epsilon’s management team. Having too many employeeson hand is a waste of money, but having too few results in verypoor customer service and the potential loss of customers.

Epsilon analysts have estimated the minimum number ofcall-center employees needed by day of week for the upcomingvacation 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 thenhave two consecutive days off. An employee may start work any dayof the week. Each call-center employee receives the same salary.Assume that the schedule cycles and ignore start-up and stopping ofthe schedule. Develop a model that will minimize the total numberof call-center employees needed to meet the minimum requirements.Find the optimal solution and determine the total number ofcall-center employees under the optimal solution. Use ExcelSolver.

Let Xi = the number of call center employees who start work onday 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