Epsilon Airlines services predominately the eastern andsoutheastern United States. A vast majority of Epsilon’s customersmake reservations through Epsilon’s website, but a small percentageof customers make reservations via phone. Epsilon employscall-center personnel to handle these reservations along with anyproblems with the website reservation system and for the rebookingof flights for customers if their plans change or their travel isdisrupted. Staffing the call center appropriately is a challengefor Epsilon’s management team. Having too many employees on hand isa waste of money, but having too few results in very poor customerservice 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:
| Day | Minimum Number of
Employees Needed |
| Monday | 75 |
| Tuesday | 50 |
| Wednesday | 45 |
| Thursday | 60 |
| Friday | 90 |
| Saturday | 75 |
| Sunday | 45 |
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. Give the number of call-center employeesthat exceed the minimum required. Use a software package LINGO orExcel Solver. If your answer is zero, enter "0".
Let Xi = the number of call center employees whostart work on day i (i = 1 = Monday, i = 2 = Tuesday…)
| Min | X1______ | + | X2______ | + | X3______ | + | X4______ | + | X5______ | + | X6______ | + | X7______ | ? | ______ |
| s.t. | | | | | | | | | | | | | | | |
| X1______ | + | X2______ | + | X3______ | + | X4______ | + | X5______ | + | X6______ | + | X7______ | ? | ______ |
| X1______ | + | X2______ | + | X2______ | + | X2______ | + | X5______ | + | X6______ | + | X7______ | ? | ______ |
| X1______ | + | X2______ | + | X3______ | + | X4______ | + | X5______ | + | X6______ | + | X7______ | ? | ______ |
| X1______ | + | X2______ | + | X3______ | + | X4______ | + | X5______ | + | X6______ | + | X7______ | ? | ______ |
| X1______ | + | X2______ | + | X3______ | + | X4______ | + | X5______ | + | X6______ | + | X7______ | ? | ______ |
| X1______ | + | X2______ | + | X3______ | + | X4______ | + | X5______ | + | X6______ | + | X7______ | ? | ______ |
| X1______ | + | X2______ | + | X3______ | + | X4______ | + | X5______ | + | X6______ | + | X7______ | ? | ______ |
| X1, X2, X3,X4, X5, X6, X7 ? 0 |
Solution:
| | |
| X1 | = | ______ |
| X2 | = | ______ |
| X3 | = | ______ |
| X4 | = | ______ |
| X5 | = | ______ |
| X6 | = | ______ |
| X7 | = | ______ |
Number of excess employees:
| | |
| Monday | = | ______ |
| Tuesday | = | ______ |
| Wednesday | = | ______ |
| Thursday | = | ______ |
| Friday | = | ______ |
| Saturday | = | ______ |
| Sunday | = | ______ |
Total Number of Employees = ______
