Problem 9-09 (Algorithmic) Epsilon Airlines services predominantly the eastern and southeastern united States. The vast majority of Epsilons customers make reservations through Epsilons website, but a small percentage of customers make reservations via phones. Epsilon employs call center personnel to handle these reservations and to deal with website reservation system problems and for the rebooking of flights for customers whose plans have changed or whose travel is disrupted. Staffing the call center appropriately is a challenge for Epsilons 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 the week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows: Day Minimum Number of Employees Needed Monday 45 Tuesday 90 Wednesday 75 Thursday 60 Friday 50 Saturday 45 Sunday 75 The call center employees work for five consecutive days and then have two consecutive days off. An employee may start work on 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.

Epsilon analysts have estimated the minimum number of call center employees needed by day of the week for the upcoming vacation season (June, July, and the first two weeks of August). These estimates are as follows: Minimum Number of Employees Needed 45 90 75 Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday 60 50 45 75 The call center employees work for five consecutive days and then have two consecutive days off. An employee may start work on 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 (i = 1 = Monday, i = 2 = Tuesday...) = Min X1 + X2 + X3 + X4 + X5 + X6 + X7 s.t. X1 + X4+ X5+ Xs+ X72 45 X1 + X2+ X5+ X6+ X72 90 X1 + X2+ X3+ + X6+ X2 75 X1 + X2+ X3+ X4+ X 60 19 X1 + X2+ X3+ X4+ X5 > 50 X2 + X3+ X4+ X5+ X6 > 45 X3 + X4+ X5+ X5+ X2 75 X1, X2, X3, X4, X5, X6 X7 > 0 Find the optimal solution. X1 = 0 X2= 1 x |X3 1 x X4 = 0 Xs = 1 x X6 Il o 1 X Total Number of Employees 95 x Give the number of call center employees that exceed the minimum required. Excess employees: Monday 10 x Tuesday Wednesday o Thursday 10 X Friday 1 Saturday 10 x Sunday 0