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	90
Tuesday	60
Wednesday	50
Thursday	75
Friday	45
Saturday	60
Sunday	50

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+	X6+	X7	, OR =	_____________
	X1 +	X2+			X5+	X6+	X7	, OR =	_____________
	X1 +	X2+	X3+			X6+	X7	, OR =	_____________
	X1 +	X2+	X3+	X4+			X7	, OR =	_____________
	X1 +	X2+	X3+	X4+	X5			, OR =	_____________
		X2 +	X3+	X4+	X5+	X6		, OR =	_____________
			X3 +	X4+	X5+	X6+	X7	, OR =	_____________
	X1,	X2,	X3,	X4,	X5,	X6,	X7		0

Find the optimal solution.

X1	=	____________
X2	=	____________
X3	=	____________
X4	=	____________
X5	=	____________
X6	=	____________
X7	=	____________

Total Number of Employees = __________

Give the number of call center employees that exceed the minimum required.

Excess employees:

Monday	=	_____________
Tuesday	=	_____________
Wednesday	=	_____________
Thursday	=	_____________
Friday	=	_____________
Saturday	=	_____________
Sunday	=	_____________