# Solved: Problem 4-09 (Algorithmic) Epsilon Airlines services predominately the eastern and southeastern

Problem 4-09 (Algorithmic) 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 Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Employees Needed 80 50 75 45 60 50 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

 Let x1 is number of employees that start on Monday x2 is number of employees that start on Tuesday x3 is number of employees that start on Wednesday x4 is number of employees that start on Thursday x5 is number of employees that start on Friday x6 is number of employees that start on Saturday x7 is number of employees that start on Sunday

So objective function will be

Minimise Z =x1+x2+x3+x4+x5+x6+x7

Don't use plagiarized sources. Get Your Custom Essay on
Solved: Problem 4-09 (Algorithmic) Epsilon Airlines services predominately the eastern and southeastern
GET AN ESSAY WRITTEN FOR YOU FROM AS LOW AS \$13/PAGE

Subject to constraints

Monday workforce-Those starting on Tuesday and Wednesday will be on leave

x1+x4+x5+x6+x7>=55

Tuesday workforce-Those starting on Wednesday and Thursday will be on leave

x1+x2+x5+x6+x7>=80

Wednesday workforce-Those starting on Thursday and Friday will be on leave

x1+x2+x3+x6+x7>=50

Thursday workforce-Those starting on Friday and Saturday will be on leave

x1+x2+x3+x4+x7>=75

Similarly for Friday

x1+x2+x3+x4+x5>=45

Saturday

x2+x3+x4+x5+x6>=60

Sunday

x3+x4+x5+x6+x7>=50

Solution obtained from solver is

Z=90 , minimum employee to be kept

The number of employees starting each day is obtained as

 Monday 5 Tuesday 35 Wednesday 0 Thursday 10 Friday 0 Saturday 15 Sunday 25