Question

A restaurant in uptown is extremely busy on some days and needs to reevaluate their employment requirement policies. They have three types of employees. Full time employees, part time employees, and interns.

The full time employees work 5 days consecutively, the part time employees work 3 days consecutively and the interns work one day per week. The full time employees are paid $1150 per week. The part time employees are paid $500 per week (of 3 working days).

The restaurant policy states that the number of part time and interns cannot be higher than the number of full time workers on any day of the week. The restaurant works 7 days a week. The daily minimum requirement of the employee is

Monday = 15

Tuesday = 12

Wednesday = 9

Thursday = 10

Friday = 20

Saturday = 25

Sunday = 18

Formulate an LP programming to minimize the total cost of an effective schedule. Make sure the staffing schedule is enough to meet the daily requirement throughout the week. Clearly state all decision variables

Answer 1

Answer

Let the no. full time employee represnted by x, No. of part time employee is y and No. of Interns is reprsented by z.

Full time employee are paid $1150 for 5 days/week, The part time employee are paid $500 for 3 days/ week.

its bebeficial to have more part time employee and adjust them in shifts.

y<x and z < x

Minimum = x*1150 + y*500

As we can see the salary of one full time employee is more than 2 part time employee, but then a full time employee works for 5 days where a part time employer works only for 3 days.

according to requirement, On saturday maximum no. of employees are required 25.Therefore to satisfy the two contratints, on this day we will have 13 full time and 12 interns. (Interns will work only on this day)

Saturday (25) => x=13 ; z=12

Now all other days

Monday (15) => x = 13 ; y = 2

Tuesday (12) => x = 7 ; y =5

Wednesday (9) => x =5 ; y =4

Thursday (10) => x =6 ; y =4

Friday (20) => x = 11 ; y = 9

Sunday (18) => x = 10 ; y = 8

Accordin to the above sequence, we have made all the constraint true. And to minimize the cost, we always have to find the middle range for the no. of employee required for that day.

Maximum no. of full time employee is 13 and part time are 9 and interns 12.

Minimum Value = 13*1150 + 9*500

= 14950+ 4500

=$ 19450