1) University library management office employs two-full time emplovees who work 8 hours per day. The library also employs students part-time at the office, who are scheduled 4-hour shifts during examination periods (i.c., the peak periods). On Saturdays, the library is open from 11:00 to 22:00 The university management wants a Saturday schedule for part-time employees that will minimize labor costs while mecting the demand during all shifts on a day. Part-time employees receive $7.60 per hour. One full-time employee starts work at 11:00, works 4 hours, thkes an hour for lunch, and returns for another 4 hours. The other full-time employee starts working at 13:00, and works for 4 hours, takes a break for dinner, and comes back for another 4 hours. Total number of full-time and part-time employees needed during several periods of the day are listed below: a) Formulate a minimum-cost schedule tor the part-time employecs using linear programming. (Excel solver) X : number of employees started to work at time slot i,i=1,11 Minimize total employee cost S.t. employee requirement is satisfied for each time slot. b) Assuming part-time employces can work either a 3-or 4-bour shift, formulate a minimum eont schedole for the part-time employees using linear programming. min DVs: X : number of employees started to work at time slot i and works for 4 hrs, i=1,11 Y : number of employees started to work at time slot i and works for 3 hrs, i=1,.11 Minimize total employee cost s.t. employee requirement is satisfied for each time slot. c) Suppose that the university management is not happy with over-employment. Formulate a linear programming model to minimize the total number of excess part-timg employeer. DVs: X: number of employees started to work at time slot i and works for 4 hrs, i=1,11 Yfi number of employees started to work at time slot i and works for 3hrs,i=1.11 S: number of over employment at time slot i,i=1,..11. Minimize total number of overemployment 5.t. employee number t overemployment is equal to employee requirement for each time slot. d) Formulate a linear program to minimize the maximum excess number of cmployees on any shift. DVs: X : number of employees started to work at time slot i and works for 4 hrs, i=1,11 Y; number of employees started to work at time slot i and works for 3 hrs, i=1,..11 S. number of over employment at time slot i,i=1,11, S: Maximum of overemployment Minimize maximum of overemployment s.t. employee number + overemployment is equal to employee requirement for each time slot. Maximum overemployment is greater than or equal to overemployment for each period
