Introduction to Management Science 12th Edition by Bernard Taylor

Exercise 39

In Problem, Corsouth Mortgage Associates is considering hiring some hourly, part-time computer operators in addition to its permanent and temporary operators. A part-time operator can process 12 accounts per hour, averages 0.16 error per hour, and is paid $4.50 per hour. Corsouth wants to know the number of permanent and temporary employees it should use, plus the number of part-time hours it should arrange for. Formulate and solve a mixed integer model for this problem.
Problem
Corsouth Mortgage Associates is a large home mortgage firm in the Southeast. It has a pool of permanent and temporary computer operators who process mortgage accounts, including posting payments and updating escrow accounts for insurance and taxes. A permanent operator can process 220 accounts per day, and a temporary operator can process 140 accounts per day. On average, the firm must process and update at least 6,300 accounts daily. The company has 32 computer workstations available. Permanent and temporary operators work 8 hours per day. permanent operator averages about 0.4 error per day, whereas a temporary operator averages 0.9 error per day. The company wants to limit errors to 15 per day. A permanent operator is paid $120 per day, whereas a temporary operator is paid $75 per day. Corsouth wants to determine the number of permanent and temporary operators it needs to minimize cost. Formulate and solve an integer programming model for this problem and compare this solution to the non-integer solution.