Single Machine Scheduling for Jobs with Individual Due Dates and a Learning effect: Genetic Algorithm Approach

In this paper, we present a genetic algorithm approach that considers the single machine scheduling problem. There are n jobs, in which each job j ( 1 2 j n = , ,..., ) has a normal processing time j p , a due date j d , earliness penalty j α , and tardiness penalty j β . The objective is to find the sequence of jobs that minimizes the weighted sum of earliness and tardiness penalty costs, with a learning effect. The machine idle times are not considered. The worker involved in doing the same operations on a machine, learns the task and the worker become efficient in that job. Thus, in scheduling problems the job processing time depends on the position of the job in a sequence. This is the learning effect. The problem of finding the optimal sequence of jobs is a difficult combinatorial optimization problem. It can be easily seen that there are n! sequences are possible for this problem. Because of the difficult nature of this problem, we use genetic algorithm to obtain the best/optimal sequence of jobs. Various issues related to genetic algorithm such as solution representation, selection methods, and genetic operators are presented. We show via numerical examples (test problems) that the genetic algorithm approach takes only small computation time to solve fairly large problems (50 jobs).