Scheduling based on earliness and tardiness criteria in assembly job shops

Abstract

In this research, the following four scheduling problems have been studied; (1) single machine problem with earliness cost minimization, (2) single machine problem with the sum of the weighted earliness and weighted tardiness cost minimization, (3) assembly job shop problem with earliness cost minimization, and (4) assembly job shop problem with the sum of weighted earliness and weighted tardiness cost minimization. Four mathematical models based on these four scheduling problems were developed in an effort to obtain optimal solutions. Six heuristic algorithms have been developed to solve the problems. The performances of the heuristic algorithms were demonstrated on some sample test problems. Quality of solutions and CPU time of solutions were the factors of interest. Several properties of optimal solutions for the single machine scheduling problem with the objective of minimizing the weighted earliness penalty have been identified In the research. Algorithms I, III, V, and VI were developed based on these identified properties while the algorithms II and IV were developed based on the tabu search concept. Algorithms I and 11 were developed to solve the first case (1) problem. The results indicate that these two algorithms are able to produce solutions close to optimal in small size problems. The results also show that algorithm I is relatively better than algorithm 11 in large size problem. Algorithms III and IV were developed to solve the second case (2) problem. Both algorithms obtained a small average deviation solutions (i.e.. less than 2%) from optimal in small size test problems. For all problems tested, the algorithm IV is the best algorithm for solving the eariiness/tardiness problems compared to algorithm III and the Ow & Morton algorithm. Algorithm V was developed to solve the third case (3) problem. It obtained an average deviation solutions less than 1% from the optimal. Algorithm VI was developed to solve the fourth case (4) problem. Algorithm VI obtained an average deviation solutions of 2.53% from the optimal.