The single machine multiple orders per job scheduling problem

The standard unit of transfer in new semiconductor wafer fabrication facilities is the front opening unified pod (FOUP). Due to automated material handling system and cost concerns, the number of FOUPs in a wafer fab is kept limited. Large 300-mm wafers allow for customer orders to be filled with less than a full FOUP of wafers in these new fabs, thereby making grouping orders from multiple customers into a job necessary. Efficient utilization of FOUP capacity while attaining good system performance is a challenge. We investigate the multiple orders per job scheduling problem, presenting a nonlinear mixed-integer program that encompasses both order grouping (job formation) and job scheduling decisions. Recognizing the tractability limitations of this formulation, we relax the nonlinear constraints so that the problem is solvable using standard commercial solvers. We examine a number of heuristic approaches in an attempt to obtain high quality solutions in an acceptable amount of computation time. We study both optimizationand heuristic-based approaches in two different machine processing environments in an attempt to minimize order total weighted completion time on a single machine. Experimental results demonstrate the difficulty of solving the problem using an optimization-based approach. However, heuristic approaches can find good solutions in a reasonable amount of computation time to this practically motivated scheduling problem.