Single machine weighted earliness–tardiness penalty problem with a common due date

In this paper, we have considered a class of single machine job scheduling problems where the objective is to minimize the weighted sum of earliness–tardiness penalties of jobs. The weights are job-independent but they depend on whether a job is early or tardy. The restricted version of the problem where the common due date is smaller than a critical value, is known to be NP-complete. While dynamic programming formulation runs out of memory for large problem instances, depth-first branch-and-bound formulation runs slow for large problems since it uses a tree search space. In this paper, we have suggested an algorithm to optimally solve large instances of the restricted version of the problem. The algorithm uses a graph search space. Unlike dynamic programming, the algorithm can output optimal solutions even when available memory is limited. It has been found to run faster than dynamic programming and depth-first branch-and-bound formulations and can solve much larger instances of the problem in reasonable time. New upper and lower bounds have been proposed and used. Experimental findings are given in detail.