Common due-window problem: Polynomial algorithms for a given processing sequence

The paper considers the Common Due-Window (CDW) problem where a single machine processes a certain number of jobs against a common due-window. Each job possesses different processing times but different and asymmetric earliness and tardiness penalties. The objective of the problem is to find the processing sequence of jobs, their completion times and the position of the given due-window to minimize the total penalty incurred due to tardiness and earliness of the jobs. This work presents exact polynomial algorithms for optimizing a given job sequence for a single machine with the run-time complexity of O(n²), where n is the number of jobs. We also provide an O(n) algorithm for optimizing the CDW with unit processing times. The algorithms take a sequence consisting of all the jobs (J_i, i = 1, 2, ..., n) as input and return the optimal completion times, which offers the minimum possible total penalty for the sequence. Furthermore, we implement our polynomial algorithms in conjunction with Simulated Annealing (SA) to obtain the best processing sequence. We compare our results with that of Biskup and Feldmann for different due-window lengths.