In this paper we consider a total penalty for the n job, one machine scheduling problem in which all jobs have a common due date. This penalty function is based on the due date value and on the earliness or the lateness of each job in the selected sequence. The main objective is to determine the optimal value of this due date and an optimal sequence to minimize a total penalty function. We prove that the optimal due date result can be generalized to the parallel machine problem. The problem of simultaneously available jobs on several parallel and identical machines. The problem is to find the optimal due date, assuming this to be the same for all jobs and we present a simple heuristic to find an approximate solution. On the basis of a limited experiment, we observe that the heuristic is very effective solution.
The Bulletin of Society for Mathematical Services and Standards (Volume 1)
J. K. Mane and K. P. Ghadle, "Common Due-Date Assignment and Job Scheduling on Single Machine and Parallel Machines", The Bulletin of Society for Mathematical Services and Standards, Vol. 1, pp. 6-13, 2012