Common due date assignment scheduling for a no-wait flowshop with convex resource allocation and learning effect

This article addresses the no-wait flowshop scheduling problem with simultaneous consideration of common due date assignment, convex resource allocation and learning effect in a two machine setting. The processing time of each job can be controlled by its position in a sequence and also by allocating extra resource, which is a convex function of the amount of a common continuously divisible resource allocated to the job. The objective is to determine the optimal common due date, the resource allocation and the schedule of jobs such that the total earliness, tardiness and common due date cost (the total resource consumption cost) are minimized under the constraint condition that the total resource consumption cost (the total earliness, tardiness and common due date cost) is limited. Polynomial time algorithms are developed for two versions of the problem.