Proportionate flowshop scheduling with position-dependent weights

This article addresses proportionate flowshop scheduling problems with position-dependent weights wherein the weight is not related to the job but to the position in which the job is scheduled. Common and slack due date assignment models are discussed under a due date assignment framework. The goal is to determine a feasible schedule for all jobs and due dates of all jobs to minimize a total cost function wherein the objective function is of the minsum type. Optimal properties for the problems are proposed, based on which polynomial time algorithms are provided to solve these two problems optimally.