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This article considers scheduling problems with resource allocation, deterioration effect and position-dependent weights on a single machine. For two different due-date assignment methods—i.e. common (CON) due-date assignment and slack (SLK) due-date assignment—a bi-criteria analysis is provided wherein the first objective is to minimize the weighted sum of the absolute value in lateness with a common due date (a common flow-allowance), and the second objective is to minimize the weighted sum of resource consumption. Optimality properties and algorithms are proposed to solve three different versions of considering these two criteria. [ABSTRACT FROM AUTHOR]

This article addresses single machine resource allocation scheduling problems with learning effects, where learning effects mean job-dependent position-based learning effects. For the common due-date assignment (CON) and slack due-date assignment (SLK) methods, a bi-cost analysis of the scheduling cost and the total weighted resource consumption cost is provided. The objective is to determine the optimal job sequence and the resource allocation simultaneously, such that the scheduling cost (the total weighted resource consumption cost) is minimized subject to the total weighted resource consumption cost (the scheduling cost) being limited. Solution procedures are provided for the problems under consideration. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]