A note on study on proportionate flowshop scheduling with due-date assignment and position-dependent weights

This article examines proportionate flow-shop scheduling with general earliness/tardiness costs under two due-date assignment models: the common and slack models. The objective is to determine the optimal job sequence and due dates to minimize a total penalty function that includes earliness and tardiness penalties, the number of early and delayed jobs, and the due-date assignment cost. Several optimal structural properties are derived, and two polynomial-time dynamic programming (DP) algorithms are proposed to solve the problems, with a time complexity of O(u 4 ), and u is the number of jobs.

We study single-machine bicriteria scheduling problems with position-dependent weights. Due date costs and penalty costs can affect the decision-maker’s profit. Therefore, how to optimize the benefits and balance of these costs for decision-makers is the focus of this research. This paper discusses three models: weighted-sum scheduling problem, constrained scheduling problem, Pareto scheduling problem. It analyzes the properties of bicriteria schedule, determines the optimal due dates (usually referred to as different due dates: DIF), and gives the corresponding polynomial solvable algorithms.

We study the problem of two-machine no-wait flowshop scheduling with learning effect and convex resource-dependent processing times. Under the condition of the due-date assignment with common flow allowance (i.e. slack (SLK) due-date assignment), we provide a bi-criteria analysis where the first criterion is to minimise the scheduling criteria (i.e. the weighted sum of earliness, tardiness and flow allowance costs), and the second criterion is to minimise the resource consumption cost (i.e. the weighted sum of resource consumption cost). The objective is to determine the optimal job sequence, resource allocations and common (flow allowance) slack time that minimise the three different versions of the two criteria. We prove that these problems can be solved in polynomial time.

Corrigendum to “Two-stage no-wait proportionate flow shop scheduling with minimal service time variation and optional job rejection” [European Journal of Operational Research, 305, 608-616