This paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs. We develop dominance properties and lower bounds, and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm. Computational experiments are performed on r...

The scheduling problem of minimizing total tardiness on a single machine is known to be NP -hard in the ordinary sense. In this paper, we consider the special case of the problem when the processing times pj and the due dates dj of the jobs j, j ∈ N = {1, 2, . . . , n}, are oppositely ordered: p1 ≥ p2 ≥ . . . ≥ pn and d1 ≤ d2 ≤ . . . ≤ dn. It is shown that already this special case is NP -hard ...

We study a common due-date assignment problem on two parallel uniform machines. The jobs are assumed to have identical processing times, and job-dependent asymmetric earliness tardiness unit costs. scheduler may process only subset of the jobs, i.e. option job-rejection is allowed. objective function consists three cost components: total earliness-tardiness all scheduled due-date, rejection cos...

This paper considers the problem of scheduling n jobs in the generalized tardiness flow shop problem with m machines. Seven algorithms are developed for finding a schedule with minimum total tardiness of jobs in the generalized flow shop problem. Two simple rules, the shortest processing time (SPT), and the earliest due date (EDD) sequencing rules, are modified and employed as the core of seque...

This paper proposes an application of probabilistic technique, namely Gaussian process regression, for estimating an optimal sequence of the single machine with total weighted tardiness (SMTWT) scheduling problem. In this work, the Gaussian process regression (GPR) model is utilized to predict an optimal sequence of the SMTWT problem, and its solution is improved by using an iterated local sear...

A partial order on a job set is called consistent, if it has a linear extension which is an optimal solution to the total tardiness problem of the job set. The concept of proper augmentations of consistent partial orders is based on Emmons’ well-known dominance theorem. In this paper, we address the question of whether the proper augmentation of a consistent partial order always results in a pa...

The job shop scheduling problem JSSP is a notoriously difficult problem in combinatorial optimization. In terms of the objective function, most existing research has been focused on the makespan criterion. However, in contemporary manufacturing systems, due-date-related performances are more important because they are essential for maintaining a high service reputation. Therefore, in this study...

The scheduling problem we consider is often faced by manufacturers who make time-sensitive products such as fashion apparel and toys, which typically have large product types and sell only during specific seasons. Consider the production and distribution scheduling decisions such a manufacturer needs to make. The customers (e.g. distributors or retailers) often set due dates on the orders they ...