Sequence-dependent group scheduling problem on unrelated-parallel machines

In this research we address a sequence-dependent group scheduling problem on a set of unrelated-parallel machines where the run time of each job differs on different machines. To benefit both producer and customers we attempt to minimize a linear combination of total weighted completion time and total weighted tardiness. Since the problem is shown to be NP-hard, meta-heuristic algorithms based on tabu search are developed to find the optimal/near optimal solution. For some small size yet complex problems, the results from these algorithms are compared to the optimal solutions found by CPLEX. The result obtained in all of these problems is that the tabu search algorithms could find solutions at least as good as CPLEX but in drastically shorter computational time, thus signifying the high degree of efficiency and efficacy attained by the former.Keywords: Bi-criteria, Group scheduling, Sequence-dependent setup time, Mixed-integer linear programming, Unrelated-parallel machines, Tabu searc

Scheduling Jobs in Flowshops with the Introduction of Additional Machines in the Future

This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/expert-systems-with-applications/.The problem of scheduling jobs to minimize total weighted tardiness in flowshops,\ud with the possibility of evolving into hybrid flowshops in the future, is investigated in\ud this paper. As this research is guided by a real problem in industry, the flowshop\ud considered has considerable flexibility, which stimulated the development of an\ud innovative methodology for this research. Each stage of the flowshop currently has\ud one or several identical machines. However, the manufacturing company is planning\ud to introduce additional machines with different capabilities in different stages in the\ud near future. Thus, the algorithm proposed and developed for the problem is not only\ud capable of solving the current flow line configuration but also the potential new\ud configurations that may result in the future. A meta-heuristic search algorithm based\ud on Tabu search is developed to solve this NP-hard, industry-guided problem. Six\ud different initial solution finding mechanisms are proposed. A carefully planned\ud nested split-plot design is performed to test the significance of different factors and\ud their impact on the performance of the different algorithms. To the best of our\ud knowledge, this research is the first of its kind that attempts to solve an industry-guided\ud problem with the concern for future developments

Heuristic Algorithm to Minimize Total Weighted Tardiness on the Unrelated Parallel Machine with Sequence Dependent Setup and Future Ready Time

This study presents a heuristic algorithm to minimize total weighted tardiness on unrelated parallel machines with sequence-dependent setup time and future ready time. We propose a new rule based on Apparent Tardiness Cost (ATC). The performance of the rule is evaluated on unrelated parallel machines. In order to solve a problem, we use a look-ahead method and a job-swap method. When a machine becomes idle, the heuristic compares the jobs on the machine and selects the one with the smallest total tardiness value to carry out a process. The propose heuristic is divided into three stages: The first stage employs the newly introduced dispatching rule, ATC with continuous setup and ready time for unrelated parallel machines (ATCSR_UP), along with a look-ahead heuristic to select the initial job for each machine. The second stage, consisting of several iterations, schedules the rest of the job on the machine. Each iteration starts by finding the job with the smallest tardiness. The ATCSR_Rm rule proposed by Lin and Hsieh (2013) concerns the unrelated-parallel-machine scheduling which this study examines, so we compare our ATC-based rule with their proposed rule. Although they study a separable setup time in their research, no other paper than Lin and Hsieh (2003) focus on unrelated parallel machine with future ready times. In their WSPT term, they consider the processing time for each job; our own rule considers processing time, setup time, job ready time, and machine time. We consider the setup time, job ready time, and machine time because — according to the continuous sequence-dependent setup rule — setup time should be included in processing time (Yue and Jang 2013). In addition, job ready time and machine time should also be included in the processing time. Adding setup time 〖(s〗_(i,j)), job ready time (r_j), and machine time (t_m) to the formula thus makes the formula more accurate. Lin and Hsieh (2013) use max(r_j,t_i+s_(i,j) ) for the slack term, and they compare the ready time with the sum of the machine available time 〖(t〗_i) and the setup time 〖(s〗_(i,j)). However, in our formula, we consider ready time, machine time, and current time. Current time (t) is used when a job might come at a future time when the machine in question is idle or has finished the job. The last term of the propose heuristic is the ready term, which uses both ready time (r_j) and machine time (t_m), because it needs to specify whether ready time (r_j) or machine time (t_m) goes first. If a job is ready to be processed but the machine is not ready, the job has to wait. We use ready time (r_j) and machine time (t_m) because this makes the formula more suitable for practical, real-world us

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for the TWT and TWET problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm for solving the preemptive relaxation formulated as a mixed integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines, and then we exploit recent advances in solving the non-preemptive single machine TWT and TWET problems for constructing non-preemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances up to 5 machines and 200 jobs

Heuristic Algorithms to Minimize Total Weighted Tardiness on the Single Machine and Identical Parallel Machines with Sequence Dependent Setup and Future Ready Time

This study generates heuristic algorithms to minimize the total weighted tardiness on the single machine and identical parallel machines with sequence dependent setup and future ready time. Due to the complexity of the considered problem, we propose two new Apparent Tardiness Cost based (ATC-based) rules. The performances of these two rules are evaluated on the single machine and identical parallel machines. Besides of these two rules, we also propose a look-ahead identical parallel machines heuristic (LAIPM). When a machine becomes idle, it selects a job to process from available jobs and near future jobs. The proposed method, LAIPM, is evaluated with other look-ahead methods on the identical parallel machines