Bi-criteria Flow Shop Research Articles

Notes on “A bicriteria flowshop scheduling with a learning effect”

The aim of this paper is to point out that the integer programming model proposed by Eren and Güner [T. Eren, E. Güner, A bicriteria flowshop scheduling with a learning effect, Applied Mathematical Modelling 32 (2008) 1719–1733] is incorrect. We propose a mixed 0–1 programming model for the same scheduling problem based on their model.

M-machine SDST flow shop scheduling using modified heuristic genetic algorithm

Bi-criteria flow shop scheduling problems with sequence dependent set up time (SDST) have seen an increasing attention of managers and researchers in recent years. A very restricted research has been reported on bi-criteria SDST flow shop scheduling problems dealing with due date related performance measures. In the present work, a modified heuristic based genetic algorithm (MHGA) has been developed for the aforesaid scheduling problem subject to the minimization of weighted sum of total weighted squared tardiness and makespan criterion. The modified heuristic algorithms, along with other available heuristics and dispatching rules in the literature have also being developed to solve the problem instances given by Taillard. A computational analysis has been made to evaluate the performance of the proposed MHGA for upto 200 jobs and 20 machines problems. Comparative analysis with the help of defined performance index known as relative percentage deviation (RPD) verifies that it is viable and effective approach when compared with others heuristic/dispatching rules based genetic algorithms for the SDST flow shop scheduling, especially for larger sized problems. Keywords: Flow shop scheduling, Modified Heuristic Genetic algorithm (MHGA), Sequence dependent set up time, makespan, total weighted squared tardiness.

A multi-objective scatter search for a bi-criteria no-wait flow shop scheduling problem

The flow shop problem as a typical manufacturing challenge has gained wide attention in academic fields. This article considers a bi-criteria no-wait flow shop scheduling problem (FSSP) in which weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a FSSP has been proved to be NP-hard in a strong sense, a new multi-objective scatter search (MOSS) is designed for finding the locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm (GA), i.e. SPEA-II. The computational results show that the proposed MOSS performs better than the above GA, especially for the large-sized problems.

A grasp algorithm for m-machine flowshop scheduling problem with bicriteria of makespan and maximum tardiness

In this paper we address the problem of minimizing the weighted sum of makespan and maximum tardiness in an m-machine flow shop environment. This is a NP-hard problem in the strong sense. An attempt has been made to solve this problem using a metaheuristic called Greedy Randomized Adaptive Search Procedure (GRASP). GRASP is a competitive algorithm and is a meta-heuristic for solving combinatorial optimization problems. We have customized the basic concepts of GRASP algorithm to solve a bicriteria flow shop problem and a new algorithm named B-GRASP (Bicriteria GRASP algorithm) is proposed. The new proposed algorithm is evaluated using benchmark problems taken from Taillard and compared with the existing simulated annealing based heuristic developed by Chakravarthy and Rajendran. Computational experiments indicate that the proposed algorithm is much better than the existing one in all cases.

A bicriteria flowshop scheduling with a learning effect

In many situations, a worker’s ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the learning effect. In this paper the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes a weighted sum of total completion time and makespan. Total completion time and makespan are widely used performance measures in scheduling literature. To solve this scheduling problem, an integer programming model with n 2 + 6 n variables and 7 n constraints where n is the number of jobs is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, the problem with up to 30 jobs can be solved. A heuristic algorithm and a tabu search based heuristic algorithm are presented to solve large size problems. Experimental results show that the proposed heuristic methods can solve this problem with up to 300 jobs rapidly. According to the best of our knowledge, no work exists on the bicriteria flowshop with a learning effect.

A local search using solution fragments for the 2-machine bicriteria scheduling problem

In this work, we introduce a local search strategy for combinatorial optimization problems which explores neighborhoods obtained using fragments of current solutions. We apply the approach to the well-known $\mathcal{NP}$ -hard 2-machine bicriteria flowshop scheduling problem. Computational experiments using benchmark data show the approach to be effective when compared to other algorithms available for the problem.

A bi-criteria two-machine flowshop scheduling problem with a learning effect

This paper addresses a bi-criteria two-machine flowshop scheduling problem when the learning effect is present. The objective is to find a sequence that minimizes a weighted sum of the total completion time and the maximum tardiness. In this article, a branch-and-bound method, incorporating several dominance properties and a lower bound, is presented to search for the exact solution for small job-size problems. In addition, two heuristic algorithms are proposed to overcome the inefficiency of the branch-and-bound algorithm for large job-size problems. Finally, computational results for this problem are provided to evaluate the performance of the proposed algorithms.

A bicriteria flowshop scheduling problem with setup times

Most of research in production scheduling is concerned with the minimization of a single criterion. However, scheduling problems often involve more than one aspect and therefore require bicriteria analysis. In this study, bicriteria two-machine flowshop scheduling problem with setup times is considered. The objective function of the problem is minimization of the weighted sum of total completion time and total tardiness. An integer programming model is developed for the problem which belongs to NP-hard class. Only small size problems with up to 20 jobs can be solved by the proposed integer programming model. Heuristic methods are also used to solve large size problems. These heuristics are four tabu search based heuristics and random search method. According to computational results the tabu search based methods are effective in finding problem solutions with up to 1000 jobs.

An Ant Colony Optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem

Consider the 2-machine flowshop scheduling problem with the objective of minimizing both the total completion time and the makespan criteria. The latter is assumed to be optimized prior to the former. In view of the NP -hardness of the problem an Ant Colony Optimization approach is proposed to solve it. The heuristic also uses feature of Simulated Annealing search and local search algorithms. Computational experiments show its effectiveness compared to existing heuristics. The extension to the total completion time problem is also studied.

An efficient branch-and-bound algorithm for the two-machine bicriteria flowshop scheduling problem

Stability problems in mechanical product assembly sequence planning have drawn a great amount of research interest in recent years. Most proposed methodologies involve complex geometric and physical analyses. As a result, even for a simple structure, it is difficult to take all the important criteria into account and find efficient solutions. It is also difficult to find an adequate product model for stable assembly analysis. In this paper, three matrices are used to represent the required assembly information for a product model. Methods for using the matrix-based product model and a genetic algorithm, in forward assembly sequence planning, are developed. Stability, contact, and reorientation measures are incorporated into the fitness function of the genetic algorithm based assembly planner. Potential assembly plans are also checked for geometric feasibility. As a result, the planner finds enhanced product assembly sequences, with respect to the initially supplied sequences, that are improved for stability, that require fewer assembly direction reorientations, and that meet product geometric assembly constraints.

An efficient branch-and-bound algorithm for the two-machine bicriteria flowshop scheduling problem

In this study, the two-machine bicriteria flowshop scheduling problem is addressed. The objective is to minimize a weighted sum of total flowtime and makespan. Different branch-and-bound algorithms have already appeared in the literature for this problem. In this study, a more efficient branch-and-bound algorithm is presented. The proposed algorithm and the existing ones are compared on randomly generated problems. The computational analysis on problems up to 20 jobs shows that the proposed branch-and-bound algorithm is more efficient than the others, including the best-known algorithm. The upper bound used in the proposed branch-and-bound algorithm, a two-phase hybrid heuristic method, is also shown to be efficient. Its overall average error on the randomly generated problems is 0.000139, that is, almost equal to the optimal solution.

A Genetic Algorithm for a Bicriteria Flow-Shop Scheduling Problem

In this paper, we consider a bicriteria two-machine flow-shop scheduling problem which is to simultaneously minimize both Cmax and Tmax criteria, and we propose a new genetic algorithm for enumerating all nondominated solutions for this problem. Our algorithm is constructed by incorporating several existing strategies developed for multi-objective optimization problems together with a new strategy which we call seeding strategy that seeds some good individuals in the initial population. We perform computational experiments in order to compare our algorithm with other existing methods.We observe from our computational results that our algorithm produces nondominated solutions very close to exact ones, and outperforms other existing heuristics.

Genetic algorithms for the two-stage bicriteria flowshop problem

This paper considers the two-stage bicriteria flow shop scheduling problem with the objective of minimizing the total flow time subject to obtaining the optimal makespan. In view of the NP-hard nature of the problem, two Genetic Algorithms (GA) based approaches are proposed to solve the problem. The effectiveness of the proposed GA based approaches is demonstrated by comparing their performance with the only known heuristic for the problem. The computational experiments show that the proposed GA based approaches are effective in solving the problem and recommend that the proposed GA based approaches are useful for solving the multi-machine, multi-criteria scheduling problems.