Bicriterion Optimization for Flow Shop with a Learning Effect Subject to Release Dates

Ji-Bo Wang,Jian Xu,Jing Yang

doi:10.1155/2018/9149510

Abstract

This paper investigates a two-machine flow shop problem with release dates in which the job processing times are variable according to a learning effect. The bicriterion is to minimize the weighted sum of makespan and total completion time subject to release dates. We develop a branch-and-bound (B&B) algorithm to solve the problem by using a dominance property, several lower bounds, and an upper bound to speed up the elimination process of the search tree. We further propose a multiobjective memetic algorithm (MOMA), enhanced by an initialization strategy and a global search strategy, to obtain the Pareto front of the problem. Computational experiments are also carried out to examine the effectiveness and the efficiency of the B&B algorithm and the MOMA algorithm.

Highlights

In many industrial systems, logistics, and service settings, the processing times of jobs can decrease due to the learning effects, i.e., firms and employees perform a job over and over and they learn how to perform more efficiently [1, 2]
In this paper, we consider the two-machine flow shop scheduling problem with position-dependent learning effect and release dates, and the objective is to minimize the weighted sum of makespan and total completion time
We considered a bicriterion makespan and total completion time minimization flow shop scheduling with a learning effect subject to release dates

Summary

Introduction

Logistics, and service settings, the processing times of jobs can decrease due to the learning effects, i.e., firms and employees perform a job (task) over and over and they learn how to perform more efficiently [1, 2]. Feng [24], Wang and Zhang [21], Wu et al [25], Shiau et al [26], Lu [27], Qin et al [28], He [29], and Wang et al [30] considered flow shop scheduling problems with learning effects, but without release dates. [20] considered the flow shop scheduling problems with time-dependent learning effect, i.e., if job J j is in position l of a schedule, the actual processing time pijl of job J j on machine. In this paper, we consider the two-machine flow shop scheduling problem with position-dependent learning effect and release dates, and the objective is to minimize the weighted sum of makespan and total completion time.

Notations and Assumptions

Dominance Conditions

Computational Study

Findings

Summary and Future Research