A Two-Stage Three-Machine Flow Shop Assembly Problem Mixed with a Controllable Number and Sum-of-Processing Times-Based Learning Effect by Simulated Annealing Algorithms

Shang-Chia Liu

doi:10.1155/2020/4085718

Abstract

The two-stage assembly scheduling problem is widely used in industrial and service industries. This study focuses on the two-stage three-machine flow shop assembly problem mixed with a controllable number and sum-of-processing times-based learning effect, in which the job processing time is considered to be a function of the control of the truncation parameters and learning based on the sum of the processing time. However, the truncation function is very limited in the two-stage flow shop assembly scheduling settings. Thus, this study explores a two-stage three-machine flow shop assembly problem with truncated learning to minimize the makespan criterion. To solve the proposed model, we derive several dominance rules, lemmas, and lower bounds applied in the branch-and-bound method. On the other hand, three simulated annealing algorithms are proposed for finding approximate solutions. In both the small and large size number of job situations, the SA algorithm is better than the JS algorithm in this study. All the experimental results of the proposed algorithm are presented on small and large job sizes, respectively.

Highlights

Scheduling models usually assumed that the processing time of the job is known and fixed [1]
Biskup, Kuo and Yang [2, 3], and Kuolamas and Kyparisis [7] introduced models that involve a learning effect on two-machine scheduling or flow shop scheduling settings following the same or different learning ideas. ere are a multitude of studies related to two-machine scheduling or flow shop scheduling settings with the learning effect consideration, including [8,9,10,11] and [12]
Wu et al [13] adopted the learning model developed by Biskup [2] to solve a two-stage flow shop scheduling problem with three machines to minimize the makespan. ey devised three simulated annealing (SA) algorithms and three cloud theory-based SA algorithms

Summary

Introduction

Scheduling models usually assumed that the processing time of the job is known and fixed [1]. Adopting the learning model in [3, 14], a branch-and-bound (B&B) algorithm is devised incorporating six (hybrid) particle swam optimization (PSO) methods to solve the two-stage flow shop assembly scheduling problem to minimize the total job completion time. The sum-of-processing times-based learning model is pertinent to process manufacturing in which an initial setup is often followed by a lengthy uninterrupted production process Motivated by this observation, this study introduces the 2-stage 3-machine assembly problem with a sum-of-processing times of already processed jobs learning to minimize the makespan criterion. After fixing the starting temperature (Ti) to 10− 3 and the cooling coefficient (Cf ) to 0.95 (please see Figure 2), we select the parameter Johnson’s algorithm test times (Nr) with a range of 1 to 20 and the interval of 1 and see the difference. It can be observed that regardless of whether the number of work pieces is 8, 10, or 12, the

CPU time Mean

Normality test

Small n

Big n