scholarly journals MILP models and valid inequalities for the two-machine permutation flowshop scheduling problem with minimal time lags

2019 ◽  
Vol 15 (S1) ◽  
pp. 223-229
Author(s):  
Imen Hamdi ◽  
Saïd Toumi
Keyword(s):  
Mixed Integer Linear Programming ◽  
Valid Inequalities ◽  
Mixed Integer ◽  
Time Lags ◽  
Scheduling Problem ◽  
Flowshop Scheduling ◽  
Permutation Flowshop ◽  
Feasible Schedule ◽  
Minimal Time ◽  
Flowshop Scheduling Problem

Abstract In this paper, we consider the problem of scheduling on two-machine permutation flowshop with minimal time lags between consecutive operations of each job. The aim is to find a feasible schedule that minimizes the total tardiness. This problem is known to be NP-hard in the strong sense. We propose two mixed-integer linear programming (MILP) models and two types of valid inequalities which aim to tighten the models’ representations. One of them is based on dominance rules from the literature. Then, we provide the results of extensive computational experiments used to measure the performance of the proposed MILP models. They are shown to be able to solve optimally instances until the size 40-job and even several larger problem classes, with up to 60 jobs. Furthermore, we can distinguish the effect of the minimal time lags and the inclusion of the valid inequalities in the basic MILP model on the results.

scholarly journals Branch and bound algorithm for solving the total weighted tardiness criterion for the permutation flowshop scheduling problem with time lags

2021 ◽  
pp. 23-23
Author(s):  
Fatmah Almathkour ◽  
Omar Belgacem ◽  
Said Toumi ◽  
Bassem Jarboui
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Total Weighted Tardiness ◽  
Time Lags ◽  
Scheduling Problem ◽  
Flowshop Scheduling ◽  
Permutation Flowshop ◽  
Weighted Tardiness ◽  
Time Requirements ◽  
Flowshop Scheduling Problem

This paper deals with the permutation flowshop scheduling problem with time lags constraints to minimize the total weighted tardiness criterion by using the Branch and Bound algorithm. A new lower bound was developed for the flowshop scheduling problem. The computational experiments indicate that the proposed algorithm provides good solution in terms of quality and time requirements.

Optimization by Pre-Assignment of Processes for Re-Entrant Flowshop Scheduling Problem

2012 ◽  
Author(s):  
Rei Hino ◽  
Tomoya Osada
Keyword(s):  
Optimal Schedule ◽  
Optimization Procedure ◽  
Flow Time ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Flowshop Scheduling ◽  
Production Schedule ◽  
Feasible Schedule ◽  
Work In Process ◽  
Flowshop Scheduling Problem

A new optimization procedure for a re-entrant flowshop scheduling problem is proposed to plan a medium sized production schedule by mixed integer programming. Flow time is an index used to evaluate production work-in-process. The flow time is calculated from the total required cycle terms after a feasible schedule is planned. In the present paper, the reverse procedure is performed: the total cycle term is assumed before the scheduling, and the feasible schedule is planned under the assumed terms. The assumption of the total cycle term restricts the pre-assignment of every process into a corresponding cycle term. Therefore some pre-assignments never yield a feasible schedule and are eliminated from the evaluation. Methods for the assumption of the total cycle terms and for the examination of the pre-assignment of the processes are described here. The amount of times required to plan the optimal schedule is evaluated for different sizes of problems in order to validate the proposed procedures.

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