No-wait scheduling of a two-machine flow-shop to minimise the makespan under non-availability constraints and different release dates

Abstract

In this paper, we consider the two-machine no-wait flow-shop scheduling problem, when every machine is subject to one non-availability constraint and jobs have different release dates. The nonavailability intervals of the machines overlap and they are known in advance. We aim to find a nonresumable schedule that minimizes the makespan. We propose several lower bounds and upper bounds. These bounding procedures are used in a branch-and-bound algorithm. Computational experiments are carried out on a large set of instances and the obtained results show the effectiveness of our method.

A Bi-Objective Approach to Minimize Makespan and Energy Consumption in Flow Shops with Peak Demand Constraint

“…Two kinds of assumptions are investigated by the researchers: (1) the unavailable intervals are known and fixed in advance; and (2) the unavailable intervals are flexible and scheduled by the manager. In the first assumption, some researchers considered one maintenance period in the horizon, for example the authors of [15][16][17] focused on scheduling resumable jobs in two-machine flow shops and the authors of [18,19] focused on the non-resumable jobs. Some researchers considered that the intervals are periodically fixed, for example the authors of [20][21][22] investigated the two-machine flow shops and the authors of [23,24] studied the multi-machine flow shops.…”

“…The purpose of our paper is to establish an integrated model to minimize the bi-objective of makespan and energy consumption in flow shops with PM constraint and peak demand constraint. Compared with the methods in [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], this paper belongs to the energy-efficient scheduling problem. Compared with the methods in , the main difference of this paper is considering the impact of PM constraint and peak demand constraint.…”

“…The constraint in Equation ( 18) means that the energy consumption of machine M j during tth interval is caused by three parts: processing jobs, idle time, and setup. The constraint in Equation (19) specifies the overlap between the processing time of each job on M j and the tth interval, based on which the energy consumption can be obtained using the power demand per unit time. The constraint in Equation (20) shows that, if one setup exists in the idle time between O [k−1] j and O [k] j , then no energy consumption occurs in this idle time; otherwise, the idle-time energy consumption needs to be accounted.…”

Two-machine flow shop with synchronized periodic maintenance

“…They presented a polynomial-time approximation scheme to minimize makespan. Ben chihaoui et al [9] considered also the no-wait process where each machine is subject to one unavailability constraint and the jobs have different release dates. They studied the non-resumable schedule that minimize the makespan.…”

Um estudo computacional de novas regras de prioridade para flow shop com tempos de setup e diferentes datas de liberação

“…e Kovalyov e Werner (1997) apresentaram esquemas de aproximação polinomial Tadei et al (1998). descreveram vários procedimentos branch-and-bound e aplicaram diferentes limitantes inferiores e esquemas de ramificação em exemplares com até 200 tarefas.Kashyrskikh, Potts e Sevastianov (2001) fizeram a análise do pior caso do algoritmo modificado dePotts (1985) Chihaoui et al (2011). desenvolveram um algoritmo branch-and bound eficiente para exemplares com até 20 tarefas para o problema no-wait (sem espera entre as operações de uma tarefa) sujeito à restrição de não disponibilidade.…”