Two-machine flow shop with synchronized periodic maintenance

Abstract

In the literature, some works deal with the two-machine flow shop scheduling problem under availability constraints. Most of them consider those constraints only for one machine at a time and also with limited unavailability periods. In this work, we were interested by the unlimited periodic and synchronized maintenance applied on both machines. The problem is NP-hard. We proposed a mixed integer programming model and a variable neighborhood search for solving large instances in order to minimize the makespan. Computational experiments show the efficiency of the proposed methods.

Scheduling with day shifts and breaks

“…Further research may focus on problems with some other criteria such as minimizing total completion time (Parsa et al., 2019; Zhu et al., 2019) and maximizing the noon break period under a given deadline for all the jobs or problems in some other production environments such as flow shop (Hakeem‐Ur‐Rehman et al., 2019; Krim et al., 2019b; Ferone et al., 2020; de Siqueira et al., 2020), job shop (Benttaleb et al., 2018, 2019; Kubiak et al., 2020), and parallel machine with a single server (Arnaout, 2017; Bektur and Saraç, 2019). It is also worth considering scheduling problems in industries that are open around the clock, such as in airports, restaurants, hospitals, movie theaters, and in some retail stores, where morning, afternoon, and night shifts are involved.…”

“…(2018, 2019), Huo and Zhao (2018), Kaabi (2019), Krim et al. (2019a, 2019b, 2020), Luo and Liu (2017), Najat et al. (2019), Shen and Zhu (2018), Touat et al.…”

Polynomial algorithms for some scheduling problems with one nonrenewable resource

“…The subchain (7, 8, 9, 10) is an OC-subchain: e α = 7, e β = 9, e γ = 10, ∆ − = −a 7 − a 8 − a 9 = 4 and ∆ + = a 10 = 1. The subchain (13,14) is an OP-subchain where β does not exists. So, ∆ − = 0 and ∆ + = a 13 + a 14 = 3 Theorem 3.2.…”

“…Flow shop scheduling is a type of scheduling where jobs need to be processed on a set of machines in identical order [25]. In [13], the authors deal with the two-machine flow shop scheduling problem with unlimited periodic and synchronized maintenance applied on both machines. Kaplan and Amir have introduced a simple method for determining the feasibility of the relocation problem [12].…”