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.
Highlights
This paper addresses the two-machine permutation flowshop scheduling problem with minimal time lags where the objective is minimizing the total tardiness
The contribution of this paper is twofold: First, we propose two mathematical formulations distinguished by the used decision variables which are: the completion time variables and the idle time variables
We exploit some dominance rules from the literature for the first set, and we propose a lower bound on the completion time for the second set
Summary
This paper addresses the two-machine permutation flowshop scheduling problem with minimal time lags where the objective is minimizing the total tardiness. At the same time, Hamdi and Loukil (2015b) extend the research about the permutation flowshop problem with minimal time lags by considering the case of m-machine and optimizing the total number of tardy jobs criterion. They proposed some heuristic procedures based on known and new rules. In the same context, Dhouib et al (2013) proposed a mixed-integer mathematical programming formulation for the permutation flowshop problem with minimal and maximal time lags while the objective is to hierarchically minimize two criteria, the primary criterion is the minimization of the number of tardy jobs and the secondary one minimizes the makespan.
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