Flexible solutions in disjunctive scheduling: General formulation and study of the flow-shop case

Abstract

We consider the context of decision support for schedule modification after the computation off-line of a predictive optimal (or near optimal) schedule. The purpose of this work is to provide the decision-maker a characterization of possible modifications of the predictive schedule while preserving optimality. In the context of machine scheduling, the anticipated modifications are changes in the predictive order of operations on the machines. To achieve this goal, a flexible solution feasible w.r.t to operations deadlines, is provided instead of a single predictive schedule. A flexible solution represents a set of semi-active schedules and is characterized by a partial order on each machine, so that the total order can be set on-line, as required by the decision maker. A flexible solution is feasible if all the complete schedules that can be obtained by extension are also feasible.In this paper we develop two main issues. The first one concerns the evaluation of a flexible solution in the worst case allowing to certify if the solution is feasible. The second issue is the computation of feasible (w.r.t deadlines) flexible solutions of maximal flexibility imposed by the decision maker. Under an epsilon-constraint framework, solving this problem allows to find compromise solutions for the flexibility criterion and any minmax regular scheduling criterion. The special case of the flow-shop scheduling problem is studied and computational experiments are carried out.

Tardiness minimisation heuristic for job shop scheduling under uncertainties using group sequences

“…This approach also known as groups of permutable operations. It was first introduced by the LAAS/CNRS laboratory of Toulouse (Erschler and Roubellat, 1989) and has been the main subject of several PhD thesis and other scientific works, such as Esswein (2003), Artigues et al (2005), Pinot (2008), Aloulou and Artigues (2010), Ourari (2011) and Artigues et al (2016).…”

“…Most of the literature findings regarding this method focus on the representation and evaluation of its quality and its robustness. For example, in the work of Artigues et al (2005); Aloulou and Artigues (2010), new measurements for the quality of the flexible schedule generated by this method have been proposed. Such quality is calculated based on a disjunctive graph representation of the groups of permutable operations using a polynomial time algorithm.…”

Single machine total tardiness maximization problems: complexity and algorithms

“…Algorithms for such maximization problems can be used to compute parts of optimal schedules for the original problems, or to cut bad sub-problems in the branching tree of branch-and-bound algorithms (Gafarov et al 2010a(Gafarov et al , 2012. In Aloulou and Artigues (2010), maximization problems were used for solving bi-criteria problems using branch and bound algorithms. On the other side, such problems separately have practical interpretations (for the problem 1(no-idle)|| max T j , they have been discussed e.g.…”