Francis Sourd This paper addresses the one machine scheduling problem in which $n$ jobs have distinct due dates with earliness and tardiness costs. Fast neighborhoods are proposed for the problem. They are based on a block representation of the schedule and can be computed in $O(n^2)$. A timing operator is presented as well as swap and extract-and-reinsert … Read more
In one-machine scheduling, MIP time-indexed formulations are often used to provide very good lower bounds through Lagrangian relaxations. In order to get an improved lower bound, we add valid cuts to a time-indexed formulation and show we still have a Lagrangian relaxation that can be solved as a shortest path in a graph. Two branch-and-bound … Read more
This paper focuses on a multi-objective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multi-objective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that … Read more
We consider the parallel machine scheduling problem where jobs have different earliness-tardiness penalties and a restrictive common due date. This problem is NP-hard in the strong sense. In this paper we define an exponential size neighborhood for this problem and prove that finding the local minimum in it is an NP-hard problem. The main contribution … Read more
This paper addresses the one-machine scheduling problem with earliness-tardiness penalties. We propose a new branch-and-bound algorithm that can solve instances with up to 50 jobs and that can solve problems with even more general non-convex cost functions. The algorithm is based on the combination of a Lagrangean relaxation of resource constraints and new dominance rules. … Read more
This paper is devoted to basic scheduling problems in which the scheduling cost of a job is not a function of its completion time. Instead, the cost is derived from the integration of a cost function over the time intervals on which the job is processed. This criterion is specially meaningful when job preemption is … Read more
This paper addresses the parallel machine scheduling problem in which the jobs have distinct due dates with earliness and tardiness costs. New lower bounds are proposed for the problem, they can be classed into two families. First, two assignment-based lower bounds for the one-machine problem are generalized for the parallel machine case. Second, a time-indexed … Read more
The one-machine scheduling problem with sequence-dependent setup times and costs and earliness-tardiness penalties is addressed. This problem is NP-complete, so that local search approaches are very useful to efficiently find good feasible schedules. In this paper, we present an extension of the dynasearch neighborhood for this problem. Finding the best schedule in this neighborhood is … Read more
This paper addresses the one-machine scheduling problem where the objective is to minimize a sum of costs such as earliness-tardiness costs. Since the sequencing problem is NP-hard, local search is very useful for finding good solutions. Unlike scheduling problems with regular cost functions, the scheduling (or timing) problem is not trivial when the sequence is … Read more
It is with the aim of solving scheduling problems with irregular cost functions that this paper focuses on the continuous assignment problem. It consists in partitioning a d dimensional region into subregions of prescribed volumes so that the total cost is minimized. The dual problem of the continuous assignment problem is an unconstrained maximisation of … Read more