Pierre Lopez

The multi‐skill project scheduling problem (MSPSP) has been first addressed in the scheduling community for more than 15 years. This article deals with a new variant of this problem, the MSPSP with partial preemption, where only a subset of resources can be released during the preemption periods. Like the standard problem, this variant is NP‐hard, because of which we propose in this article a series of heuristic algorithms to solve instances arising from an industrial application. First, we present a serial greedy algorithm, based on priority rules and a flow problem for resource allocation. To improve the solutions of the greedy algorithm, we then introduce a binary tree based search algorithm and a greedy randomized adaptive search procedure (GRASP). Finally, we propose a large neighborhood search (LNS) algorithm integrating exact and heuristic methods. The best results in terms of solution quality and execution time are obtained by combining the GRASP algorithm and LNS approach. Furthermore, the proposed GRASP algorithm is able to find new best results on 56 of 216 instances on a standard MSPSP instance set, which shows the quality of the approach even on special cases of the considered problem.

This paper addresses a scheduling problem with a cumulative, continuously-divisible and renewable resource with limited capacity. During its processing, each task consumes a part of this resource, which lies between a minimum and a maximum requirement. A task is finished when a certain amount of energy is received by it within its time window. This energy is received via the resource and an amount of resource is converted into an amount of energy with a non-decreasing, continuous and linear efficiency function. The goal is to minimize the resource consumption. The paper focuses on an event based mixed integer linear program, providing several valid inequalities which are used to improve the performance of the model. Furthermore, we give a minimal description of the polytope of all feasible assignments to the on/off binary variable for a single activity along with a dedicated separation algorithm. Computational experiments are reported in order to show the effectiveness of the results.