Polyhedral results and valid inequalities for the Continuous Energy-Constrained Scheduling Problem - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Access content directly
Journal Articles Discrete Applied Mathematics Year : 2019

Polyhedral results and valid inequalities for the Continuous Energy-Constrained Scheduling Problem

Abstract

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.
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Dates and versions

hal-01391403 , version 1 (03-11-2016)

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Margaux Nattaf, Tamás Kis, Christian Artigues, Pierre Lopez. Polyhedral results and valid inequalities for the Continuous Energy-Constrained Scheduling Problem. Discrete Applied Mathematics, 2019, 258, pp.188-203. ⟨10.1016/J.DAM.2018.11.008⟩. ⟨hal-01391403⟩
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