On electrical load tracking scheduling for a steel plant

Nolde and Morari (2010) study a steel manufacturing scheduling problem where the tasks must be scheduled such that electricity consumption matches to a pre-specified periodic energy chart. They propose a continuous time integer linear programming formulation to solve the problem. In this note, we present an alternative continuous time formulation, focused on the relative positions of tasks and time periods, that improves significantly the computation time

The energy scheduling problem: Industrial case-study and constraint propagation techniques

This paper deals with production scheduling involving energy constraints, typically electrical energy. We start by an industrial case-study for which we propose a two-step integer/constraint programming method. From the industrial problem we derive a generic problem,the Energy Scheduling Problem (EnSP). We propose an extension of specific resource constraint propagation techniques to efficiently prune the search space for EnSP solving. We also present a branching scheme to solve the problem via tree search.Finally,computational results are provided

Parallel machine scheduling with precedence constraints and setup times

This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. Limited discrepancy search methods mixed with local search principles, dominance conditions and specific lower bounds are proposed. The proposed methods are evaluated on a set of randomly generated instances and compared with previous results from the literature and those obtained with an efficient commercial solver. We conclude that our propositions are quite competitive and our results even outperform other approaches in most cases

Frequency assignment in a SDMA satellite communication system with beam decentring feature

International audienceIn satellite communication, Spatial Division Multiple Access (SDMA) has become one of the most promising techniques that can accommodate continuing increase in the number of users and traffic demands. The technology is based on radio resource sharing that separates communication channels in space. It relies on adaptive and dynamic beam-forming technology and well-designed algorithms for resource allocation among which frequency assignment is considered. This paper studies static Frequency Assignment Problem (FAP) in a satellite communication system involving a satellite and a number of users located in a service area. The objective is to maximize the number of users that the system can serve while maintaining the signal to interference plus noise ratio of each user under a predefined threshold. Traditionally, interference is treated as fixed (binary interferences or fixed minimal required separation between frequencies) . In this paper, the interference is cumulative and variable. To solve the problem, we work on both discrete and continuous optimizations. Integer linear programming formulations and greedy algorithms are proposed for solving the discrete frequency assignment problem. The solution is further improved by beam decentring algorithm which involves continuous adjustment of satellite beams and deals with non-linear change of interference

Schedule generation schemes for the job-shop problem with sequence-dependent setup times: dominance properties and computational analysis

We consider the job-shop problem with sequence-dependent setup times. We focus on the formal definition of schedule generation schemes (SGSs) based on the semi-active, active, and non-delay schedule categories. We study dominance properties of the sets of schedules obtainable with each SGS. We show how the proposed SGSs can be used within single-pass and multi-pass priority rule based heuristics. We study several priority rules for the problem and provide a comparative computational analysis of the different SGSs on sets of instances taken from the literature. The proposed SGSs significantly improve previously best-known results on a set of hard benchmark instances

Ordonnancement sous contraintes d'énergie et de ressources humaines

Ce travail s’intéresse à l’ordonnancement dans un atelier de fonderie. Il s’inspire du cas d’une usine de fabrication de tubes. La spécificité de cet exemple vient d’un objectif et de contraintes liés à la consommation d’électricité, de la variabilité des durées opératoires en fonction de la puissance allouée aux fours, ainsi que de la présence d’opérateurs en nombre limité. L’objectif est de minimiser la facture énergétique. Un premier modèle, basé sur une discrétisation fine, a été exposé dans Trépanier et al (2005), suite à l’étude d’une politique de délestage. Nous présentons ici un nouveau modèle en temps continu

An hybrid CP/MILP method for scheduling with energy costs

This paper deals with energy-related job scheduling for a foundry, in order to minimize the electricity bill. Accounting for energy and human resource constraints leads to better solutions in terms of cost and overall energy consumption. We propose a hybrid heuristic based on a two-step constraint/mathematical programming approach that improves significantly the computation time, compared to the full MILP model

Event-based MILP models for resource-constrained project scheduling problems

International audienceIn this paper we make a comparative study of several mixed integer linear programming (MILP) formulations for resource-constrained project scheduling problems (RCPSPs). First, we present three discrete and continuous time MILP formulations issued from the literature. Second, instead of relying on the traditional discretization of the time horizon, we propose two original MILP formulations for the RCPSP based on the concept of event : the Start/End formulation and the On/Off formulation. These formulations present the advantage of involving fewer variables than the formulations indexed by time. Because the variables of this type of formulations are not function of the time horizon, we have a better capacity to deal with instances of very large scheduling horizon. We also illustrate our contribution with a series of tests on various types of instances with the three MILP formulations issued from the literature together with our two new formulations, and we draw some conclusions on their use

Cooperation of constraint programming and operations research in scheduling

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The Resource-Constrained Project Scheduling Problem

This chapter describes the Resource-constrained project scheduling problem as a combinatorial optimization problem. Different combinatorial models of the resource constraints and characterizations of dominant schedule sets are given. In particular, the properties of the order-based representation are studied