Christian Artigues

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.

Mixed-Integer Linear Programming Formulations

In this chapter, (mixed-)integer linear programming formulations of the resource-constrained project scheduling problem are presented. Standard formulations from the literature and newly proposed formulations are classified according to their size in function of the input data. According to this classification, compact models (of polynomial size), pseudo-polynomial sized models, and formulations of exponential size are presented. A theoretical and experimental comparison of these formulations is then given. The complementarity of the formulations for different usages is finally discussed and directions for future work, such as hybridization with other methods, are given.

Scheduling and planning the outbound baggage process at international airports

The scheduling of outbound baggage at international airports is a challenging tasks in the airport industry. The issue is to control the incoming baggage flow in order to balance the workload over the system. The resource consumption of the different activities, which have to be scheduled, are depending on the arrival process of the baggage. Because of high complexity we suggest a decomposition heuristic to tackle this problem.

A note on event-based MILP models for resource-constrained project scheduling problems

Recently, new mixed integer linear programming formulations for the resource-constrained project scheduling problem were proposed by Kone et al. [3]. Unfortunately, the presentation of the first new model (called start/end-based formulation SEE) was not correct. More precisely, a set of necessary constraints representing the relative positioning of start and end events of activities was unintentionally omitted in the paper although it was present in the integer program used for the computational experiments. After presenting a counterexample showing the incorrectness, we provide a disaggregated and an aggregated variant of the set of necessary constraints, the disaggregated formulation yielding in theory a better linear programming relaxation. We present computational results showing that although the linear programming relaxations of both formulations yield equivalently poor lower bounds, the disaggregated formulation shows in average a better performance for integer solving of a well-known set of 30-activity instances.

Frequency allocation problem in a SDMA satellite communication system

SDMA (Spatial Division Multiple Access) is a principle of radio resource sharing that relies on the division of the space dimension into separated communication channels. It can be used with common Frequency DivisionMultiple Access (FDMA), Time Division Multiple Access (TDMA) or Code Division Multiple Access (CDMA) techniques. Main terrestrial communication standards already implement SDMA. SDMA basically relies on adaptive and dynamic beam-forming associated to a clever algorithm in charge of resource allocation. As satellite communication systems move towards an increasing number of users and a larger throughput for each of them, SDMA is one of the most promising techniques that can reach these two goals. This paper studies static Frequency Allocation Problems (FAP) in a satellite communication system involving a gateway connected to a terrestrial network and some user terminals located in a service area. Two scenarios are considered: one based on SDMA and the other based on usual spot coverage. We propose original integer linear programming formulations and greedy allocation algorithms for the FAP which involve unusual cumulative interference constraints. By considering the link budget of each user, the objective is to maximize the number of users that the system can serve. We show through computational experiments on realistic data that the FAP associated with the SDMA system can be solved efficiently, yielding substantial improvement compared to the traditional system.

A greedy approach combined with graph coloring for non-uniform beam layouts under antenna constraints in multibeam satellite systems

Because of the ever-increasing traffic and quality demands for both internet and television, satellite systems must aim at designs that use the satellite resources in the most efficient way possible. In the case of multibeam satellite systems, this is achieved by making optimal use of the plurality of beams in terms of frequency reuse, power allocation, and quality of the layout. That last point is the one addressed in this paper, the optimisation of the beam layout being a complex but crucial task for the resulting telecommunication system since it directly affects its performances and cost. In the case of broadband systems, the key data is the repartition of the traffic demand over the zone to be covered which is never rigorously uniform. Though, it is common for satellite system design tools to rely on this fairly unrealistic assumption to provide regular coverage which is therefore often suboptimal : inappropriate beamwidths, over-provisioned or unsatisfied user stations, unprofitable beams. Nonetheless, one strong advantage of the regular scheme is that it is known to be compatible with the single feed per beam antenna constraint of minimum angular distance for all the couples of beams coming from the same reflector. The aim of this paper is to present a randomized multi-start heuristic to build a non-uniform layout, driven by the different telecommunication mission criteria and by the aforementioned antenna constraint that is dealt with by a graph recoloring procedure via local search and simulated annealing.

Mixed-integer linear programming for multibeam satellite systems design: Application to the beam layout optimization

In a society where the demand for multimedia applications and data exchange is experiencing an unstoppable growth, multibeam systems have proven to be one of the most relevant solutions for satellite-based communication systems. Though already well represented among the geostationary satellites today, there are still several unresolved design optimization challenges for these complex systems that could lead to improved performances and to better system costs. The satellite platform, the repeater, and the antennas are examples of subsystems that should be designed jointly in order to reach an optimized technical solution that fulfills the service requirements. Traditionally, such complex tasks are addressed through a decomposition of the overall system design into a sequence of smaller decision problems. In this article, we propose to rely on operations research techniques to, on the one hand, take into account explicitly the interdependencies of these decomposed problems, and on the other hand, to handle the own constraints of each subsystem and their interactions. In this paper, the focus is laid on the optimization of the beam layouts of the multibeam satellites. Indeed, in addition to being a perfect example of the aforementioned importance of dealing with subsystem constraints, this problem appears early in the chain of design of a multibeam satellite system and is therefore critical for the quality of the telecommunication system: the weaknesses of a beam layout cannot be made up for later on in the system design. For this crucial optimization phase, the strength of the methodology we propose in this paper is to use mixed-integer linear programming to incorporate explicitly technological feasibility constraints of the subsystems involved, while preparing at best the subsequent design problems. Most importantly, our approach allows to overcome several resisting flaws of the already existing algorithms.

A batch sizing and scheduling problem on parallel machines with different speeds, maintenance operations, setup times and energy costs

This paper considers a production scheduling problem in a Chilean company from the metalworking industry. This company produces steel balls of different diameters on parallel production lines. There are different types of production lines and each production line may have a different speed for producing each diameter. Furthermore a setup time occurs when changing the diameter produced on each machine. Besides these production and setup operations, maintenance operations have to be scheduled. These electrical machines yield high energy demands. It is therefore crucial to minimize total energy consumption, which depends on batch/machine assignment, and maximum demand on peak hours. We consider the batch sizing and scheduling problem involving electricity costs in a non-uniform parallel machine context. Given a demand for each family of steel balls, the problem consists in splitting the demand in sublots (batches) that have to be assigned and scheduled on the parallel machines together with the required maintenance operations. The goal is to complete the schedule before a common deadline while minimizing electricity costs. We propose to tackle this problem through mixed integer linear programming. We propose a global formulation and a two-phase matheuristic. Computational results on realistic instances are provided.

An exact method for the bi-objective one-machine problem with maximum lateness and unit family setup cost objectives

This paper deals with an NP-hard bi-objective one-machine problem with ready times involving maximum lateness and unit family setup cost objectives. Considering separately both objectives, the maximum lateness one-machine problem is also NP-hard but efficiently solved by Carliers algorithm while the unit family setup cost one machine-problem with two families can be solved in polynomial timeby Dartes algorithm, even when precedence constraints are considered. Under the epsilon (Porson)-constraint framework we propose a branch-and-bound method to minimize the first objective with a given upper bound on the second.

Reinsertion Principles for Multi-Resource Shop Scheduling with Sequence-Dependent Setup Times

Abstract A workshop made of disjunctive and cumulative resources is considered. Jobs that have to be performed on this resources are characterized by release dates, due dates and non-linear routings. A sequence dependent setup activity may be needed on some disjunctive resources before performing a processing operation. This setup activity can be decomposed into setup operations that may require complementary resources. A polynomial insertion procedure of a new processing operation in an existing schedule is proposed.