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We propose exact hybrid methods based on integer linear programming and constraint programming for an integrated employee timetabling and job-shop scheduling problem. Each method we investigate uses a constraint programming (CP) formulation associated with a linear programming (LP) relaxation. Under a CP framework, the LP-relaxation is integrated into a global constraint using in addition reduced cost-based filtering techniques. We propose two CP formulations of the problem yielding two different LP relaxations. The first formulation is based on a direct representation of the problem. The second formulation is based on a decomposition in intervals of the intervals of the possible operation starting times. We show the theoretical interest of the decomposition-based representation compared to the direct representation through the analysis of dominant schedules. Computational experiments on a set of randomly generated instances confirms the superiority of the decomposition-based representation. In both cases, the hybrid methods outperforms pure constraint programming for employee cost minimization while it is not the case for makespan minimization. The experiments also investigate the interest of the proposed integrated method compared to a sequential approach and show its potential for multiobjective optimization

In 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

In this paper, we consider a dial-a-ride problem where the objective is to maximize the passenger occupancy rate. The problem arises from an on-demand transportation system developed in a rural zone in France, where the objective of encouraging people meeting is pursued. We address the solution of the problem with a column generation approach, applied to a set partitioning formulation where the objective function is fractional. Based on the literature on linear fractional programming, two methods are developed to deal with this fractional objective. Experiments permit to compare these two approaches and to evaluate the impact of the new objective compared to a standard min-cost or min-time optimization.

We propose a new solution approach for the Job Shop Problem with Sequence Dependent Setup Times (SDST-JSP). The problem consists in scheduling jobs, each job being a set of elementary operations to be processed on different machines. The objective pursued is to minimize the completion time of the set of operations. We investigate a relaxation of the problem related to the traveling salesman problem with time windows (TSPTW). Our approach is based on a Branch and Bound procedure, including constraint propagation and using this relaxation. It compares favorably over the best available approaches from the literature on a set of benchmark instances.

In this paper we present a scheduling problem dealing with energy constraints (typically electrical energy). Mainly we propose an extension of specific resource constraint propagation techniques (known as "energy reasoning") to efficiently prune the search space and then to facilitate its resolution. We also present dominance rules and a branching scheme to solve the problem via tree search. Finally, computational results are provided.

In this paper, we present a solution approach based on Chvátal's Resolution Search [2] to solve combinatorial optimization problems. Resolution Search constitutes an alternative to classical enumeration methods and possesses strong connections to nogood recording approaches, and in particular dynamic backtracking, though it is designed to deal with binary linear programming problems. Accordingly, we suggest to hybridize the procedure using constraint programming techniques, in order to apply it to Constraint Satisfaction Problems (CSP). Furthermore, the introduction of such techniques allows some specific improvements that speed up the process and let many outcomes for further research. In order to evaluate the interest of the proposed method, we use it to tackle some particular graph coloring instances, known as the Queens n 2 problem. The experimental results obtained so far prove the validity of the approach and compete with state-of-the-art complete solution methods.

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The class of vehicle routing problems involves the optimization of freight or passenger transportation activities. These problems are generally treated via the representation of the road network as a weighted complete graph. Each arc of the graph represents the shortest route for a possible origin-destination connection. Several attributes can be defined for one arc (travel time, travel cost. . .), but the shortest route modeled by this arc is computed according to a single criterion, generally travel time. Consequently, some alternative routes proposing a different compromise between the attributes of the arcs are discarded from the solution space. We propose to consider these alternative routes and to evaluate their impact on solution algorithms and solution values through a multigraph representation of the road network. We point out the difficulties brought by this representation for general vehicle routing problems, which drives us to introduce the so-called fixed sequence arc selection problem (FSASP). We propose a dynamic programming solution method for this problem. In the context of an on-demand transportation (ODT) problem, we then propose a simple insertion algorithm based on iterative FSASP solving and a branch-and-price exact method. Computational experiments on modified instances from the literature and on realistic data issued from an ODT system in the French Doubs Central area underline the cost savings brought by the proposed methods using the multigraph model.

In this paper, we consider a frequency assignment problem occurring in a military context. The main originality of the problem pertains to its dynamic dimension: new communications requiring frequency assignments need to be established throughout a deployment. The problem decomposes in three phases: assignment of an initial kernel of communications, dynamic assignment of new communication links and reparation when no assignment is possible. Different solution methods are proposed and many computational tests are carried out on realistic instances.

The ROADEF challenge is organized every two years by the French Society of Operations Research and Decision-Making Aid. The goal is to allow industrial partners to witness recent developments in the field of Operations Research and Decision Analysis, and researchers to face up a decisional problem, often complex, occurred in industry. In 2005, the subject of this challenge has been proposed by the car manufacturer RE-NAULT and concerned a car sequencing problem. This problem involves scheduling cars along an assembly line with hard and soft capacity constraints. The industrial problem considered in the challenge differs from the standard problem since, besides capacity constraints imposed by the assembly shop, it also introduces paint batching constraints to minimize the consumption of solvents in the paint shop. We review the exact and heuristic methods of the literature proposed to solve the standard problem and we present the industrial context and the specificities of the challenge problem. We describe the process of the ROADEF'2005 challenge and the methods proposed by the competing teams. We also analyse the results of these methods on the car sequencing instances provided by RENAULT. The final ranking of the candidates is reported and directions for future research based on the results are drawn.

The purpose of this paper is to propose models for project scheduling when there is considerable uncertainty in the activity durations, to the extent that the decision maker cannot with confidence associate probabilities with the possible outcomes of a decision. Our modeling techniques stem from robust optimization, which is a theoretical framework that enables the decision maker to produce solutions that will have a reasonably good objective value under any likely input data scenario. We develop and implement a scenario-relaxation algorithm and a scenario-relaxation-based heuristic. The first algorithm produces optimal solutions but requires excessive running times even for medium-sized instances; the second algorithm produces high-quality solutions for medium-sized instances and outperforms two benchmark heuristics.

This paper addresses an extension of the resource-constrained project scheduling problem that takes into account storage resources which may be produced or consumed by activities. To solve this problem, we propose the generalization of two existing mixed integer linear programming models for the classical resource-constrained project scheduling problem, as well as one novel formulation based on the concept of event. Computational results are reported to compare these formulations with each other, as well as with a reference method from the literature. Conclusions are drawn on the merits and drawbacks of each model according to the instance characteristics.

W e propose a cooperation method between constraint programming and integer programming to com- pute lower bounds for the resource-constrained project scheduling problem (RCPSP). The lower bounds are evaluated through linear-programming (LP) relaxations of two different integer linear formulations. Efficient resource-constraint propagation algorithms serve as a preprocessing technique for these relaxations. The originality of our approach is to use additionally some deductions performed by constraint propagation, and particularly by the shaving technique, to derive new cutting planes that strengthen the linear programs. Such new valid linear inequalities are given in this paper, as well as a computational analysis of our approach. Through this analysis, we also compare the two considered linear formulations for the RCPSP and confirm the efficiency of lower bounds computed in a destructive way.

Operation management of underground passenger transport systems is associated with combinatorial optimization problems (known as crew and train scheduling and rostering) which belong to the np-hard class of problems. Therefore, their resolution in real situations is generally addressed using heuristic methods. This paper considers the duty generation problem, which consists of identifying an optimal trips set that the conductors should complete in a labor day. With regard to the operational and labor conditions, the trains should be driven with the lowest number of conductors and a minimized total idle time between trips. The problem is modeled and solved using a constructive hybrid approach, which has the advantage of visualizing a solution construction similar to the approach typically used by operators who manually solve the problem. This approach takes advantage of the benefits offered by evolutionary methods, which hardly store a candidate solutions population in each stage, controlling in this way the combinatorial explosion of possible solutions. The results that we obtained for problems with similar characteristics to those that are performed manually in the Santiago Metro System were compared with two alternative approaches based on tabu search and a greedy method. The hybrid method 2 produced similar results to those generated by the tabu search, and both found better results than the greedy method.

This paper considers the resource-constrained activity insertion problem with minimum and maximum time lags. The problem consists in inserting a single activity in a partial schedule while preserving its structure represented through resource flow networks and minimizing the makespan increase caused by the insertion. In the general case, we show that finding a feasible insertion that minimizes the project duration is NP-hard. When only minimum time lags are considered and when activity durations are strictly positive, we show the problem is polynomially solvable, generalizing previously established results on activity insertion for the standard resourceconstrained project scheduling problem.