This paper presents the approach that we developed to solve the ROADEF 2003 challenge problem. This work is part of a research program whose aim is to study the benefits and the computer-aided generation of hybrid solutions that mix constraint programming and meta-heuristics, such as large neighborhood search (LNS). This paper focuses on three contributions that were obtained during this project: an improved method for propagating Hamiltonian chain constraints, a fresh look at limited discrepancy search and the introduction of randomization and de-randomization within our combination algebra. This algebra is made of terms that represent optimization algorithms, following the approach of SALSA [1], which can be generated or tuned automatically using a learning meta-strategy [2]. In this paper, the hybrid combination that is investigated mixes constraint propagation, a special form of limited discrepancy search and large neighborhood search.

Fractionnal mathematical programs appear in numerous operations research, computer science and economic domains. We consider in this paper the problem of maximizing the sum of 0–1 hyperbolic ratios (SRH). In contrast to the single ratio problem, there has been little work inthe literature concerning this problem. We propose two mixed-integer linear programming formulations of SRH and develop two different strategies to solve them. The first one consists in using directly a general-purpose mixed-integer programming solver. The second one is based on a specialized branch and bound algorithm that reformulates more precisely the problem at every node of search tree. We also propose a heuristic method and we exploit the obtained solution in order to improve the first strategy. We present computational experiments that allow to compare the different approaches.

In the course of globalization, many enterprises change theirstrategies and are coupled in partnerships with suppliers,subcontractors and customers. This coupling forms supply chainscomprising several geographically distributed productionfacilities. Production planning in a supply chain is a complicatedand difficult task, as it has to be optimal both for the localmanufacturing units and for the whole supply chain network. Inthis paper two analytical models are used to solve the productionplanning problem in supply chain involving several enterprises.Generally in practice, for competitive and/or practical reasons,frequently each enterprise prefers to optimize its production planwith little care about the other members of the supply chain. Thiscase is presented through a simple model of decentralizedoptimization. The aim of this study is to analyze and compare thetwo types of optimization: centralized and decentralized. Theinitial question is: what are the profit and the optimal policy ofglobal (centralized) optimization in contrast to local(decentralized)? We characterize this gain by comparing theoptimal profits obtained in both cases.

In on-line computation, the instance of the problem dealt is notentirely known from the beginning of the solution process, but itis revealed step-by-step. In this paper we deal with on-lineindependent set. On-line models studied until now for this problemsuppose that the input graph is initially empty and revealedeither vertex-by-vertex, or cluster-by-cluster. Here we present anew on-line model quite different to the ones already studied. Itassumes that a superset of the final graph is initially present(in our case the complete graph on the order n of the finalgraph) and edges are progressively removed until the achievementof the final graph. Next, we revisit the model introduced in[Demange, Paradon and Paschos, Lect. Notes Comput. Sci.1963 (2000)326–334] and study relaxations assuming that somepaying backtracking is allowed.

A bound for the greedy heuristic applied to the K-facility location problem can be calculated,using values gathered during the calculation of the heuristic. The bound strengthens awell-known bound for the heuristic. Computational experiments show that this bound can bebeneficial when the number of facilities is small or close to the total number of potential sites. In addition, it is consistent with previous results about the influence of the data characteristicsupon the optimal value.

Periodic Vehicle Routing Problem: classification and heuristic for tactical planning.The Periodic Vehicle Routing Problem (PVRP) consists in assigning customer visits to vehicle routes in some periods of a time horizon so as to satisfy some service level requirements that can take theform of frequency of visit, constraint on time lag between visits, or pre-defined visit patterns. We present different variants of this problem and propose a classification. Then, we consider a model for tactical planning for which we propose a heuristic: we optimise theplanning of customer visits to achieve both workload balancing andregionalisation of the routes. The objective of regionalisation reflects a desire to specializeroutes to restricted geographical area. The standard minimisation of distancetravelled is left for the underlying operational decision making model.Our heuristic achieves practical solutions for an industrialinstance with 16658 visits to schedule over a horizon of 20 days.

Markov Decision Processes (MDPs) are a classical framework forstochastic sequential decision problems, based on an enumerated statespace representation. More compact and structured representations havebeen proposed: factorization techniques use state variablesrepresentations, while decomposition techniques are based on apartition of the state space into sub-regions and take advantage ofthe resulting structure of the state transition graph. We use a familyof probabilistic exploration-like planning problems in order to studythe influence of the modeling structure on the MDP solution. We firstdiscuss the advantages and drawbacks of a graph based representationof the state space, then present our comparisons of two decompositiontechniques, and propose to use a global approach combining both statespace factorization and decomposition techniques. On the explorationproblem instance, it is proposed to take advantage of the naturaltopological structure of the navigation space, which is partitionedinto regions. A number of local policies are optimized within eachregion, that become the macro-actions of the global abstract MDPresulting from the decomposition. The regions are the correspondingmacro-states in the abstract MDP. The global abstract MDP is obtainedin a factored form, combining all the initial MDP state variables andone macro-state “region” variable standing for the different possiblemacro-states corresponding to the regions. Further research ispresently conducted on efficient solution algorithms implementing thesame hybrid approach for tackling large size MDPs.

In the wine AOC system, the regulation of quantities performed by the professionalorganizations is aimed to smooth the variations of the quality of the wine due to thevariations in the climate that affect the quality of the grapes. Nevertheless, this regulationcould be damaging to the consumers due to the price increase resulting from the reduction ofthe quantities sold on the market. We propose a stochastic control model and a simulation toolable to measure the effects of this mechanism on the producer's profit and the consumer'ssurplus.