This paper presents a heuristic column generation method for solving vehicle routing problems with a heterogeneous fleet of vehicles. The method may also solve the fleet size and composition vehicle routing problem and new best known solutions are reported for a set of classical problems. Numerical results show that the method is robust and efficient, particularly for medium and large size problem instances.

This paper is motivated by operating self service transport systemsthat flourish nowadays. In cities where such systems have been setup with bikes, trucks travel to maintain a suitable number of bikesper station.It is natural to study a version of the C-delivery TSP defined byChalasani and Motwani in which, unlike their definition, C is partof the input: each vertex v of a graph G=(V,E) has a certainamount xv of a commodity and wishes to have an amount equal toyv (we assume that $\sum_{v\in V}x_v=\sum_{v\in V}y_v$ and allquantities are assumed to be integers); given a vehicle of capacityC, find a minimal route that balances all vertices, that is,that allows to have an amount yv of the commodity on each vertexv.This paper presents among other things complexity results, lowerbounds, approximation algorithms, and a polynomial algorithm whenG is a tree.

The simple plant location problem (SPLP) is considered and a genetic algorithm is proposed to solve this problem. By using the developed algorithm it is possible to solve SPLP with more than 1000 facility sites and customers. Computational results are presented and compared to dual based algorithms.

This paper deals with a special case of Project Scheduling problem: there is a project to schedule, which is made up of activities linked by precedence relations. Each activity requires specific skills to be done. Moreover, resources are staff members who master fixed skill(s). Thus, each resource requirement of an activity corresponds to the number of persons doing the corresponding skill that must be assigned to the activity during its whole processing time. We search for an exact solution that minimizes the makespan, using a Branch-and-Bound method.

In this paper, we develop some stochastic dominancetheorems for the location and scale family and linear combinations ofrandom variables and for risk lovers as well as risk averters thatextend results in Hadar and Russell (1971) and Tesfatsion (1976). Theresults are discussed and applied to decision-making.

The aim of this paper is to present a new branch and boundmethod for solving the Multi-Processor Flow-Shop. This method is based on the relaxation of the initial problem to m-machine problems corresponding to centers. Release dates and tails are associated with operations andmachines. The branching scheme consists in fixing the inputs of a critical centerand the lower bounds are those of the m-machine problem. Several techniques for adjusting release dates and tails have also been introduced. As shown byour personal study, the overall method is very efficient.

A special class of scheduling problems is studied in this paper, named Hybrid Flowshop, n jobs have to be performedin a shop and each of them has the same routing (so this is a flowshop). A job consists in k different operations. A set of machines are able to perform each operation and thisset is called a stage. So when a job consists in two operations,there are two stages in the shop. After introducing the scheduling generalities, we define our preocupations and we propose a notationin order to identify precisely and rapidly a problem. Then a state of the art is proposed and presented in two parts. The first one is dedicated to the 2-stage hybrid flowshops and the second to thegeneral case of the k-stage. Then a summary puts to the fore that many problems remain unsolved.

This paper presents a state-of-the-art survey on multicriteria scheduling and introduces a definition of a multicriteria scheduling problem. It provides a framework that allows to tackle multicriteria scheduling problems, according to Decision Aid concepts. This problem is decomposed into three different problems. The first problem is about obtaining a model. The second one is how to take criteria into account and the third one is about solving a scheduling problem. An extension to an existing notation for scheduling problems is proposed for multicriteria scheduling problems. Then, basic results from the literature on multicriteria optimization are presented. These results are used to build the final scheduling problem to solve. Finally a survey is presented for one-machine, parallel machines and flowshop multicriteria scheduling problems.

This article deals with the vehicle routing problem with timewindows (VRPTW). This problem consists in determining a least-costset of trips to serve customers during specific time windows. Theproposed solution method is a memetic algorithm (MA), a geneticalgorithm hybridised with a local search. Contrary to most paperson the VRPTW, which minimize first the number of vehicles, ourmethod is also able to minimize the total distance travelled. Theresults on 56 classical instances are compared to those of thebest metaheuristics. The efficiency of the MA is similar for theclassical criterion, but it becomes the best algorithm availablefor the total distance, being much faster and improving 20best-known solutions.

The standard multiple criteria optimization starts with anassumption that the criteria are incomparable. However, there are manyapplications in which the criteria express ideas of allocation ofresources meant to achieve some equitable distribution. This paperfocuses on solving linear multiple criteria optimization problems withuniform criteria treated in an equitable way. An axiomatic definition ofequitable efficiency is introduced as an refinement ofPareto-optimality. Various generation techniques are examined and thestructure of the equitably efficient set is analyzed.

We address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is NP-hard. We propose mixed integer programming heuristics based on a planning horizon decomposition strategy to find a feasible solution. The planning horizon is partitioned into several sub-horizons over which a freezing or a relaxation strategy is applied. Some experimental results showing the effectiveness of the approach on real-world instances are presented. A sensitivity analysis on the parameters of the heuristics is reported.

The purpose of this article is to show the great interest of theuse of propagation (or pruning) techniques, inside classicalinterval Branch-and-Bound algorithms. Therefore, a propagationtechnique based on the construction of the calculus tree isentirely explained and some properties are presented without theneed of any formalism (excepted interval analysis). This approachis then validated on a real example: the optimal design of anelectrical rotating machine.

Data envelopment analysis (DEA) has been proven as an excellent data-oriented efficiency analysis method for comparing decision making units (DMUs) with multiple inputs and multiple outputs. In conventional DEA, it is assumed that the status of each measure is clearly known as either input or output. However, in some situations, a performance measure can play input role for some DMUs and output role for others. Cook and Zhu [Eur. J. Oper. Res. 180 (2007) 692–699] referred to these variables as flexible measures. The paper proposes an alternative model in which each flexible measure is treated as either input or output variable to maximize the technical efficiency of the DMU under evaluation. The main focus of this paper is on the impact that the flexible measures has on the definition of the PPS and the assessment of technical efficiency. An example in UK higher education intuitions shows applicability of the proposed approach.

A reformulation of a mathematical program is a formulation whichshares some properties with, but is in some sense better than, theoriginal program. Reformulations are important with respect to thechoice and efficiency of the solution algorithms; furthermore, it isdesirable that reformulations can be carried outautomatically. Reformulation techniques are widespread in mathematicalprogramming but interestingly they have never been studied under aunified framework. This paper attempts to move some steps in thisdirection. We define a framework for storing and manipulatingmathematical programming formulations and give several fundamentaldefinitions categorizing useful reformulations in essentially fourtypes (opt-reformulations, narrowings, relaxations andapproximations). We establish some theoretical results and givereformulation examples for each type.

In this paper, a solution procedure is proposed to solve fuzzy linear fractionalprogramming (FLFP) problem where cost of the objective function, the resources and thetechnological coefficients are triangular fuzzy numbers. Here, the FLFP problem istransformed into an equivalent deterministic multi-objective linear fractional programming(MOLFP) problem. By using Fuzzy Mathematical programming approach transformed MOLFPproblem is reduced single objective linear programming (LP) problem. The proposedprocedure illustrated through a numerical example.

In this paper we consider the operational planning problem of physical distribution via a fleet of hired vehicles, for which the travelling cost is solely a function of the sequence of locations visited within all open delivery routes, while vehicle fixed cost is inexistent. The problem is a special class of vehicle routing and is encountered in the literature as the Open Vehicle Routing Problem (OVRP), since vehicles are not required to return to the depot. The goal is to distribute in an optimal way finished goods from a central facility to geographically dispersed customers, which pose daily demand for items produced in the facility and act as sales points for consumers. To solve the problem, we employ an annealing-based method that utilizes a backtracking policy of the threshold value when no acceptances of feasible solutions occur during the search process. Computational results on a set of benchmark problems show that the proposed method consistently outperforms previous algorithms for solving the OVRP. The approach can serve as the means for effective fleet planning in real-life problems.

A second order optimality condition for multiobjective optimization with a set constraint is developed; this condition is expressed as the impossibility of nonhomogeneous linear systems. When the constraint is given in terms of inequalities and equalities, it can be turned into a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced.

We address the 3-Machine Assembly-Type Flowshop Scheduling Problem (3MAF). This problem is known to be NP-complete in the strongsense. We propose an exact branch and bound method based on a recursiveenumeration of potential inputs and outputs of the machines. Using this algorithm,several large size instances have been solved to optimality.

The notion of treewidth is of considerable interest in relation to NP-hard problems.Indeed, several studies have shown that the tree-decomposition method can be used to solve many basic optimization problems in polynomialtime when treewidth is bounded, even if, for arbitrary graphs, computingthe treewidth is NP-hard.Several papers present heuristics with computational experiments.For many graphs the discrepancy between the heuristic resultsand the best lower bounds is still very large. The aim of this paper is to propose two new methodsfor computing the treewidth of graphs: a heuristic and a metaheuristic.The heuristic returns good results in a short computation time,whereas the metaheuristic (a Tabu search method)returns the best results known to have been obtained so far for all the DIMACS vertex coloring / treewidth benchmarks (a well-known collection of graphs used for both vertex coloring and treewidth problems.) Our results actually improve on the previous best results for treewidth problems in 53% of the cases. Moreover, we identify properties of the triangulation processto optimize the computing time of our method.

This paper addresses the problem of managing a waiting list for elective surgery todecide the number of patients selected from the waiting list and to schedule them inaccordance with the operating room capacity in the next period. The waiting listprioritizes patients not only by their initial urgency level but also by their waitingtime. Selecting elective surgery patients requires a balance between the waiting time forurgent patients and that for less urgent patients. The problem is formulated as aninfinite horizon Markov Decision Process. Further, the study proposes a schedulingprocedure based on structural properties of an optimal policy by taking a sampling-basedfinite horizon approximation approach. Finally, we examine the performance of the policyunder various conditions.