求解指派问题的一个算法

为了便于建立与指派问题有关的决策支持系统，本给出了一个求解指派问题的数值算法，证明了算法的理论依据。该算法能求得问题的最优解，并具有易于编程实现、收敛性好等优点，大量数值实验表明该算法非常实用有效。     

产销平衡运输问题的表上作业法解法的一个注记

本文给出了用表上作业法求解产销平衡运输问题当出现退化时在相应空格填“O”的更为明确的规则，利用该规则可以避免可能存在的多余计算。本文还给出了用改进后的表上作业法求解指派问题的方法和步骤，该方法与求解指派问题的常用方法“匈牙利法”相比，具有手工计算更为简便的优点。     

总延误问题的关键位置法

对于工期递增的工件序列，取最长工时的工件作后移变换，便得到一组总延误值，能使这组总延误值最早达到最小值的那个位置便称为关键位置。在本文中，我们提出了关键位置法如下：在工期递增的工件序列中，将最长工件后移至关键位置，并以此分为二个子问题，然后对一切子问题亦这样做。我们证明了该算法必能得到相邻交换意义下的局部解，并得到了该算法的最坏情形性能性。同时，我们还对该算法给出了计算试验报告及若干讨论。     

固定-固定型无阻尼弹簧质点系统的质量约束问题

本文讨论了系统总质量约束下的固定一固定型无阻尼弹簧质点系统的构造问题，得到了该问题的可解性条件，给出了解的表达式和数值算法，算例说明算法是有效的．     

光学视角下的线段和最值问题解决策略研究

线段和的最值问题是初中数学的难点，为降低难度，许多师生按动点轨迹、式子类型等将该问题分为不同种类，这样使得问题的研究变得零散，运用物理中的费马原理和折射定律可使得该类型问题的解决具有统一性.     

一类特殊二次分配问题的线性化求解新方法

许多抽象于实际的二次分配问题，其流矩阵与距离矩阵中有很多零元素，求解该类二次分配问题时，可通过先行利用零元素的信息减小问题规模，缩短计算时间．以二次分配问题的线性化模型为基础，提出了一种求解流矩阵与距离矩阵中同时存在大量零元素的二次分配问题新方法，不仅从理论上证明了方法的可行性，而且从实验的角度说明了该方法比以往方法更加优越．     

需求区间型运输问题的求解算法

为了便于建立与需求区间型运输问题有关的决策支持系统，本给出了一个求解需求区间型运输问题的数值算法，证明了算法的理论依据，并举例说明算法的应用，该算法能求得问题的最优解，并具有易于编程实现、收敛性好等优点，大量数值实验表明该算法有较高的计算效率。     

直线与圆锥曲线相交过定点问题的统一性质

如何利用坐标法简化解答，突破思维障碍，文[1]给出了解答问题的关键，获得了“完美”解答，读来颇受益．笔者从该问题的另一角度思考探究，得出直线与圆锥曲线过定点问题的一些性质，并从几何特征出发获得该问题的一般解法．     

下料问题数学模型研究

本文讨论了关于合理下料问题线性规则模型的建立，给出了该问题正确的线性规划模型，用反例说明了某些模型的错误并进行了分析。     

问题式教学法在线代数教学中的应用

简要介绍了作设计的线性代数问题式教学法，该方法以解决求解线性方程组时的三个问题为线索，一一引出该课程的所有概念和理论。     

A cogenerator for preseparated superconvex spaces

We construct a cogenerator for the category of preseparated superconvex spaces, and we describe separated convex spaces, i.e. convex spaces for which the morphisms into the unit interval separates points.Presented at the European Colloquium of Category Theory, Tours, France, 25–31 July 1994.     

Personnel scheduling in the Call Center industry

We discuss the main results of the author’s PhD thesis (Canon 2005) presented in December 2005 at the Université François-Rabelais de Tours and supervised by J.-C. Billaut and J.-L. Bouquard. This thesis is written in French and is available from the author upon request. It deals with three different problems arising in the call center industry: the problem of dimensioning a call center, the annualisation problem and finally the Shift Design Problem.     

A Birkhoff theorem for partial algebras via completion

An equational theory (a Birkhoff theorem) for functorial partial algebras is established via the corresponding theory for functorial total algebras.This work was done with partial support of the DFG (BRD).Presented at the European Colloquium of Category Theory, Tours, France, 25–31 July 1994.     

Methods to solve multi-skill project scheduling problem

This is a summary of the author’s PhD thesis supervised by P. Martineau and E. Néron and defended on 28 November 2006 at the Université François-Rabelais de Tours. The thesis is written in French, and is available upon request from the author. This work deals with the problem of scheduling a project. The activities of this project requires skills that may not be mastered by all persons involved. First of all, the problem is defined in the introduction part. Then we propose different methods to solve it: lower bounds in part 2, different heuristics and meta-heuristics in part 3, and finally a branch-and-bound procedure in the last part.     

Process synchronisation as fusion

Process algebras based on the notion of concurrent processes cooperating on common actions are commonplace in the literature. Here we give a categorical model of such a notion of interprocess synchronisation, and indicate how it can be extended to a model of full process algebra. Our main tool is the notion of bimodule over an enriched category: this turns out to be precisely the machinery needed to fuse the behaviours of processes together and thus describe synchronisation. Maximal (CSP-style) synchronisation can then be given a universal characterisation.On leave from the Department of Computer Science, University of Birmingham.Presented at the European Colloquium of Category Theory, Tours, France, 25–31 July 1994.     

Heuristics to Schedule Service Engineers within Time Windows

This paper describes the development of a set of heuristics for tackling vehicle routeing problems with time windows (VRPTW) subject to uncertain demand where schedules are prepared interactively. Many public utility companies, e.g. gas, water, electricity, are now having to quote very specific times for visits to customers, both for regular service and emergency call-outs. The heuristics developed produce good tours by sequencing visits on the basis of closeness to existing visits. Tours are developed as and when demand occurs so that the customer is given an immediate appointment time, rather than waiting for a number of requests for service to be received. Simple methods to construct time windows will also be discussed.     

Composites in offshore technology in the next century

The advisability of application of advanced composites in deep-water offshore technology is shown using risers and tendons as examples. Numerical estimations of the parameters of multilayered metal-composite risers are obtained. Two new processes of spatial braiding for creating the external jackets of compound tendons are considered. Advanced composites are the only possible choice for exploitation of deposits at depths greater than 1500 m. That is why they are the most promising structural materials for offshore technology in the next century. This report was presented at the Symposium “Composites for the Next Millennium” in honor of Stephen Tsai's 70th birthday, Tours, France, 2–3 July, 1999. Institute of Polymer Mechanics, University of Latvia, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 549–560, September–October, 1999.     

Multicriteria tour planning for mobile healthcare facilities in a developing country

A multiobjective combinatorial optimization (MOCO) formulation for the following location-routing problem in healthcare management is given: For a mobile healthcare facility, a closed tour with stops selected from a given set of population nodes has to be found. Tours are evaluated according to three criteria: (i) An economic efficiency criterion related to the tour length, (ii) the criterion of average distances to the nearest tour stops corresponding to p-median location problem formulations, and (iii) a coverage criterion measuring the percentage of the population unable to reach a tour stop within a predefined maximum distance. Three algorithms to compute approximations to the set of Pareto-efficient solutions of the described MOCO problem are developed. The first uses the P-ACO technique, and the second and the third use the VEGA and the MOGA variant of multiobjective genetic algorithms, respectively. Computational experiments for the Thiès region in Senegal were carried out to evaluate the three approaches on real-world problem instances.     

An algebraic approach to chaos

The aim of this paper is to study chaotic actions on objects other than metric spaces, e.g. locales and commutative rings. To do so, point-free versions of topologically transitivity and the density of periodic points are obtained for actions on a locale, and then generalized to a category which includes the desired objects of study.Presented at the European Colloquium of Category Theory, Tours, France, 25–31 July 1994.     

A tabu search heuristic for the dynamic transportation of patients between care units

The problem studied in this paper stems from a real application to the transportation of patients in the Hospital Complex of Tours (France). The ambulance central station of the Hospital Complex has to plan the transportation demands between care units which require a vehicle. Some demands are known in advance and the others arise dynamically. Each demand requires a specific type of vehicle and a vehicle can transport only one person at a time. The demands can be subcontracted to a private company which implies high cost. Moreover, transportations are subject to particular constraints, among them priority of urgent demands, disinfection of a vehicle after the transportation of a patient with contagious disease and respect of the type of vehicle needed. These characteristics involve a distinction between the vehicles and the crews during the modeling phase. We propose a modeling for solving this difficult problem and a tabu search algorithm inspired by Gendreau et al. (1999). This method supports an adaptive memory and a tabu search procedure. Computational experiments on a real-life instance and on randomly generated instances show that the method can provide high-quality solutions for this dynamic problem with a short computation time.