二次松弛法求解资源配置型整数规划

针对资源配置型整数规划问题,将与优化机制无关的两类约束条件作二次松弛处理,应用领域整点搜索法求解资源配置型整数规划,大大地降低了运算规模和求解难度,为在管理实践中应用整数规划方法求解规模较大的复杂问题创造了有利条件.     

整数规划在数学建模竞赛中的应用初探

介绍了整数规划的基本概念、基本知识和基本模型,以探讨整数规划在2005高教社杯全国大学生数学建模竞赛中的应用为例,使学生初步了解并掌握在数学建模竞赛中怎样利用整数规划的思想、方法建立数学模型．     

A modified one-sample test for goodness-of-fit

This paper introduces a modified one-sample test of goodness-of-fit based on the cumulative distribution function. Damico [A new one-sample test for goodness-of-fit. Commun Stat – Theory Methods. 2004;33:181–193] proposed a test for testing goodness-of-fit of univariate distribution that uses the concept of partitioning the probability range into n intervals of equal probability mass 1/n and verifies that the hypothesized distribution evaluated at the observed data would place one case into each interval. The present paper extends this notion by allowing for m intervals of probability mass r/n, where r≥1 and n=m×r. A simulation study for small and moderate sample sizes demonstrates that the proposed test for two observations per interval under various alternatives is more powerful than the test proposed by Damico (2004).     

椭圆曲线y^2=px（x^2±1）的正整数点

设P是素数．该文利用w．Ljunggren关于四次Diophantine方程的结果证明了：（i）椭圆曲线了y^2=px（x^2-1）仅当p=5和p=29时各有一组正整数点（x．y）=（9，60）和（x,y）=（9801,5225220）．（ii）当p≠1（mod 8）时．椭圆曲线y^2=px（x^2＋1）仅当p=2时有正整数点（x,y）=（1，2）；当p≡1（mod 8）时，该曲线至多有一组正整数点（x，y）．     

A convolution algorithm for calculating coefficients of jensen's bivariate f distribution

An algorithm for computing probabilities from Jensen's Bivariate F Distribution was given by McAllister, Lee and Holland (1981). One portion of their algorithm involves the calculation of coefficients that require summing over all nonnegative integer partitions of 0,1,2,…,N of size r. Presented here is an alternative method for generating the coefficients by successive convolutions which significantly reduces computation time.     

考虑不同碳排放处理模式的动态供应商选择及采购批量问题研究

不同的碳排放处理模式及不确定的市场需求等因素影响下,如何选择供应商并确定采购批量直接影响企业的运营和效益。本文在多时间周期、多产品种类、多供应商及随机需求情形下,同时考虑不同碳排放处理模式,分析动态供应商选择及采购批量等最优决策问题,构建混合整数非线性规划模型。通过设计变异算子和扰动因子来改进粒子群算法,力求在短时间内求解大规模决策问题。针对不同规模供应商选择及采购批量决策问题,采用精确方法、近似方法和改进粒子群算法求解。数值实验验证了模型及改进粒子群算法的有效性和可行性,分析了碳税、碳交易价格及碳限额对供应链管理的影响,并给出了供应商选择及碳排放处理的决策参考建议。     

Multilocation plant sizing and timing problem: a study of spatial—temporal decomposition procedure

An attempt has been made to develop a spatial-temporal decomposition procedure to solve the multilocation plant sizing and timing problem (MLPSTP). MLPSTP involves the determination of site, location, timing and utilization of the plants to meet the demands of geographically distributed customers. These decisions are assumed to interact through a common objective of minimizing the net present value (NPV) of capital costs and streams of operating and transportation costs. A solution procedure for MLPSTP is proposed using aggregation and disaggregation methodology. In the aggregation phase, MLPSTP is considered to be a single-period problem. This problem is decomposed over different geographical areas to obtain a set of feasible sites and projects. These projects are then sequenced over a finite planning horizon in the disaggregation phase. A multiple criteria based evaluation of spatial decomposition, temporal decomposition, and spatial-temporal decomposition is provided.     

The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach

In this paper, we consider a variant of the Location-Routing Problem (LRP), namely the LRP with simultaneous pickup and delivery (LRPSPD). The LRPSPD seeks to minimize total cost by simultaneously locating the depots and designing the vehicle routes that satisfy pickup and delivery demand of each customer at the same time. We propose two polynomial-size mixed integer linear programming formulations for the problem and a family of valid inequalities to strengthen the formulations. While the first formulation is a node-based formulation, the second one is a flow-based formulation. Furthermore, we propose a two-phase heuristic approach based on simulated annealing, tp_SA, to solve the large-size LRPSPD and two initialization heuristics to generate an initial solution for the tp_SA. We then empirically evaluate the strengths of the proposed formulations with respect to their ability to find optimal solutions or strong lower bounds, and investigate the performance of the proposed heuristic approach. Computational results show that the flow-based formulation performs better than the node-based formulation in terms of the solution quality and the computation time on small-size problems. However, the node-based formulation can yield competitive lower bounds in a reasonable amount of time on medium-size problems. Meantime, the proposed heuristic approach is computationally efficient in finding good quality solutions for the LRPSPD.     

关于广义Fibonacci函数的整数值

设a是正整数，数列满足遍推关系u0＝1，u1＝a，um＋2＝aum1＋um（m≥0），函数本。文证明了：对于任何正整数a，当且仅当X＝0或者X＝u2n-1／u2n（n∈N）时，U（x）是正整数上述结果完整地解决了Brugia、DiPorto和Filipponi提出的一个公开问题     

装卸工人调配问题新解法及其证明

阐述了现代物流技术中装卸工人调配问题、装卸工问题、限制情况下装卸工问题及其数学模型,证明了装卸工人调配问题与限制情况下装卸工问题的数学模型是等价的.通过分析装卸工人调配问题的数学性质得出该问题的一种新解法并给出其证明.新解法给出了该问题的所有最优解.