An Algorithm for Solving a Resource Allocation Problem

The paper discusses the solution of a resource allocation problem and a new method for solving a special case of the problem. An algorithm for solving the general problem is presented, and computational experience comparing it with existing methods is given.     

On Reducing a Resource Allocation Problem to a Single One-Dimensional Minimization of a Differentiable Convex Function

By very elementary arguments on Lagrangian duality it is shown that the classical resource allocation problem can be reduced to a single one-dimensional minimization of a differentiable convex function. An optimality condition is given that can be used for testing optimality of some proposed heuristic solutions.     

凸多乘积问题的完全多项式时间近似算法

针对凸多乘积问题,提出一种求其全局最优解的近似算法.首先,通过引入参量获得一个等价问题,然后估计问题中每一乘积项的上下界,进而借助网格结点,获得一些凸规划问题,通过求解这些凸规划问题获得原问题的近似最优解.最后,给出了该算法的收敛性证明和计算复杂性分析.     

A Polynomial Cutting Surfaces Algorithm for the Convex Feasibility Problem Defined by Self-Concordant Inequalities

Consider a nonempty convex set in ^m which is defined by a finite number of smooth convex inequalities and which admits a self-concordant logarithmic barrier. We study the analytic center based column generation algorithm for the problem of finding a feasible point in this set. At each iteration the algorithm computes an approximate analytic center of the set defined by the inequalities generated in the previous iterations. If this approximate analytic center is a solution, then the algorithm terminates; otherwise either an existing inequality is shifted or a new inequality is added into the system. As the number of iterations increases, the set defined by the generated inequalities shrinks and the algorithm eventually finds a solution of the problem. The algorithm can be thought of as an extension of the classical cutting plane method. The difference is that we use analytic centers and convex cuts instead of arbitrary infeasible points and linear cuts. In contrast to the cutting plane method, the algorithm has a polynomial worst case complexity of O(Nlog 1/) on the total number of cuts to be used, where N is the number of convex inequalities in the original problem and is the maximum common slack of the original inequality system.     

基于多种运输渠道的经济批量问题的多项式时间算法

为了集中管理, 降低成本, 增强竞争优势, 供应商通常只负责生产,而把产品的配送业务外包给某个配送中心, 由配送中心按照零售商的需求决定发货运输的方式和时间.这样供应商, 配送中心和零售商就构成了二级供应链系统.本文研究的是运输方式为不同参数的全单位数量折扣结构时, 二级供应链系统的经济批量问题.分析了最优解的性质,并对此问题的一种特殊情形给出一个多项式时间算法.     

多供应商多零售商下经济批量问题的多项式时间算法研究

基于多供应商和多零售商构成的经济批量问题,通过构建优化模型,分析了订购费用为全部单位数量折扣和增加数量折扣两种情形模型最优解的相关性质。将这些性质应用到动态规划算法设计中,对订购费用为全部单位数量折扣时的一种特殊情形及增加数量折扣的一般情形分别设计了求解问题最优解的多项式时间算法,并用算例说明了算法的执行过程和有效性。     

满足多断点折扣费用函数的经济批量问题的多项式时间算法

在进货费用为全单位数量折扣函数的基础上,建立了一类有限时期内的经济批量问题.通过分析最优解的性质,设计了一个计算复杂性为O(T3+mT2)的动态规划算法,其中m为全单位数量折扣费用中的断点数,T为时期数.最后的算例进一步说明了该算法的有效性.     

一种新的求解凸二次规划的原始-对偶多项式内点算法

对凸二次规划问题提出了一种新的原始-对偶路径跟踪算法,算法迭代方向的求解是不同于传统的牛顿法,而是借助于一种新的工具找到搜寻方向.最后证明了算法具有多项式复杂性.     

一类带时间窗车辆分配问题的贪婪算法

本文对一类带时间窗的车辆分配问题进行了分析,引入了车辆任务的概念,并将问题转化为车辆与车辆任务的匹配问题,同时制订了运输任务选择和车辆选择的贪婪策略,并在此基础上设计了车辆分配问题的贪婪算法,最后通过实例验证了算法的有效性。     

Efficient Resource Allocation with Non-Concave Objective Functions

We consider resource allocation with separable objective functions defined over subranges of the integers. While it is well known that (the maximization version of) this problem can be solved efficiently if the objective functions are concave, the general problem of resource allocation with non-concave functions is difficult. In this article we show that for fairly well-shaped non-concave objective functions, the optimal solution can be computed efficiently. Our main enabling ingredient is an algorithm for aggregating two objective functions, where the cost depends on the complexity of the two involved functions. As a measure of complexity of a function, we use the number of subintervals that are convex or concave.     

凸可行问题的一种强收敛算法

无限维Hilbert空间中,解凸可行问题的平行投影算法通常是弱收敛的.本文对一般的平行投影算法进行改进,设计了一种解凸可行问题的具有强收敛性的新算法.该算法主要是在原有算法基础上引入了一个参数序列,在参数序列满足一定的控制条件下保证了算法的强收敛性.为了简单证明算法的强收敛性,我们构建了一个新的积空间,然后把原空间的这种改进平行投影算法转换为积空间中的交替投影算法.这样,改进的平行投影算法的强收敛性就可以通过交替投影算法的收敛性证明得到.     

具有恶化效应和凸资源分配关系的单机排序问题

研究工件加工时间具有恶化效应和凸资源关系的单机排序问题,其中工件的实际加工时间是其正常的加工时间,工件开工时间(具有恶化效应)及消耗资源量的函数。目标为在最大完工时间(总完工时间、总等待时间、完工时间总绝对差与等待时间总绝对差)小于或等于给定常数的条件下找到工件的最优排序和最优的资源分配使工件的总资源消耗量最少。在单机状态下,证明了此问题是多项式时间可解的,并给出了求解该问题的算法和数值实例。     

An Algorithm for the Allocation Problem

This paper* sets out a procedure for solving allocation problems, on different lines from procedures based on linear programming.     

A Bilinear Algorithm for Optimizing a Linear Function over the Efficient Set of a Multiple Objective Linear Programming Problem

The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not be globally optimal. Indeed, this is due to the fact that the feasible region of Q is, in general, a nonconvex set. In this paper we present a monotonically increasing algorithm that finds an exact, globally-optimal solution for Q. Our approach does not require any hypothesis on the boundedness of neither the efficient set EP nor the optimal objective value. The proposed algorithm relies on a simplified disjoint bilinear program that can be solved through the use of well-known specifically designed methods within nonconvex optimization. The algorithm has been implemented in C and preliminary numerical results are reported.     

线性分式规划问题的多项式时间近似算法

本文针对线性比式和分式规划问题,提出一种求其全局最优解的完全多项式时间近似算法,并从理论上证明该算法的收敛性和计算复杂性,数值算例也说明了算法是可行的.     

项目多技能人力资源指派与调度混合算法

研究多技能人力资源在项目活动上的指派与调度问题.首先,从问题特点出发,把原始问题分解为指派问题子模型和调度问题子模型.然后,对项目活动间的重叠关系进行识别,将其转化为对指派问题的有效约束,构建数学规划与约束规划相结合的混合算法对问题求解,并采用CPLEX编程实现.研究表明,算法可有效缩减指派问题的可行域,快速地找到问题的近优解,从而提高多技能人力资源的使用效率,是求解项目多技能人力资源指派与调度问题的一个有效方法.