广义指派问题

广义指派问题可以表述为：指派ｍ位人员执行ｎ项任务,指派人员ｉ执行任务ｊ的收益为ｃｉｊ,需指派人员ｉ执行ａｉ至ａｉ项任务和ｂｊ至ｂｊ位人员执行任务ｊ,问如何指派使总效益最优。广义指派问题可以转化为一个能用对偶运输解法求解的容量运输问题     

广义指派问题及其在军事装备运输中的推广应用

军事装备中的运输问题复杂多样,如何建立数学模型是寻求优化方案的关键.本文首先将最优线性指派模型推广到广义指派模型并给出其两种算法,其次对带有时间约束的运输问题进行建模,并设法将其转化为广义指派问题来处理,从而为这类运输问题提供了一种有效可行的算法.     

基于可信性理论的模糊广义指派问题研究

鉴于广义指派问题的参数确定上通常包含不确定性,因此,将模型的主要参数,即单位费用、资源消耗量,用梯形模糊变量来刻画,从而建立模糊广义指派模型.在模型求解过程中,结合到决策者的实际要求,利用可信性理论将目标函数和约束条件进行清晰化处理,进而通过参数分解法求解.最后,通过数值例子说明模糊广义指派问题的应用,并检验所提方法的有效性.     

分配小于人数和任务数的指派问题的反点算法

摘要：本文对从 个人中派出 个人去完成 项任务中的 项任务使总效率最高这类指派问题给出了新算法,通过对这类指派问题引入了反点的概念,讨论了反点所具有的一些性质并证明了相关结论,利用这些结论找到了通过增加反点来解决此类指派问题的反点算法。     

指派问题的解法及其适用范围的拓广

一、前言 指定m个人(或物)去完成m项任务,分派哪个人承担哪项任务,能够使他们花费的总时间为最小(或获得的总效益为最大)?诸如此类的问题,统称为指派问题. 指派问题分成最小化和最大化两类.关于它们的解法,即最优指派方案的计算步骤,本文准备给予周详的阐述. 指派问题的解法,是针对“m个人完成m项任务”提出来的,应用上存在着一定的局限性.为了拓广适用范围,本文就“m个人完成n(相似文献   

基于可能度排序法的区间信息指派方法

针对具有区间数信息的多目标指派问题,利用区间数可能度排序方法,给出了一种新的指派方法.该方法充分利用实际所给的区间信息进行求解,克服了以往这类指派问题最后由多目标问题转换为单目标问题时权数确定主观性大的缺陷.最后给出了该方法的一个算例.     

基于全局搜索算法的不平衡指派问题研究

目前求解不平衡指派问题的主要是将其转化为平衡的指派问题后再去处理.针对不平衡指派问题提出了全局搜索算法,算法不用将不平衡问题转化为平衡问题进行求解,而是基于全局最优策略对任务进行指派,方法理论更加简单,操作更加方便,使得不平衡指派问题得到了很好地解决,同时,这种算法对平衡指派问题、运输问题等依然有效.     

一类广义Catalan数及其应用

引进了一类广义Catalan数,并赋予这类广义Catalan数组合意义,用这类广义Catalan数得到一类不定方程的解数.     

松弛工期窗口指派和截断控制学习效应资源约束单机排序问题

研究松弛工期窗口指派资源约束单机排序问题,决策者需要在一台处理机上连续处理n个独立的任务.每个任务有一个待定的松弛工期窗口,任务的处理时间通过分配资源可控,且是所在位置的递减函数,当函数递减到一定程度时,需要用一个控制参数替换.目的是在可用资源量有限条件下求出任务的处理顺序和工期窗口以及资源分配方案,使得任务中最大费用取最小值.分两步处理:首先将问题转化为非线性凸规划问题,利用凸规划理论求出任务的资源数量;其次通过解指派问题得到任务最优处理顺序,进而求得任务的工期窗口.给出了多项式时间的最优算法,提供一个算例说明算法的有效性和运算过程.     

非平衡指派模型及其在航空机务维修中的应用

非平衡指派问题是最优平衡指派问题的推广与深化,在航空机务维修工作中,维修任务的合理配置对及时完成维修任务,保障训练作战计划非常重要.本文从装备完好率和人力资源的优化配置角度出发,按照不考虑维修任务等待时间和考虑维修任务等待时间两种情况分别建立了非平衡指派优化模型,并给出了这两种情况下效益矩阵的构造方法,进而将优化模型转化为最优平衡指派模型进行求解,从而为航空机务维修工作中维修人员的优化配置提供了一种科学、合理的决策方法.     

Generalized cover facet inequalities for the generalized assignment problem

The generalized assignment problem is that of finding an optimal assignment of agents to tasks, where each agent may be assigned multiple tasks and each task is performed exactly once. This is an NP-complete problem. Algorithms that employ information about the polyhedral structure of the associated polytope are typically more effective for large instances than those that ignore the structure. A class of generalized cover facet-defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from generalized cover inequalities.     

Heuristic Solution Methods for the Multilevel Generalized Assignment Problem

The multilevel generalized assignment problem is a problem of assigning agents to tasks where the agents can perform tasks at more than one efficiency level. A profit is associated with each assignment and the objective of the problem is profit maximization. Two heuristic solution methods are presented for the problem. The heuristics are developed from solution methods for the generalized assignment problem. One method uses a regret minimization approach whilst the other method uses a repair approach on a relaxation of the problem. The heuristics are able to solve moderately large instances of the problem rapidly and effectively. Procedures for deriving an upper bound on the solution of the problem are also described. On larger and harder instances of the problem one heuristic is particularly effective.     

Multi-criteria assignment problem with incompatibility and capacity constraints

The considered assignment problem generalizes its classical counterpart by the existence of some incompatibility constraints limiting the assignment of tasks to processing units within groups of mutually exclusive tasks. The groups are defined for each processing unit and the constraints allow at most one task from each group to be assigned to the corresponding processing unit. The processing units can normally process a certain number of tasks without any cost; this capacity can be extended, however, at some extra marginal cost that is non-decreasing with the number of additional tasks. Each task has to be assigned to exactly one processing unit and has some preference for the assignment; it is expressed for each pair ‘task-processing unit’ by a dissatisfaction degree. The quality of feasible assignments is evaluated by three criteria: g ₁-the maximum dissatisfaction of tasks, g ₂-the total dissatisfaction of tasks, g ₃-the total cost of processing units. If there is no feasible assignment, tasks and processing units creating a blocking configuration are identified and all actions of unblocking are proposed. Formal properties of blocking configurations and unblocking actions are proven, and an interactive procedure for exploring the set of non-dominated assignments is described together with illustrative examples processed by special software.     

关于“一类最优指派问题的动态规划模型”的注记

考虑一类较一般的最优指派问题 :欲指派 m个人做 n项工作 (m≥n) ,要求每个人只做一项工作 ,第j项工作可以由 bj个人共同去做 ,其中 bj是待求未知数 ,满足 dj≤ bj≤ ej(即 ej,dj为第 j项工作所需人数的上下限 )及 ∑nj=1bj=m(即每个人都有工作 ) ,dj,ej为已知常数 ,j =1 ,… ,n.第 i人做第 j项工作的效益为 cij≥ 0 ,i =1 ,… ,m;j =1 ,… ,n.本文建立求解上述最优指派问题 (使总的效益最大 )的动态规划模型 ,并将文 [1]作为本文的特例 .     

The elastic generalized assignment problem

The generalized assignment problem (GAP) has been studied by numerous researchers over the past 30 years or so. Simply stated, one must find a minimum-cost assignment of tasks to agents such that each task is assigned to exactly one agent and such that each agent's resource capacity is honoured. The problem is known to be NP-hard. In this paper, we study the elastic generalized assignment problem (EGAP). The elastic version of GAP allows agent resource capacity to be violated at additional cost. Another version allows undertime costs to be assessed as well if an agent's resource capacity is not used to its full extent. The EGAP is also NP-hard. We describe a special-purpose branch-and-bound algorithm that utilizes linear programming cuts, feasible solution generators, Lagrangean relaxation and subgradient optimization. We present computational results on a large collection of randomly generated ‘hard’ problems with up to 4000 binary variables.     

The auction algorithm: A distributed relaxation method for the assignment problem

We propose a massively parallelizable algorithm for the classical assignment problem. The algorithm operates like an auction whereby unassigned persons bid simultaneously for objects thereby raising their prices. Once all bids are in, objects are awarded to the highest bidder. The algorithm can also be interpreted as a Jacobi — like relaxation method for solving a dual problem. Its (sequential) worst — case complexity, for a particular implementation that uses scaling, is O(NAlog(NC)), where N is the number of persons, A is the number of pairs of persons and objects that can be assigned to each other, and C is the maximum absolute object value. Computational results show that, for large problems, the algorithm is competitive with existing methods even without the benefit of parallelism. When executed on a parallel machine, the algorithm exhibits substantial speedup.Work supported by Grant NSF-ECS-8217668. Thanks are due to J. Kennington and L. Hatay of Southern Methodist Univ. for contributing some of their computational experience.     

A Lagrangian relaxation-based heuristic for the vehicle routing with full container load

We address a problem of vehicle routing that arises in picking up and delivering full container load from/to an intermodal terminal. The substantial cost and time savings are expected by efficient linkage between pickup and delivery tasks, if the time of tasks and the suitability of containers for cargo allow. As this problem is NP-hard, we develop a subgradient heuristic based on a Lagrangian relaxation which enables us to identify a near optimal solution. The heuristic consists of two sub-problems: the classical assignment problem and the generalized assignment problem. As generalized assignment problem is also NP-hard, we employ an efficient solution procedure for a bin packing based problem, which replaces the generalized assignment problem. The heuristic procedure is tested on a wide variety of problem examples. The test results demonstrate that the procedure developed here can efficiently solve large instances of the problem.     

Dynamic Generalized Assignment Problems with Stochastic Demands and Multiple Agent--Task Relationships

The assignment problem is a well-known operations research model. Its various extensions have been applied to the design of distributed computer systems, job assignment in telecommunication networks, and solving diverse location, truck routing and job shop scheduling problems.This paper focuses on a dynamic generalization of the assignment problem where each task consists of a number of units to be performed by an agent or by a limited number of agents at a time. Demands for the task units are stochastic. Costs are incurred when an agent performs a task or a group of tasks and when there is a surplus or shortage of the task units with respect to their demands. We prove that this stochastic, continuous-time generalized assignment problem is strongly NP-hard, and reduce it to a number of classical, deterministic assignment problems stated at discrete time points. On this basis, a pseudo-polynomial time combinatorial algorithm is derived to approximate the solution, which converges to the global optimum as the distance between the consecutive time points decreases. Lower bound and complexity estimates for solving the problem and its special cases are found.     

Repulsive Assignment Problem

Standard assignment is the problem of obtaining a matching between two sets of respectively persons and positions so that each person is assigned exactly one position and each position receives exactly one person, while a linear decision maker utility function is maximized. We introduce a variant of the problem where the persons individual utilities are taken into account in a way that a feasible solution must satisfy not only the standard assignment constraints, but also an equilibrium constraint of the complementarity type, which we call repulsive. The equilibrium constraint can be, in turn, transformed into a typically large set of linear constraints. Our problem is NP-hard and it is a special case of the assignment problem with side constraints. We study an exact penalty function approach which motivates a heuristic algorithm. We provide computational experiments that show the usefulness of a heuristic mechanism inspired by the exact approach. The heuristics outperforms a state-of-the-art integer linear programming solver.     

The equilibrium generalized assignment problem and genetic algorithm

The well-known generalized assignment problem (GAP) is to minimize the costs of assigning n jobs to m capacity constrained agents (or machines) such that each job is assigned to exactly one agent. This problem is known to be NP-hard and it is hard from a computational point of view as well. In this paper, follows from practical point of view in real systems, the GAP is extended to the equilibrium generalized assignment problem (EGAP) and the equilibrium constrained generalized assignment problem (ECGAP). A heuristic equilibrium strategy based genetic algorithm (GA) is designed for solving the proposed EGAP. Finally, to verify the computational efficiency of the designed GA, some numerical experiments are performed on some known benchmarks. The test results show that the designed GA is very valid for solving EGAP.