A parametric-based heuristic program for the quadratic assignment problem

In this article we study the quadratic assignment problem by embedding the actual data in a data space which satisfies an extension of the metric triangle property. This leads to simpler computations for the determination of heuristic solutions. Bounds are given for the loss of optimality which such heuristic solutions would involve in any specific instance. © 1993 John Wiley & Sons, Inc.     

Bicriteria multiresource generalized assignment problem

In this study, we consider a bicriteria multiresource generalized assignment problem. Our criteria are the total assignment load and maximum assignment load over all agents. We aim to generate all nondominated objective vectors and the corresponding efficient solutions. We propose several lower and upper bounds and use them in our optimization and heuristic algorithms. The computational results have shown the satisfactory behaviors of our approaches. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 621–636, 2014     

多目标广义指派问题的模糊匈牙利算法求解

提出和讨论了两类多目标的广义指派决策问题,分别给出了它们的多目标整数线性规划数学模型,并结合模糊理论与解决传统指派问题的匈牙利方法提出了一种新的求解算法:模糊匈牙利法.最后给出了一个数值例子.     

Heuristics for the multi‐resource generalized assignment problem

The well‐known generalized assignment problem (GAP) involves the identification of a minimum‐cost assignment of tasks to agents when each agent is constrained by a resource in limited supply. The multi‐resource generalized assignment problem (MRGAP) is the generalization of the GAP in which there are a number of different potentially constraining resources associated with each agent. This paper explores heuristic procedures for the MRGAP. We first define a three‐phase heuristic which seeks to construct a feasible solution to MRGAP and then systematically attempts to improve the solution. We then propose a modification of the heuristic for the MRGAP defined previously by Gavish and Pirkul. The third procedure is a hybrid heuristic that combines the first two heuristics, thus capturing their relative strengths. We discuss extensive computational experience with the heuristics. The hybrid procedure is seen to be extremely effective in solving MRGAPs, generating feasible solutions to more than 99% of the test problems and consistently producing near‐optimal solutions. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 468–483, 2001     

A multifaceted heuristic for the orienteering problem

The orienteering problem involves the selection of a path between an origin and a destination which maximizes total score subject to a time restriction. In previous work we presented an effective heuristic for this NP-hard problem that outperformed other heuristics from the literature. In this article we describe and test a significantly improved procedure. The new procedure is based on four concepts—center of gravity, randomness, subgravity, and learning. These concepts combine to yield a procedure which is much faster and which results in more nearly optimal solutions than previous procedures.     

A branch‐and‐price approach for the stochastic generalized assignment problem

In this article, we address a stochastic generalized assignment machine scheduling problem in which the processing times of jobs are assumed to be random variables. We develop a branch‐and‐price (B&P) approach for solving this problem wherein the pricing problem is separable with respect to each machine, and has the structure of a multidimensional knapsack problem. In addition, we explore two other extensions of this method—one that utilizes a dual‐stabilization technique and another that incorporates an advanced‐start procedure to obtain an initial feasible solution. We compare the performance of these methods with that of the branch‐and‐cut (B&C) method within CPLEX. Our results show that all B&P‐based approaches perform better than the B&C method, with the best performance obtained for the B&P procedure that includes both the extensions aforementioned. We also utilize a Monte Carlo method within the B&P scheme, which affords the use of a small subset of scenarios at a time to estimate the “true” optimal objective function value. Our experimental investigation reveals that this approach readily yields solutions lying within 5% of optimality, while providing more than a 10‐fold savings in CPU times in comparison with the best of the other proposed B&P procedures. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 131–143, 2014     

A linear programming solution to the generalized rectangular distance weber problem

The Weber Problem generalized to the location of several new points with respect to existing points is formulated as a linear programming problem under the assumption that distances are rectangular. The dual problem is then formulated and subsequently reduced to a problem with substantially fewer variables and constraints than required by an existent alternative linear programming formulation. Flows may exist between new as well as between new and existing points. Linear constraints can be imposed to restrict the location of new points. Pairwise constraints limiting distances between new points and between new and existing points can also be accommodated.     

A decomposition heuristic for the twin robots scheduling problem

This article provides an efficient heuristic based on decomposition for the twin robots scheduling problem (TRSP). TRSP concerns two moving robots executing storage and retrieval requests in parallel along a shared pathway. The depots are located at both ends of the line and a dedicated robot is assigned to each of them. While moving goods between their respective depots and some storage locations on the line, noncrossing constraints among robots need to be considered. Our heuristic uses a dynamic programming framework to determine the schedule of one robot while keeping the other one's fixed. It finds near‐optimal solutions even for large problem instances with hundreds of jobs in a short time span. © 2014 Wiley Periodicals, Inc. 62:16–22, 2015     

A stochastic assignment problem

There are n boxes with box i having a quota value Balls arrive sequentially, with each ball having a binary vector attached to it, with the interpretation being that if X_i = 1 then that ball is eligible to be put in box i. A ball's vector is revealed when it arrives and the ball can be put in any alive box for which it is eligible, where a box is said to be alive if it has not yet met its quota. Assuming that the components of a vector are independent, we are interested in the policy that minimizes, either stochastically or in expectation, the number of balls that need arrive until all boxes have met their quotas. © 2014 Wiley Periodicals, Inc. 62:23–31, 2015     

A heuristic network procedure for the assembly line balancing problem

Proposed is a Heuristic Network (HN) Procedure for balancing assembly lines. The procedure uses simple heuristic rules to generate a network which is then traversed using a shortest route algorithm to obtain a heuristic solution. The advantages of the HN Procedure are: a) it generally yields better solutions than those obtained by application of the heuristics, and b) sensitivity analysis with different values of cycle time is possible without having to regenerate the network. The rationale for its effectiveness and its application to problems with paralleling are presented. Computational experience with the procedure on up to 50 task test problems is provided.     

A heuristic solution procedure for the multiconstraint zero-one knapsack problem

In this article a new heuristic procedure is proposed. This procedure makes use of surrogate duality in solving multiconstraint knapsack problems. Computational effort involved in the procedure is bounded by a polynomial in the number of variables. Extensive computational testing indicates that the procedure generates good feasible solutions regardless of the problem structure. In 98% of the problems solved, the solution generated by the heuristic was within 1% of the optimal solution. This procedure was also tested against other heuristics and was found to compare favorably.     

A generalized assignment model for dynamic supply chain capacity planning

We consider a generalization of the well‐known generalized assignment problem (GAP) over discrete time periods encompassed within a finite planning horizon. The resulting model, MultiGAP, addresses the assignment of tasks to agents within each time period, with the attendant single‐period assignment costs and agent‐capacity constraint requirements, in conjunction with transition costs arising between any two consecutive periods in which a task is reassigned to a different agent. As is the case for its single‐period antecedent, MultiGAP offers a robust tool for modeling a wide range of capacity planning problems occurring within supply chain management. We provide two formulations for MultiGAP and establish that the second (alternative) formulation provides a tighter bound. We define a Lagrangian relaxation‐based heuristic as well as a branch‐and‐bound algorithm for MultiGAP. Computational experience with the heuristic and branch‐and‐bound algorithm on over 2500 test problems is reported. The Lagrangian heuristic consistently generates high‐quality and in many cases near‐optimal solutions. The branch‐and‐bound algorithm is also seen to constitute an effective means for solving to optimality MultiGAP problems of reasonable size. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

A lagrangean relaxation algorithm for the constrained matrix problem

We present variants of a convergent Lagrangean relaxation algorithm for minimizing a strictly convex separable quadratic function over a transportation polytope. The algorithm alternately solves two “subproblems,” each of which has an objective function that is defined by using Lagrange multipliers derived from the other. Motivated by the natural separation of the subproblems into independent and very easily solved “subsubproblems,” the algorithm can be interpreted as the cyclic coordinate ascent method applied to the dual problem. We exhibit our computational results for different implementations of the algorithm applied to a set of large constrained matrix problems.     

线性规划的一种并行修正松弛算法

对求解线性规划问题的松弛算法进行了修正,在此基础上提出了一种基于cluster结构的并行算法,分析了算法的性能;基于曙光3000大规模并行计算机,给出了算法用于求解线性规划问题实例的实验结果.理论分析和实验结果表明,修正算法改进了松弛算法的实际性能,同时具有较好的并行性和稳定性,可用于求解此类大规模科学与工程规划问题的高性能计算.     

The Hungarian method for the assignment problem

This paper has been presented with the Best Paper Award. It will appear in print in Volume 52, No. 1, February 2005.     

Suboptimal algorithms for the quadratic assignment problem

The idea of combining relatively simple continuous methods with discrete procedures is used for the construction of suboptimal algorithms for quadratic assignment problems. Depending on the nature of the special problem these steps may vary in complexity. The simplest procedures require minimum storage space and result in tolerable computation times. Different choices of parameters and random variations may be used in order to obtain statistical distributions of suboptimal solutions. Computational results for sample problems indicate improvements on results of Steinberg, Gilmore, and Hillier and Connors.     

A generalized euclidean procedure for integer linear programs

This paper investigates a new procedure for solving the general-variable pure integer linear programming problem. A simple transformation converts the problem to one of constructing nonnegative integer solutions to a system of linear diophantine equations. Rubin's sequential algorithm, an extension of the classic Euclidean algorithm, is used to find an integer solution to this system of equations. Two new theorems are proved on the properties of integer solutions to linear systems. This permits a modified Fourier-Motzkin elimination method to be used to construct a nonnegative integer solution. An experimental computer code was developed for the algorithm to solve some test problems selected from the literature. The computational results, though limited, are encouraging when compared with the Gomory all-integer algorithm.     

A new reformulation approach for the generalized partial covering problem

In this paper, we consider a situation in which a group of facilities must be constructed in order to serve a given set of customers, where the facilities might not be able to guarantee an absolute coverage to the different customers. We examine the problem of maximizing the total service reliability of the system subject to a budgetary constraint. We propose a new reformulation of this problem that facilitates the generation of tight lower and upper bounds. These bounding mechanisms are embedded within the framework of a branch‐and‐bound procedure. Computational results on problem instances ranging in size up to 100 facilities and 200 customers reveal the efficacy of the proposed exact and heuristic approaches. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

A mixed optimization technique for the generalized machine replacement problem

A mixed optimization technique for optimal machine replacement is presented which allows much more flexibility than previous models. Optimal purchase, maintenance and sale of a given machine between any two given points in time is treated as a subproblem, which one may choose to solve via control theory, dynamic programming, or practical engineering considerations. (A control theory formulation is used in the paper as an illustration.) These subproblem solutions are then incorporated into a Wagner-Whitin formulation for solution of the full problem. The technique is particularly useful for problems with such asymmetries as an existing initial machine or uneven technological change. A simple numerical example is solved in the Appendix.