Showing papers on "Assignment problem published in 1975"

A branch and bound algorithm for the generalized assignment problem

Abstract: This paper describes what is termed the “generalized assignment problem”. It is a generalization of the ordinary assignment problem of linear programming in which multiple assignments of tasks to agents are limited by some resource available to the agents. A branch and bound algorithm is developed that solves the generalized assignment problem by solving a series of binary knapsack problems to determine the bounds. Computational results are cited for problems with up to 4 000 0–1 variables, and comparisons are made with other algorithms.

On the Combined Distribution-Assignment of Traffic

Abstract: It has been remarked that in the practice of transportation planning the distribution and assignment computations are treated sequentially as independent problems, although ideally they should be solved simultaneously. A case has been made by many practitioners for repeating the distribution and assignment computations in order to obtain more consistent results. The purpose of this paper is to shed some light on the eventual results of sequentially solving the distribution and assignment problem. Our conclusion, based on rigorous arguments, is that such practice does not lead to valid results. Also, we develop an approach to solving the distribution and assignment problem simultaneously and relate it to other methods that were proposed for this problem. A numerical example illustrates the conclusions drawn.

A Primal-Dual Traffic Assignment Algorithm

Abstract: A new algorithm for solving the traffic assignment problem is presented. This is a primal-dual algorithm which utilizes a flow augmentation primal and a shortest path dual procedure. At each iteration a feasible solution is known together with a measure of “goodness” of the solution. It is shown that the algorithm converges to an optimal solution. Experience with the algorithm suggests that this convergence is very rapid.

Hamiltonian Circuits and the Travelling Salesman Problem

Abstract: The problem of finding a hamiltonian circuit in a directed graph is discussed and two algorithms are described and compared. Exact methods for the solution of the travelling salesman problem are given with particular emphasis being placed on the calculation of tight bounds that can be used in a variety of tree-search algorithms. Procedures using the assignment and shortest spanning tree problems to provide such bounds and to direct the tree-search are surveyed.

Pole assignment techniques for multivariable systems using unity rank output feedback

Abstract: The problem of pole assignment in linear multivariable systems by means of unity rank output feedback is studied in this paper. It is shown that when the number of specified poles is equal to the number of inputs or outputs of the system, exact pole assignment can be achieved and the feedback matrix is calculated from a set of simple linear equations. When the number of specified poles exceeds this value, the pole assignment problem becomes non-linear. Three different formulations of the problem are considered and three numerical techniques are described for the calculation of the feedback matrix. Numerical examples are given for illustration.

Modelling Techniques and Heuristics for Combinatorial Problems

Abstract: This paper will give a survey of the different methods to approach combinatorial optimization problems. The main emphasis will lie upon integer programming modelling, tree-search (branch and bound) methods, and heuristic methods. The paper is divided into the following sections: 1. Objectives of the paper; 2. Morphology of combinatorial problems; 3. The general approach to solving combinatorial problems; 4. Integer programming formulations; 5. Explicit enumeration; 6. Tree-search (branch and bound) methods; 7. Heuristic methods; 8. Conclusions.

Near-optimal heuristics for an assignment problem in mass storage

Abstract: This paper deals with the assignment of items to an array based on access probabilities so that the expected access time is minimized. The only necessary condition for optimality known to date is that of pairwise majorization. This condition, however, is far from being sufficient. Procedures are developed (1) to enumerate all configurations that satisfy this condition and (2) to obtain tight lower bounds for the optimal solution. An algorithm based on stepwise minimization is proposed and is demonstrated to give near-optimal performance. Numerical results are presented to show that the heuristics yield an actual cost within 0.8 % of the optimal regardless of the underlying distribution and the array size. Furthermore, this algorithm only depends on the ranking of access frequencies and not on the exact values.

Communication networks: Delay-capacity functions and reliable topological structures

Abstract: : A store-and-forward communication network is considered. The network is represented as a linear graph with line capacity weights and Poisson terminal message streams. A maximal message-delay measure is chosen as the network's delay criterion. Considering the capacity assignment problem, the product of a prescribed network maximal message-delay and the associated minimal overall network capacity (bandwidth) is shown to be separated into the sum of two terms. The first term involves the overall internal traffic flow. The second one, called the Delay-Capacity product number, depends only on the routing discipline and the topological structure of the network, and yields the delay-capacity product for a reduced capacity-assignment problem.

The Traveling Salesman Problem and its Implications

Abstract: The aim of this review is to outline the main exact and approximate approaches to the traveling salesman problem (TSP), the various problems arisen from recent work on this subject, the particular cases in which an efficient solution method can be implemented and the connections of the TSP with other topics of combinatorial optimization such as matroids and computational complexity.