Showing papers on "Assignment problem published in 1986"
TL;DR: The Hungarian linear assignment algorithm is now less sensitive to the range of the cost coefficients, and it is shown that the algorithm is essentially equivalent to assignment algorithms based on shortest augmenting paths.
237 citations
TL;DR: This paper defines a branch-and-bound algorithm for solving APSC to optimality that employs a depth-first, polychotomous branching strategy in conjunction with a bounding procedure that utilizes subgradient optimization.
Abstract: Many resource-constrained assignment scheduling problems can be modeled as 0-1 assignment problems with side constraints APSC. Unlike the well-known assignment problem of linear programming, APSC is NP-complete. In this paper we define a branch-and-bound algorithm for solving APSC to optimality. The algorithm employs a depth-first, polychotomous branching strategy in conjunction with a bounding procedure that utilizes subgradient optimization. We also define a heuristic procedure for obtaining approximate solutions to APSC. The heuristic uses subgradient optimization to guide the search for a good solution as well as to provide a bound on solution quality. We present computational experience with both procedures, applied to over 400 test problems. The algorithm is demonstrated to be effective across three different classes of resource-constrained assignment scheduling problems. The heuristic generates solutions for these problems that are, on average, within 0.8% of optimality.
98 citations
TL;DR: Efficient algorithms based upon Balinski's signature method are described for solving then × n assignment problem and are shown to have computational bounds of O(n3) space and O(mn + n2 logn) time in the worst case.
Abstract: Efficient algorithms based upon Balinski's signature method are described for solving then × n assignment problem. These algorithms are special variants of the dual simplex method and are shown to have computational bounds of O(n3). Variants for solving sparse assignment problems withm arcs that require O(m) space and O(mn + n2 logn) time in the worst case are also presented.
42 citations
TL;DR: A sequential stochastic assignment problem in a stationary Markov chain, where the states are not known explicitly, is considered, and an optimal policy and the total expected reward under this policy are obtained.
Abstract: A sequential stochastic assignment problem in a stationary Markov chain, where the states are not known explicitly, is considered. This is an optimization problem in a partially observable Markov chain, and an optimal policy and the total expected reward under this policy are obtained. Here we specify the learning procedure by the Bayes' theorem, and the optimal policy is not always a critical number policy. As a special case of this problem, a problem of optimal selections is considered, and a relation to former results of a sequential stochastic assignment problem is observed.
37 citations
TL;DR: In this paper, a branch and bound tree is proposed to solve the multi-period assignment problem, which is an optimization model that describes the situation of assigning people to activities, or jobs over time.
29 citations
01 Mar 1986
TL;DR: The principal modifications proposed to improve the rate of convergence of the original method are examined and a new modification to the Frank-Wolfe algorithm is presented.
Abstract: This paper discusses the slow-convergence characteristics of the Frank-Wolfe algorithm in the solution of the traffic assignment problem in transportation networks. The principal modifications proposed to improve the rate of convergence of the original method are examined and a new modification to the Frank-Wolfe algorithm is presented. Convergence of the algorithm is proved and computational results are reported to demonstrate the validity of the proposed method.
24 citations
01 Jan 1986
TL;DR: In this paper, the complexity analysis of certain matching problems with ties in preference lists was studied and it was shown that the option of allowing ties in the preference lists can significantly affect the computational complexity of the problems.
Abstract: This thesis concerns the complexity analysis of certain matching problems. The description of each of these matching problems consists of a group of agents, and, for each agent, a preference list over the agents with whom the agent can be matched. A solution to the problem is a matching that has the property that no pair of agents that are eligible for each other, prefer each other to their assigned mates. A matching that satisfies this property is called a stable matching.
The variants of this problem that will be dealt with are: (1) The marriage problem: matching of men and women into couples; (2) The roommate problem: matching of students into rooms of two occupants; (3) The intern assignment problem: the assignment of interns to hospital positions; (4) The intern assignment problem with couples: same problem as (3) except that some of the interns are married couples.
These matching problems can be defined to allow or disallow ties in the preference lists. When ties are allowed, stability is defined as the absence of an unmatched pair that strictly prefer each other to their assigned mates.
This thesis will show that the option of allowing ties in the preference lists can significantly affect the computational complexity of the problems. It will be shown that, when ties are allowed, the roommate problem and the intern assignment problem with couples are NP-complete. In contrast, the roommate problem without ties, is solvable in polynomial time. The computational complexity of the intern-hospital assignment problem with couples is unresolved. A variant of the marriage problem that allows ties will be shown to be logspace P-complete. Finally, the intern-hospital assignment problem with couples, but without ties, will be shown to be logspace P-hard.
20 citations
TL;DR: In this paper, the authors present a review of the formulation, interpretation and solution methodology of the traffic assignment problem, and an attempt is made to classify it into non-equilibrium assignment models.
Abstract: This study reviews in two parts the formulation, interpretation and solution methodology of the traffic assignment problem. An extensive literature exists on this subject, and in the study an attempt is made to classify it. The first paper (Part I) is devoted to non‐equilibrium assignment models. The accompanying paper (Part II) examines algorithmic approaches which are based on or make use of the Wardropian principle of equal travel times and which are thereafter characterized as equilibrium assignments. Non‐equilibrium models are classified into: (1) all‐or‐nothing assignments; (2) capacity‐restraint assignments; (3) diversion models; (4) multipath assignments; and (5) combined models. In each category the operating principles are described in brief, together with other details such as advantages‐disadvantages, validation efforts and applications of these models.
14 citations
TL;DR: A ‘new’ approach for solving assignment problems which builts upon Monge's observation is presented, to transform an arbitrary assignment problem into an ‘equivalent’ one where Monge’s condition is fulfilled.
13 citations
TL;DR: The particular structure of the problem and the use of reduced costs make it possible to devise an efficient “threshold” algorithm to solve these sub-problems of the minimum cost bipartite matching problem.
01 Dec 1986
TL;DR: This paper proposes efficient parallel algorithms for multi-input controllability problem and the single-input pole assignment problem that have potentials for implementations on some existing and future parallel processors.
Abstract: The design and analysis of time-invariant linear control systems give rise to a variety of interesting linear algebra problems. Numerically viable sequential algorithms now exist for most of these problems; however, efficient parallel algorithms are virtually nonexistent. In this paper, we propose efficient parallel algorithms for multi-input controllability problem and the single-input pole assignment problem. A desirable feature of these algorithms is that they are composed only of basic linear algebraic operations such as vector-matrix multiplication, solution of a linar system and computation of eigenvalues or singular values of a symmetric matrix, for which efficient parallel algorithms have already been developed. Thus, the proposed algorithms have potentials for implementations on some existing and future parallel processors.
01 Jan 1986
TL;DR: Some new efficient solution techniques are outlined and a recent application concerning the assignment of time-slots in a time division multiple access system is described.
Abstract: Recent developments for linear and quadratic assignment problems are surveyed. In particular some new efficient solution techniques are outlined and a recent application concerning the assignment of time-slots in a time division multiple access system is described. Finally assignment problems are used to solve a problem in channel routing.
01 Sep 1986
TL;DR: The shortest augmenting path method can be used as basis for a so called “in-core/out-of-core” approach for solving large assignment problems in which the data cannot be kept in central memory of a computer.
Abstract: We describe how the shortest augmenting path method can be used as basis for a so called “in-core/out-of-core” approach for solving large assignment problems in which the data cannot be kept in central memory of a computer. Here we start by solving the assignment problem on a sparse subgraph and then we introduce the remaining edges in an outpricing/reoptimization phase. We introduce several strategies which enable to keep the working subgraph sparse throughout the procedure and even lead to an all in-core code which is faster than the basic shortest augmenting path code.
TL;DR: In this paper, a linear programming (L.P) formulation of the problem was proposed and obtained the same optimal result via considering the L.P. dual problem, where the optimal value of the common due-date coincides with one of the job completion times for a given job sequence.
Abstract: This note considers the n-job, one-machine scheduling problem with common due-dates. Previous research has shown that the optimal value of the common due-date coincides with one of the job completion times for a given job sequence. In this note, we propose a linear programming (L.P.) formulation of the problem and obtain the same optimal result via considering the L.P. dual problem.
18 Jun 1986
TL;DR: In this paper, the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.
Abstract: The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.
TL;DR: In this method, not only traffic volume but also the length and waiting time of stationary traffic congestion can be expected, and the solution algorithm is enough practical.
Abstract: Equilibrium traffic assignment on a congested network is dealt by considering queues at intersections. The travel time on a link with congested flow is expressed as the sum of running time at non-congested flow regime and imaginary waiting time at the end of link. Traffic volume on links and waiting time in queues are required through equilibrium conditions. The problem is formed as a convex programming, which has explicit capacity restraints. The problem is transformed the ordinary traffic assignment problem by use of interior penalty function method. The solution is required as the limit value of solutions of them. The waiting time on a congested link is equivalent to the derivative of penalty function. A feasible point search using the solution algorithm itself is suggested. In this method, not only traffic volume but also the length and waiting time of stationary traffic congestion can be expected, and the solution algorithm is enough practical.
TL;DR: In this article, a multi-machine, multi-product production environment with an automated material handling system for the conveyance of parts is considered, where each individual machine in the system is capable of performing many different operations and each machine part may have alternative routes through the system.
TL;DR: In this paper, the pole assignment problem of a class of 2-dimensional linear discrete systems is solved and an algorithm for a larger class of systems is presented, where the most robust feedback gain matrix is found.
Abstract: In Kaczorek (1983) the pole-assignment problem of a class of 2-dimensional linear discrete systems is solved. In this paper, an algorithm for a larger class of systems is presented. If degrees of freedom permit, the most 'robust' feedback gain matrix can be found. Numerical examples are included.
01 Dec 1986
TL;DR: The classical state-feedback pole assignment problem of time-invariant systems to linear periodic systems is extended to present conditions for the robust stabilizability of systems, in the sense that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized.
Abstract: In this paper we extend the classical state-feedback pole assignment problem of time-invariant systems to linear periodic systems. This concept is used to present conditions for the robust stabilizability of systems, in the sense that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. Upper bounds on the norm of the feedback matrix and on the transient response are also minimized, and an estimation is given of the maximum disturbance which can be made to the closed-loop system such that stability is retained.
TL;DR: The capacity assignment problem in a packet-switching communication network is examined with a new look and under general assumptions about the form of the network cost function and a general class of delay measures, which includes as special cases all the previously proposed delay criteria as discussed by the authors.
01 Jan 1986
TL;DR: In this paper, the basic concept of the state space approach to linear computer control is discussed, and the main part of the paper is devoted to the problem of the system state estimation and to the principles of deterministic synthesis.
Abstract: The tutorial paper deals with the basic concept of the state space approach to linear computer control e.g. to command control and to compensation of disturbances. Besides the introductory notions concerning system state and state equations, stability and generation of control variables, the main part of the paper is devoted to the problem of the system state estimation and to the principles of deterministic synthesis. This regards the pole assignment problem, finite number of control steps, feedforward controllers and quadratic cost functions.
18 Dec 1986
TL;DR: Experimental results establish the superiority of the new heuristics over earlier ones in the via assignment problem that arises when the single row routing approach to the interconnection problem is used.
Abstract: We examine the via assignment problem that arises when the single row routing approach to the interconnection problem is used. Some new complexity results and two new heuristics are obtained. Experimental results establish the superiority of the new heuristics over earlier ones.
TL;DR: In this article, the coefficient assignment problem by periodic feedback for 2-D linear systems described by the Roesser model is considered and sufficient conditions for the existence of a solution to the problem are established.
Abstract: The coefficient assignment problem by periodic feedback for 2-D linear systems described by the Roesser model is considered. Sufficient conditions for the existence of a solution to the problem are established. A procedure for finding a sequence of feedback gain matrices is presented and illustrated by a numerical example.
TL;DR: A problem is formulated where a set of processes is assigned on the multiprocessor system so that the overall processing time is minimized and the optimum number of PEs is determined by introducing an approximation to the waiting time for the CN.
Abstract: This paper discusses the process assignment problem in the multiprocessor system with communication contentions due to interprocess communications (IPCs) As a model for the multiprocessor system, a system is considered in which the processing elements (PEs) with local memory (LM) are connected through a communication network (CN) As a model for the distributed-type algorithm realized on such a system, a scheme is considered in which the process assigned on a PE is executed with IPC with other processes Based on these models, a problem is formulated where a set of processes is assigned on the multiprocessor system so that the overall processing time is minimized Especially, for the problem where a single common bus is used as the CN and the processes are assumed as uniform, the optimum number of PEs is determined by introducing an approximation to the waiting time for the CN The strict solution obtained by exhaustive search is compared with the approximate solution, and the validity of the approximate solution is evaluated
TL;DR: In this article, an optimal solution to a special case in which the partially ordered sets are trees and forests is presented, and a related enumeration problem is studied also in this paper.
Abstract: A personnel assignment problem is formulated as a problem of embedding a partially ordered set into another one In this paper, an optimal solution to a special case in which the partially ordered sets are trees and forests is presented Also, a related enumeration problem is studied
01 Jun 1986
TL;DR: In this article, a micro-computer based scheduling algorithm is developed to assist UPT schedulers in finding feasible solutions to daily scheduling problems, where the problem is formulated as a two level network flow problem.
Abstract: : Undergraduate Pilot Training (UPT) is a dynamic, high pressure program which produces front line aviators for the United States Air Force. The eleven month curriculum contains a complicated assortment of academic, flight, and simulator training. Recent expansions in the UPT program and increased emphasis on cost effective scheduling have rendered the current manual scheduling methods obsolete. This thesis develops a micro-computer based scheduling algorithm which aids UPT schedulers in finding feasible solutions to daily scheduling problems. We formulate the problem as a two level network flow problem. Level 1 uses both maximum flow and minimum cost flow formulations to solve the instructor assignment problem. Level 2 addresses student scheduling and uses a two pass, optimization based heuristic which assigns students via a network transportation formulation. The bi-level network formulation produces feasible daily schedules in minutes on an IBM PC/XT compared to the hours required for the manual method. It also performs feasibility checks at both levels and allows scheduler interaction to effectively generate daily schedules.
01 Jan 1986
TL;DR: This paper presents mathematical programming models for the problem of estimating a trip matrix from network data based on the results of Nguyen (1977) who has shown that trip matrices that reproduces observed linkflows in a congested network can be obtained by solving an elastic demand traffic assignment problem with a specific linear demand function.
Abstract: In this paper we present mathematical programming models for the problem of estimating a trip matrix from network data. The models presented are based on the results of Nguyen (1977) who has shown that trip matrices that reproduces observed linkflows in a congested network can be obtained by solving an elastic demand traffic assignment problem with a specific linear demand function.
TL;DR: In this article, the traveling salesman problem is modeled as an assignment problem with subtour elimination constraints, and the optimal solution to the assignment problem serves as a lower bound to the travelling salesman problem.