Graph Methods for Solving the Unconstrained and Constrained Optimal Assignment Problem for Locomotives on a Single-Line Railway Section

2021 ◽  
Vol 82 (5) ◽  
pp. 780-797
Author(s):  
L. Yu. Zhilyakova ◽  
N. A. Kuznetsov
Keyword(s):  
Assignment Problem ◽  
Single Line ◽  
Optimal Assignment

scholarly journals Topology-Aware Strategy for MPI-IO Operations in Clusters

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Weifeng Liu ◽  
Jie Zhou ◽  
Meng Guo
Keyword(s):  
Phase I ◽  
Execution Time ◽  
Assignment Problem ◽  
Optimal Assignment ◽  
Local Data ◽  
Two Phase ◽  
File Access ◽  
Linear Assignment Problem ◽  
Linear Assignment

This paper presents the topology-aware two-phase I/O (TATP), which optimizes the most popular collective MPI-IO implementation of ROMIO. In order to improve the hop-bytes metric during the file access, topology-aware two-phase I/O employs the Linear Assignment Problem (LAP) for finding an optimal assignment of file domain to aggregators, an aspect which is not considered in most two-phase I/O implementations. The distribution is based on the local data stored by each process, and its main purpose is to reduce the total hop-bytes of the I/O collective operation. Therefore, the global execution time can be improved. In most of the considered scenarios, topology-aware two-phase I/O obtains important improvements when compared with the original two-phase I/O implementations.

scholarly journals Perturbation of eigenvalues of matrix pencils and the optimal assignment problem

2004 ◽  
Vol 339 (2) ◽  
pp. 103-108 ◽  
Author(s):  
Marianne Akian ◽  
Ravindra Bapat ◽  
Stéphane Gaubert
Keyword(s):  
Assignment Problem ◽  
Optimal Assignment ◽  
Matrix Pencils

Pose verification as an optimal assignment problem

1991 ◽  
Vol 12 (1) ◽  
pp. 45-53 ◽  
Author(s):  
Suchendra M. Bhandarkar ◽  
Minsoo Suk
Keyword(s):  
Assignment Problem ◽  
Optimal Assignment

OPTIMAL SUBCUBE ASSIGNMENT FOR PARTITIONABLE HYPERCUBES

1992 ◽  
Vol 02 (01) ◽  
pp. 89-95
Author(s):  
RAMESH KRISHNAMURTI ◽  
BHAGIRATH NARAHARI
Keyword(s):  
Execution Time ◽  
Assignment Problem ◽  
Parallel Architectures ◽  
Log P ◽  
Optimal Assignment ◽  
Assignment Algorithm ◽  
Multiple Tasks ◽  
Independent Tasks

This paper formulates and discusses a processor assignment problem arising in partitionable parallel architectures. A partitionable hypercube multiprocessor can simultaneously execute multiple tasks where each task is independently executed on a subcube. Given a p processor hypercube and n independent tasks, where a task can be assigned a subcube of any size, an assignment determines the size of the subcube — i.e., the number of processors — to be assigned to each task. The objective of our problem is to find the optimal assignment which minimizes the maximum execution time among all tasks. We present an O(n log p max { log log p, log n}) algorithm that determines an optimal assignment. This algorithm can be efficiently parallelized, on the p processor hypercube, to obtain an O((n/p) log p log 2(n log p)) parallel assignment algorithm.

SENSITIVITY ANALYSIS OF OBJECTIVE FUNCTION COEFFICIENTS OF THE ASSIGNMENT PROBLEM

2007 ◽  
Vol 24 (02) ◽  
pp. 203-221 ◽  
Author(s):  
CHI-JEN LIN ◽  
UE-PYNG WEN
Keyword(s):  
Sensitivity Analysis ◽  
Assignment Problem ◽  
Optimal Solution ◽  
The Other ◽  
Sensitivity Analyses ◽  
Basic Solution ◽  
Optimal Assignment ◽  
Cost Matrix ◽  
Sensitivity Range ◽  
Optimal Basic Solution

Information of sensitivity analysis, in a linear programming problem, is usually more important than the optimal solution itself. However, traditional sensitivity analysis, which perturbs exactly one coefficient and then determines the range preserving the optimality of the current optimal base, is impractical for the assignment problem. An optimal basic solution of the assignment problem is inherently degenerate, so it may be that the optimal base has changed but the optimal assignment remains unchanged. Furthermore, elements of a column (or row) in a cost matrix of assignment problem are usually closely related and change simultaneously, not uniquely. This paper focuses on two kinds of sensitivity analyses for the assignment problem. One is to determine the sensitivity range, over which the current optimal assignment or all the optimal assignments remain optimal, while perturbing the elements of one column (or row) in a cost matrix of the assignment problem simultaneously but dependently. The other is to perturb elements of one column (or row) in a cost matrix of the assignment problem simultaneously but independently. Numerical illustrations are presented to demonstrate that the approaches are useful in practice.

THE SEQUENTIAL STOCHASTIC ASSIGNMENT PROBLEM WITH POSTPONEMENT OPTIONS

2012 ◽  
Vol 27 (1) ◽  
pp. 25-51 ◽  
Author(s):  
Tianke Feng ◽  
Joseph C. Hartman
Keyword(s):  
Stochastic Process ◽  
Decision Maker ◽  
Assignment Problem ◽  
Lower Risk ◽  
Care Management ◽  
Optimal Assignment ◽  
Threshold Policies ◽  
Stochastic Assignment ◽  
Sequential Stochastic Assignment ◽  
Heterogeneous Resources

The sequential and stochastic assignment problem (SSAP) has wide applications in logistics, finance, and health care management, and has been well studied in the literature. It assumes that jobs with unknown values arrive according to a stochastic process. Upon arrival, a job's value is made known and the decision-maker must immediately decide whether to accept or reject the job and, if accepted, to assign it to a resource for a reward. The objective is to maximize the expected reward from the available resources. The optimal assignment policy has a threshold structure and can be computed in polynomial time. In reality, there exist situations in which the decision-maker may postpone the accept/reject decision. In this research, we study the value of postponing decisions by allowing a decision-maker to hold a number of jobs which may be accepted or rejected later. While maintaining this queue of arrivals significantly complicates the analysis, optimal threshold policies exist under mild assumptions when the resources are homogeneous. We illustrate the benefits of delaying decisions through higher profits and lower risk in both cases of homogeneous and heterogeneous resources.

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