View in EDS

Approximation algorithm for generalized budgeted assignment problems and applications in transportation systems.

Saved in:
Bibliographic Details
Title: Approximation algorithm for generalized budgeted assignment problems and applications in transportation systems.
Authors: Jiang, Hongyi1 (AUTHOR) hongyi.jiang@cityu.edu.hk, Samaranayake, Samitha2 (AUTHOR) samitha@cornell.edu
Source: Discrete Applied Mathematics. Dec2024, Vol. 359, p383-399. 17p.
Subjects: Approximation algorithms, Budget, Transportation planning, Bins, Motivation (Psychology), Bin packing problem
Abstract: Motivated by a transit line planning problem in transportation systems, we investigate the following capacitated assignment problem under a budget constraint. Our model involves L bins and P items. Each bin l has a utilization cost c l and an n l -dimensional capacity vector. Each item p has an n l -dimensional binary weight vector r l p , where the 1s in r l p (if any) appear in consecutive positions, and its assignment to bin l yields a reward v l p. The objective is to maximize total rewards through an assignment that satisfies three constraints: (i) the total weights of assigned items do not violate any bin's capacity; (ii) each item is assigned to at most one open bin; and (iii) the overall utilization costs remain within a total budget B. We propose the first randomized rounding algorithm with a constant approximation ratio for this problem. We then apply our framework to the motivating transit line planning problem, presenting corresponding models and conducting numerical experiments using real-world data. Our results demonstrate significant improvements over previous approaches in addressing this critical transportation challenge. [ABSTRACT FROM AUTHOR]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:Motivated by a transit line planning problem in transportation systems, we investigate the following capacitated assignment problem under a budget constraint. Our model involves L bins and P items. Each bin l has a utilization cost c l and an n l -dimensional capacity vector. Each item p has an n l -dimensional binary weight vector r l p , where the 1s in r l p (if any) appear in consecutive positions, and its assignment to bin l yields a reward v l p. The objective is to maximize total rewards through an assignment that satisfies three constraints: (i) the total weights of assigned items do not violate any bin's capacity; (ii) each item is assigned to at most one open bin; and (iii) the overall utilization costs remain within a total budget B. We propose the first randomized rounding algorithm with a constant approximation ratio for this problem. We then apply our framework to the motivating transit line planning problem, presenting corresponding models and conducting numerical experiments using real-world data. Our results demonstrate significant improvements over previous approaches in addressing this critical transportation challenge. [ABSTRACT FROM AUTHOR]
ISSN:0166218X
DOI:10.1016/j.dam.2024.09.020