Modeling and Developing Appropriate Algorithm to Solve Generalized Probabilistic Vehicle Routing Problem

TL;DR

This thesis introduces a stochastic generalized vehicle routing problem model and develops exact and heuristic algorithms to solve it efficiently across various problem sizes, including theoretical foundations and computational validation.

Contribution

First formalization of the stochastic generalized routing problem with new models and algorithms, addressing its NP-hard nature with heuristic solutions for large-scale instances.

Findings

Heuristic algorithms effectively solve large-scale problems.

Computational results validate the efficiency of proposed methods.

The model extends classical routing problems to stochastic and generalized contexts.

Abstract

This thesis introduces stochastic generalized routing problem model and proposes exact and heuristic algorithms to solve it efficiently, in a wide range of problem sizes. At first, the classic routing problem with its common variations in deterministic form is reviewed. Its mathematical models are demonstrated and exact and heuristic algorithms are described. Next, stochastic generalized routing problem is formalized and discussed. Since this problem is introducing for the first time in this thesis, it is necessary to review the required theoretical principles of the problem in terms of stochastic integer programming and linear algebra in discrete spaces. Thus before modeling the problem and developing exact and heuristic algorithms, the required bases to understand the proposed model and algorithms to solve it is discussed. In the next stage with regard to NP-Hard nature of the problem, heuristic algorithms are proposed to efficiently solve it in the large scale sizes. Finally, computational results in different sizes are analyzed. Keywords: Stochastic integer optimization, Stochastic Generalized Routing, Optimal Cut, L-Shape Method