EURO 2025 Leeds
Abstract Submission

1173. Two-index formulations for the traveling purchaser problem with incompatibily constraints

Invited abstract in session WD-58: Exact Algorithms for Vehicle Routing, stream Vehicle Routing and Logistics.

Wednesday, 14:30-16:00
Room: Liberty 1.13

Authors (first author is the speaker)

1. Raquel Bernardino
ISEG, CEMAPRE, UL
2. Daniel Santos
CEGIST, Instituto Superior Técnico, Universidade de Lisboa

Abstract

The Traveling Purchaser Problem with Incompatibility Constraints (TPP-IC) generalizes the classical Traveling Purchaser Problem (TPP) by introducing constraints that prevent certain items from being transported together. This problem arises in various real-world applications, such as hazardous materials transportation, where incompatible products must be handled separately to ensure safety and compliance.
In this study, we propose a novel mixed-integer programming (MIP) formulation that models item incompatibilities using compatibility graphs. Compatibility graphs are used to model the incompatibility constraints implicitly, which makes it possible to use two-index formulations rather than a traditional three-index formulation to formulate the TPP-IC. Several compact and non-compact formulations are proposed for the TPP-IC, which are compared both theoretically and empirically. Additionally, valid inequalities are used to improve the quality of the linear programming relaxation values obtained by the formulations. A branch-and-cut framework is used to address the non-compact models.
Preliminary computational results show that the two-index formulations provide better linear programming relaxation values than the three-index formulation, which we hope will contribute to the two-index models being more efficient than the three-index models in obtaining the optimal values.

Keywords

Status: accepted


Back to the list of papers