On the feasibility of solutions to the split delivery vehicle routing problem represented as edge variables

Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We show that this recognition problem depends on the formulation's constraints and...

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Vydané v:	Operations research letters Ročník 58; s. 107209
Hlavní autori:	Pessoa, Artur, de Araujo, Daniel, Uchoa, Eduardo
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.01.2025
Predmet:	Edge formulation Polynomial algorithm Split delivery Vehicle routing Polynomial algorithm Edge formulation Vehicle routing Split delivery
ISSN:	0167-6377
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Shrnutí:	Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We show that this recognition problem depends on the formulation's constraints and prove that it's strongly NP-hard for a recent formulation. With subtour elimination constraints, we provide an O(nlog⁡n)-time recognition algorithm. This challenges assumptions about edge-based formulations and provides new insights into SDVRP solution verification complexity.
ISSN:	0167-6377
DOI:	10.1016/j.orl.2024.107209