A split-embedded metaheuristic for the heterogeneous inventory routing problem with batch size

Diego Perdigão Martino, Philippe Lacomme and Katyanne Farias

European Journal of Operational Research, 2026, vol. 328, issue 1, 91-104

Abstract: Handling transportation and inventory management simultaneously is a challenging problem. The most famous optimization problem in this domain, known as the Inventory Routing Problem (IRP), aims to determine the routes and quantities to be delivered by a set of vehicles to meet customer demands at a minimum total inventory and transportation cost. The vast majority of works carried out so far on the IRP consider a homogeneous fleet of vehicles. This paper addresses, instead, a new IRP variant that considers intrinsic characteristics of real supply chains, such as a period-dependent heterogeneous fleet of vehicles and batch sizes for the delivered quantities. We model the problem with a Mixed Integer Linear Programming (MILP) formulation and propose a Split-Embedded Metaheuristic with a Post-Optimization phase (SEMPO) to solve it. Extensive computational experiments are conducted on a set of 80 new benchmark instances with up to 183 customers and a challenging time horizon of up 7 to 28 time periods to evaluate the performance of our approaches. The proposed SEMPO algorithm provides high-quality solutions and faster convergence compared to the MILP formulation.

Keywords: Logistics; Inventory routing problem; Batch size; Heterogeneous fleet; Split algorithm (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:328:y:2026:i:1:p:91-104

DOI: 10.1016/j.ejor.2025.05.044

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