Large Neighborhood and Hybrid Genetic Search for Inventory Routing Problems

TL;DR

This work introduces a Delivery Schedule (DS) operator for the Inventory Routing Problem (IRP) that optimizes replenishment decisions over an entire planning horizon via a dynamic-programming (DP) cost-to-go formulation. The DS operator, supported by preprocessing functions $F_t(q_i^t)$ and piecewise-linear representations of $C_t(I_i^t)$, is integrated into Hybrid Genetic Search (HGS) to solve IRP at large scale with high efficiency. Empirical results on standard benchmarks and SAHS instances show unprecedented solution quality, including many new best-known solutions, and demonstrate the approach’s robustness across stock-out penalties and inventory settings. The authors also outline extensions to backorders and more complex IRP variants, highlighting broad applicability to dynamic and stochastic contexts. Overall, the DS operator provides a scalable, metaheuristic-friendly mechanism to jointly optimize routing and inventory across time for IRP.

Abstract

The inventory routing problem (IRP) focuses on jointly optimizing inventory and distribution operations from a supplier to retailers over multiple days. Compared to other problems from the vehicle routing family, the interrelations between inventory and routing decisions render IRP optimization more challenging and call for advanced solution techniques. A few studies have focused on developing large neighborhood search approaches for this class of problems, but this remains a research area with vast possibilities due to the challenges related to the integration of inventory and routing decisions. In this study, we advance this research area by developing a new large neighborhood search operator tailored for the IRP. Specifically, the operator optimally removes and reinserts all visits to a specific retailer while minimizing routing and inventory costs. We propose an efficient tailored dynamic programming algorithm that exploits preprocessing and acceleration strategies. The operator is used to build an effective local search routine, and included in a state-of-the-art routing algorithm, i.e., Hybrid Genetic Search (HGS). Through extensive computational experiments, we demonstrate that the resulting heuristic algorithm leads to solutions of unmatched quality up to this date, especially on large-scale benchmark instances.

Figures (7)

• Figure 1: Illustration of the DS neighborhood
• Figure 2: The evolution of the cost function $C_t(I_i^t)$
• Figure 3: Illustration of a function $F_t(q_i^t)$
• Figure 4: An example of computation of the superposition of two piecewise linear functions.
• Figure 5: High-level description of the HGS-IRP algorithm