A hybrid genetic search for the inventory routing problem

A heuristic algorithm based on beam search and iterated local search for the maritime inventory routing problem

Inventory routing for humanitarian water distribution in drought-affected regions

Production routing problems (PRPs) are integrated planning problems that combine vehicle routing and lot-sizing decisions. Given a discrete finite time horizon and a set of customers, the basic PRP consists of deciding for each period if and how much to produce, the inventories at the supplier and the customers, and the vehicle routes. The latter include the decisions on which customers to serve and the quantities delivered. The objective is to minimize the total cost over the planning horizon consisting of production, inventory, and routing cost. In this paper, we consider the PRP with time windows (PRPTW) and propose a branch-price-and-cut (BPC) algorithm for its solution. The BPC relies on a path-based formulation that explicitly specifies which demands are satisfied by which deliveries and employs several families of valid inequalities. The performance of the BPC is assessed in an extensive computational study on existing benchmark instances for the related inventory routing problem with time windows (IRPTW) and newly created instances for the PRPTW. Our BPC outperforms the current state-of-the-art BPC for the IRPTW, closing 62 previously open instances. Finally, we derive managerial insights from our PRPTW instances.

This paper addresses the Distance-Constrained Inventory Routing Problem (DCIRP), a complex problem that combines inventory management and vehicle routing in a logistics context. The problem arises in the context of a specialty gas delivery company that maintains a specialty gas holding facility at each customer’s site and uses several trucks to deliver specialty gas, with the additional constraint that drivers are limited to the number of kilometers they can drive each day. A Mixed Integer Linear Programming (MILP) formulation is proposed to model the DCIRP. The DCIRP is a variant of the Inventory Routing Problem (IRP), and an NP-hard combinatorial optimization problem. The main objective of this research is to improve the efficiency and effectiveness of DCIRP resolution, while accounting for vehicle capacity constraints, customer inventory levels, and delivery route distance constraints. By optimizing routes and inventory management, the company’s operations become more sustainable. To solve the problem, three solution approaches are proposed. The first is an exact method based on the MILP formulation. The second is a matheuristic that uses an inventory-first, route-second (IFRS) approach, including a minimum route cost approximation and a local search procedure. The results show that the proposed matheuristic produces high-quality solutions with a reasonable computational effort.

Effective hybrid branch-and-cut algorithm for the inventory routing problem with open vehicle routing constraints

Rural freight mobility and logistics face persistent challenges, including inadequate road infrastructure, high transportation costs, safety risks, tolls at link access points, and dispersed demand. Traditional inventory routing models often fail to address these complexities, especially in rural contexts where alternative routing options and integrated in-haul/back-haul operations are essential for improving efficiency and reducing empty miles. This study proposes a bi-objective mathematical model for the inventory routing problem in rural logistics, incorporating multiple routing attributes (transportation costs, risks, link-access tolls, and distances) and inventory dynamics (integrated in-haul and back-haul visits). The model aims to minimize total logistics costs and accident risk while balancing operational expenses and safety considerations. Risk estimation is derived from crash data along rural road links connecting distribution nodes. A real-world case study involving Walmart distribution centers in Macclenny, Baker County, Florida, and several rural Supercenters is conducted to validate the model. A modified Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is developed and compared with CPLEX for solution efficiency across small and large-scale problem instances. Results indicate that the proposed approach outperforms classical methods, improves routing decisions in rural logistics systems, and achieves cost savings of up to 17% for the evaluated objectives, emphasizing the importance of using multi-attribute, multi-route network structures in rural logistics optimization.

In the current e-commerce domain, rising customer demands for diversity, responsiveness, and service quality create major challenges in inventory management and logistics optimisation. To address these, this paper introduces the multi-period and multi-product inventory routeing problem with procurement decisions (MIRP-PD) in self-operated e-commerce, supported by a generative AI and discriminative AI–based forecasting method. The goal is to optimise (i) procurement from geographically dispersed suppliers, (ii) transportation to a central warehouse, and (iii) product pickup from suppliers to the warehouse. Based on AI-generated forecasts, an integer programming model for MIRP-PD is developed. To solve medium- and large-scale problems, a hybrid bi-level heuristic is proposed, combining genetic algorithms (GA) for procurement planning and ant colony optimisation (ACO) for routeing, enhanced by a Lagrangian constraint–based repair operator. A rolling-horizon framework is further applied to mitigate forecast errors. A real-life case study with 15 scenarios demonstrates that the proposed GA–ACO achieves superior performance compared with Gurobi and a GA-only baseline. Comparative execution tests confirm that AI-based forecasting substantially reduces excess holding, transportation, and stockout costs. Sensitivity analyses provide managerial insights into transport strategies, warehousing–transport trade-offs, and service-level penalties, highlighting the role of generative and discriminative AI in enabling robust replenishment decisions.

ABSTRACT Two‐echelon distribution systems with an intermediate urban consolidation centre are one of the key innovations proposed in city logistics. We focus on a business‐to‐business context in which urban retailers are delivered by suppliers via such a city hub. Specifically, we investigate the benefits of simultaneously optimising routing decisions from the Urban Consolidation Center and inventory decisions at the retailers. For this, we extend the classical Inventory Routing Problem (IRP) to an urban setting, considering complexities like time windows, heterogeneous vehicles, and multiple trips per vehicle per day. We propose a two‐phase matheuristic solution algorithm, and compare its results to a baseline approach in which inventory and routing decisions are made sequentially. Computational results demonstrate that the integrated approach consistently outperforms the traditional sequential approach. A detailed analysis of instance characteristics influencing the outcome of these scenarios highlights the impact of variables such as the number of retailers and suppliers, and holding costs. A sensitivity analysis identifies critical factors affecting the implementation of the integrated scenario, emphasising the importance of retailer storage capacity, order costs, and retailer participation. The findings highlight the overall potential benefits of integration, including cost savings, improved resource utilisation, and positive impacts on all stakeholders involved.

Inventory routing with heterogeneous vehicles and hazardous material backhauling

The stochastic and dynamic inventory routing problem with fine time granularity: A reinforcement learning approach

The inventory routing problem with two-dimensional loading constraints

To enhance the cost efficiency and response effectiveness of the equipment maintenance material support system, the inventory routing problem (IRP) is applied to demand points characterized by low capacity to sales ratios. An IRP model is developed under material supply constraints, specifically tailored to these demand points. An innovative genetic algorithm is designed to solve this model. Based on the unique features of the problem, two structural solution arrays are formulated, and a parallel vehicle multiple delivery initial solution generation process is constructed. The traditional genetic algorithm operations, including selection, crossover, and mutation, are modified in accordance with the characteristics of the initial solution structure. The model is implemented and tested using MATLAB and compared against the Gurobi optimization solver. Results indicate that the proposed algorithm performs comparably to Gurobi in small-scale scenarios while demonstrating superior performance in large-scale instances. These findings confirm the validity and effectiveness of both the proposed IRP model and the associated solution algorithm.

Maritime inventory routing with an application to fish feed distribution

Large neighborhood and hybrid genetic search for inventory routing problems

The inventory routing problem (IRP) in a retail supply chain setting allows for the simultaneous optimisation of delivery schedules, vehicle routes, and delivery quantities. The IRP relies on the adoption of a vendor-managed inventory strategy which has the potential to reduce transportation, inventory, and stock-out costs in a supply chain. In this paper, we introduce a mathematical model for a new IRP variant, the heterogeneous fixed fleet IRP with time-windows (HeFIRPTW) with route and schedule unpredictability, in the form of a bi-objective mixed-integer linear programming problem. This model simultaneously incorporates route and schedule unpredictability aimed at mitigating inherent safety and security threats experienced during the transportation of valuable goods. Delivery routes and schedules are generated that minimise the operational costs incurred whilst also ensuring that route segments are not traversed too regularly and that customers are not visited during overlapping daily time intervals. The feasibility of adopting an exact ϵ -constrained model solution solution method is investigated empirically by solving small, adapted benchmark instances of the problem. An investigation into the model solution complexity for varying problem sizes reveals that unpredictability, particularly with tightened constraints, increases the computational time. The complexity implications of multiple vehicles and the imposition of time-windows are also examined. The results highlight the computational demands of the proposed model, demonstrating a clear need for a faster, perhaps approximate, solution approach capable of generating high-quality solutions for realistic problem instances within reasonable time-frames. • An inventory routing problem with route and schedule unpredictability is proposed. • A novel bi-objective, mixed-integer linear programming model is formulated. • The model is validated in the context of a benchmark data set. • An iterative ϵ -constraint method is adopted to solve problem instances. • The time complexity of adopting an exact solution approach is studied empirically.

Inventory routing problem of automotive parts considering time-varying demands: A machine learning enhanced branch-and-price approach

The study is devoted to a comprehensive investigation and synthesis of optimization models and digital technologies for managing multimodal cargo flows with conflicting logistics regulations, inert materials, and refrigerated cargoes, in the context of the Trans-European Transport Network corridors (TEN-T). The aim of the study is to develop a conceptual framework for integrated management of the specified flows, oriented toward improving the operational performance, resilience, and fault tolerance of logistics chains. The methodological basis includes a systematic review of the scientific literature on vehicle routing problems (VRP) and inventory routing problems (IRP), as well as a content analysis of European Union strategic documents and industry reports. The analysis records a persistent structural imbalance in the modal split of freight transport in the EU: the dominance of road transport contradicts the strategic goals of decarbonization. As a response, a multilayer conceptual architecture is proposed, integrating the Internet of Things (IoT) and blockchain to ensure data integrity and traceability, digital twins for predictive modeling, and multi-agent systems (MAS) for decentralized autonomous coordination. The conclusion of the study is that replacing centralized planning with decentralized orchestration of logistics services is a necessary condition for overcoming existing barriers and unlocking the potential of the TEN-T network. The material presented in the study will be of interest to researchers in logistics and supply chain management, transport planning specialists, and decision-makers in the development of transport infrastructure.

This study addresses a single-period multi-product inventory routing problem (IRP) considering reactive lateral transhipment with the optimisation objective of logistics ratio, defined as logistics cost per unit of product value. The problem is modelled in two stages: in the first stage, the distribution is planned based on imperfect forecasted demand. In the second stage, actual demand is revealed, and reactive lateral transhipment is executed based on first-stage decisions. We develop a basic fractional programming (BFP) model with deterministic demand for both stages. Considering demand uncertainty, we extend a robust fractional programming (RFP) model and a two-stage robust fractional programming (TSRFP) model for first-stage IRP and propose structural uncertainty sets. We apply Dinkelbach's algorithm and the robust counterpart transformation to tackle the RFP model. We employ the column and constraint generation algorithm to address the TSRFP model with Dinkelbach's algorithm. The results indicate that the proposed TSRFP is suits scenarios with high stockout penalties and at medium demand uncertainty levels. Managers can select between TSRFP, RFP, and BFP to optimise inventory management based on demand uncertainty and product attributes.

Optimizing multi-vehicle inventory routing problem for waste collection with overflow-level-dependent service times in bins