The inventory-routing problem (IRP) dates back 30 years. It can be described as the combination of vehicle-routing and inventory management problems, in which a supplier has to deliver products to a number of geographically dispersed customers, subject to side constraints. It provides integrated logistics solutions by simultaneously optimizing inventory management, vehicle routing, and delivery scheduling. Some exact algorithms and several powerful metaheuristic and matheuristic approaches have been developed for this class of problems, especially in recent years. The purpose of this article is to provide a comprehensive review of this literature, based on a new classification of the problem. We categorize IRPs with respect to their structural variants and the availability of information on customer demand.

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Thirty Years of Inventory Routing

Ship routing and scheduling in the new millennium

In this paper, we survey the literature on matheuristics proposed to solve vehicle routing problems. A matheuristic makes use of mathematical programming models in a heuristic framework. Matheuristics have been applied to several different routing problems and include a number of different approaches. We propose a classification in three classes of matheuristics: decomposition approaches, improvement heuristics and branch-and-price/column generation-based approaches. The contribution of this paper is to offer to researchers interested in routing problems a structured overview of the most successful ideas to combine heuristic schemes and mathematical programming models to obtain high quality solutions. Moreover, we analyze the state of the art and provide insights and hints for future research.

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A survey on matheuristics for routing problems

The combined operation of distribution and inventory control achieved through a vendor-managed inventory strategy creates a synergetic interaction that benefits supplier and customers. Inventory-Routing Problems (IRPs) arise when inventory and routing decisions must be taken simultaneously, which yields a difficult combinatorial optimisation problem. While most IRP research deals with a single product, there are often several products involved in distribution activities. In this paper, we propose a branch-and-cut algorithm for the solution of IRPs with multiple products and multiple vehicles. We formally define and model the problem, and we solve it exactly. We also consider the inclusion of consistency features that are meaningful in a multi-product environment and help improve the quality of the service offered.

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A branch-and-cut algorithm for the multi-product multi-vehicle inventory-routing problem

A concise guide to existing and emerging vehicle routing problem variants

In this paper a maritime inventory routing problem for one of the world's largest producers of liquefied natural gas (LNG) is presented. The producer is responsible for the LNG inventories at the liquefaction plant, the loading port with a limited number of berths, and the routing and scheduling of a heterogeneous fleet of LNG ships. In addition, the producer has to fulfill a set of long-term contracts to customers all around the world. The goal is to create an annual delivery program (ADP) to fulfill the long-term contracts at minimum cost, while maximizing revenue from selling LNG in the spot market. An ADP is a complete schedule of every ship's sailing plan for the coming year. A mixed integer programming (MIP) formulation of the ADP planning problem is presented, and it is based on a priori generation of all possible scheduled voyages within the planning horizon. Due to the size and complexity of the problem, a rolling horizon heuristic (RHH) is proposed. The RHH solves the problem by iteratively solving sub-problems with shorter planning horizons. The RHH finds solutions to the problem within a reasonable amount of time, and creates very good ADPs according to the problem owner.

Christian Rørholt Moe

Papers

A rolling horizon heuristic for creating a liquefied natural gas annual delivery program

A construction and improvement heuristic for a liquefied natural gas inventory routing problem