Multi-vehicle Inventory Routing Problem Research Articles

An Effective Matheuristic for the Multivehicle Inventory Routing Problem

This study considers the multivehicle inventory routing problem in which a supplier has to build a distribution plan over a discrete time horizon to replenish a set of customers that faces a given demand. Transportation costs as well as inventory costs at the supplier and at the customers are to be minimized. A matheuristic algorithm is proposed that is based on sequentially solving different mixed integer linear programs. The algorithm merges the advantage of being easy to design and implement, as it is mainly based on the problem formulation, with the benefit of providing high-quality solutions. A computational study is performed on benchmark test instances by comparing the results with the ones obtained from previous algorithms proposed in the literature. The results show that the matheuristic algorithm outperforms the existing heuristic algorithms and finds a significant number of new best solutions in both small and large instances.

A matheuristic for solving inventory sharing problems

In this paper, we addressed a two-level supply chain in which a company manufactures products and sells them through its point of sale network. The problem of concern is a multi-product, multi-vehicle inventory sharing routing problem. We formulated it as a mixed-integer linear programming problem. We also designed a two-phase matheuristic that integrates mathematical modelling strengthened with relevant derived valid inequalities and hybridisation of sophisticated metaheuristics: Genetic Algorithm and Simulated Annealing. We tested 660 best known instances designed for the single and multi-vehicle inventory routing problem, and the results showed that the matheuristic outperformed the best known algorithms regarding computational times and enhanced 156 solutions for large instances. Extra experiments were conducted on a set of data specially designed for the multi-product multi-vehicle inventory sharing routing problem. Computational results highlighted the benefits of sharing inventory on the overall supply chain. Finally, a sensitivity analysis was conducted, which revealed the extent to which inventory sharing among different points of sale can be cost-effective by the savings it brings to reduce lost sales and inventory holding.

A kernel search heuristic for the multivehicle inventory routing problem

AbstractIn this paper an inventory routing problem is studied in which the goal is to determine an optimal distribution plan to replenish a set of customers by routing a limited fleet of capacitated vehicles over a discrete planning horizon. Each customer consumes a per period quantity of product and has a maximum inventory capacity. The goal is to minimize the total distribution cost that comprises the routing and the inventory holding costs. A matheuristic is presented, which uses the information gathered by a tabu search to build a sequence of mixed‐integer linear programming problems of small size. Extensive computational experiments are conducted on a large set of benchmark instances. The results show that the matheuristic outperforms other state‐of‐the‐art algorithms in terms of average solution quality.

Multi-product multi-vehicle inventory routing problem with vehicle compatibility and site dependency: A case study in the restaurant chain industry

We study an inventory routing problem (IRP) for the restaurant chain. We proposed a model a multi-product multi-vehicle IRP (MMIRP) with multi-compatibility and site-dependency (MMIRP-MCSD). The problem was formulated as a mixed integer programming (MIP). This model is difficult to solve because it is a problem that integrates MMIRP, a multi-compartment vehicle routing problem (MCVRP), and a site dependent VRP (SDVRP), each of which is difficult even by itself. Therefore, in this study, we proposed three-stage Math Heuristics based on the cluster-first and route-second method. In the numerical experiment, verification was performed using actual data, and knowledge on the decision making of the optimum vehicle type was obtained.

A Matheuristic for the Multivehicle Inventory Routing Problem

We consider the inventory routing problem, in which a supplier has to replenish a set of customers by means of a limited fleet of capacitated vehicles over a discrete time horizon. The goal is to minimize the total cost of the distribution that comprises the inventory cost at the supplier and at the customers and the routing cost. We present a matheuristic that combines a tabu search and mathematical programming formulations. When compared with two exact methods on 640 small instances, the matheuristic finds 192 (48%) optima over the 402 instances with known optima and improves 125 upper bounds. Tested on 240 large instances (with up to 200 customers) for which no optimal solutions are known, it improves the best solution for 220 (92%) of the 240 instances. The online supplement is available at https://doi.org/10.1287/ijoc.2016.0737 .

GVNS based heuristic for solving the multi-product multi-vehicle inventory routing problem

We address a multi-product version of the IRP, in which a supplier is responsible for the distribution of several products to a set of geographically dispersed customers using a feet of heterogeneous vehicles. We deal with a deterministic version of demand rates in which the supplier has full knowledge of future demands. To generate good solutions, we have developed an algorithm based on the Variable Neighborhood Search capable of solving this variant. Our comparative tests on a large set of artificial instances have shown that our heuristic can produce high quality solutions.

A Hybrid Heuristic based on Iterated Local Search for Multivehicle Inventory Routing Problem

We study a multivehicle inventory routing problem (MIRP) in which supplier delivers one type of product along a finite planning horizon, using a homogeneous fleet of vehicles. The main objective is to minimize the total cost of storage and transportation. In order to solve MIRP, we propose an algorithm based on iterated local search (ILS) metaheuristic, using a variable neighborhood descent with random neighborhood ordering (RVND) in the local search phase. Moreover, we combined this algorithm with an exact procedure based on mathematical programming to solve specifically the inventory management as a subproblem. To validate our approach, computational tests were performed on 560 benchmark instances, achieving very competitive results in comparison to the best known algorithms.

GRASP-based heuristic algorithm for the multi-product multi-vehicle inventory routing problem

In this paper, we introduce an improved Greedy Randomized Adaptive Search Procedure (GRASP) based heuristic for the multi-product multi-vehicle inventory routing problem (MMIRP). The inventory routing problem, which combines the vehicle-routing problem and the inventory control decisions, is one of the most important problems in combinatorial optimization field. To deal with the MMIRP, we develop a GRASP-based heuristic (GBH). Each GBH iteration consists of two sequential phases; the first phase is a Greedy Randomized Procedure, in which, the best tradeoff between the inventory holding cost and routing cost is looked. Then, in the second phase, as local search for the GRASP, we use the Tabu search (TS) meta-heuristic to improve the solution found in the first phase. The GBH two phases are repeated until some stopped criterion is met. Our proposed method is evaluated on two benchmark data sets, and successfully compared with two state-of-the-art algorithms.

Políticas de distribuição com lote econômico de entrega em problemas de roteirização com estoque gerenciado pelo fornecedor e sistema logístico em três níveis

Em sistemas de gerenciamento de estoque pelo fornecedor (Vendor Managed Inventory - VMI), as decisões logísticas são centralizadas no Centro de Distribuição (CD), possibilitando uma redução simultânea dos custos de armazenagem e transporte. Sua operação requer a resolução de um complexo problema de otimização combinatória, denominado Problema de Roteirização e Estoques (PRE) que consiste no gerenciamento do estoque do cliente, no estabelecimento da frequência e quantidade de produto entregue, além do roteiro percorrido pelo veículo ao longo de um horizonte de planejamento. Este trabalho apresenta três novas políticas de distribuição baseadas no cálculo de lote econômico de entrega para o PRE. Um modelo de Programação Linear Inteira Mista Binária (PLIMB) foi proposto considerando um sistema logístico de três níveis, sendo uma Base de Fornecimento (BF), um CD e um conjunto de clientes. Também foi proposta uma nova abordagem heurística que decompõe o PRE em dois subproblemas: o primeiro é responsável pela programação das entregas e a formação de grupos de atendimento ao longo do horizonte de planejamento. O segundo subproblema constrói os roteiros para os grupos formados no primeiro estágio, empregando heurísticas clássicas de construção de rotas, juntamente com procedimento de melhorias intrarrotas. Ajustes entre rotas são realizados por uma nova estratégia de busca ampla em vizinhança. Cenários de pequeno, médio e grande porte, com variações no custo de estocagem e de transporte, foram gerados a partir de dados da literatura e parametrizados no contexto da pesquisa. Extensivos testes computacionais foram conduzidos a fim de evidenciar a eficiência das políticas de distribuição propostas e a efetividade da estratégia heurística utilizada.

New Formulation for an Economic Order Quantity Distribution Policy in Vendor-Managed Inventory Routing Problems

In vendor managed inventory systems, logistics decisions are centralized at the vendor, allowing inventory storage and transportation costs to be reduced simultaneously. Operation of such systems requires the solution of a complex combinatorial optimization problem, known as the Inventory Routing Problem (IRP), which involves managing client inventory and determining the frequency and size of product deliveries as well as the route taken by the vehicle over a given planning horizon. We present a new formulation based on an economic order quantity distribution policy for the multivehicle inventory routing problem (MIRP). A mathematical programming model with additional practical constraints was used for the MIRP. A new heuristic approach that breaks the MIRP down into the following two sub-problems was also proposed: one dealing with the scheduling of deliveries and the formation of delivery clusters over the planning horizon, and the second sub-problem, which builds the routes for the delivery clusters using classic route construction heuristics and a procedure for intra-route improvements. Adjustments between routes are performed with the aid of a new large neighborhood search (LNS) strategy. Small, medium-sized and large scenarios with different storage and transportation costs were generated using parameters based on data from the literature. Extensive computational tests were carried out to determine the effectiveness of the proposed distribution policy and the heuristic used.