Modelling and solving the combined inventory routing problem with risk consideration

A matheuristic solution approach for the production routing problem with visit spacing policy

CARE: Heuristics for two-stage multi-product inventory routing problems with replenishments

A practical solution approach for the cyclic inventory routing problem

The inventory routing problem (IRP) is an integration of vehicle routing and inventory management problems. In the recent years, it has increasingly drawn the attention of the researchers because of its potentially significant practical value. The IRP is classified as NP-hard problem since it subsumes the vehicle routing problem (VRP). This fact led to the development of many heuristic or metaheuristic approaches, although a small number of exact methods have been introduced recently. Heuristic methods offer the advantage of shorter time scales, i.e., greater computational efficiency, on the expense of course of the accuracy of the results. The immediate trigger for this study is our concern about results validation, which has been debatable in early papers, and only recently a systematic effort to create a set of optimally solved benchmark instances has been made. This article presents the heuristic methods for solving the basic variants of IRP found in the literature, stressing the computational results and the solution verification approach, rather than the methodology of the algorithms. The paper concludes with a discussion on the quality of the performance assessment of the proposed algorithms.

An integrated model of the periodic delivery problems for vending-machine supply chains

Production and inventory routing problems consider a single-product supply chain operating under a vendor-managed inventory system. A plant creates a production plan and vehicle routes over a planning horizon to replenish its customers at minimum cost. In this paper, we present two- and three-index formulations, implement a branch-and-cut algorithm based on each formulation, and introduce a local search matheuristic-based algorithm to solve the problem. In order to combine all benefits of each algorithm, we design a parallel framework to integrate all three fronts, called the three-front parallel branch-and-cut algorithm (3FP-B&C). We assess the performance of our method on well-known benchmark instances of the inventory routing problem (IRP) and the production routing problem (PRP). The results show that our 3FP-B&C outperforms by far other approaches from the literature. For the 956 feasible small-size IRP instances, our method proves optimality for 746, being the first exact algorithm to solve all instances with up to two vehicles. 3FP-B&C finds 949 best known solutions (BKS) with 153 new BKS (NBKS). For the large-size set, our method provides two new optimal solutions (OPT), and finds 82% of BKS, being 70% of NBKS for instances with up to five vehicles. This result is more than twice the number of BKS considering all heuristic methods from the literature combined. Finally, our 3FP-B&C finds the best lower bounds (BLB) for 1,169/1,316 instances, outperforming all previous exact algorithms. On the PRP, our method obtained 278 OPT out of the 336 instances of benchmark set of small- and medium-size instances being 19 new ones in addition to 335 BKS (74 NBKS) and 313 BLB (52 new ones). On another set of PRP with medium- and large-size instances, our algorithm finds 1,105 BKS out of 1,440 instances with 584 NBKS. Besides that, our 3FP-B&C is the first exact algorithm to solve the instances with an unlimited fleet, providing the first lower bounds for this subset with an average optimality gap of 0.61%. We also address a very large-size instance set, the second exact algorithm to address this set, outperforming the previous approach by far. Finally, a comparative analysis of each front shows the gains of the integrated approach. History: This paper has been accepted for the Transportation Science Special Issue: DIMACS Implementation Challenge: Vehicle Routing. Funding: C. M. Schenekemberg was supported by the São Paulo Research Foundation (FAPESP) [Grant 2020/07145-8]. A. A. Chaves was supported by FAPESP [Grants 2018/15417-8 and 2016/01860-1] and Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 312747/2021-7 and 405702/2021-3]. L. C. Coelho was supported by the Canadian Natural Sciences and Engineering Research Council [Grant 2019-00094]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0261 .

In This Issue

The Multi-vehicle Mutli-product Inventory-Routing Problem (MMIRP) is one of the recent issues in Supply Chain. It is an extension of the inventory routing problems (IRP) taking into account multiple products and multiple vehicles, which is closer to real life problems. Like the IRP, the MMIRP is usually developed in the context of the “Vendor-Managed Inventory” (VMI) where the supplier manages the stock at the customer. We apply this method in a Moroccan company of bottled water in which a unique plant delivers a set of regional depots. We consider the case when all destinations are replenished with direct deliveries and we propose a mixed integer linear program to solve the problem.

A genetic algorithm-Taguchi based approach to inventory routing problem of a single perishable product with transshipment

With the increasing demand for hazardous materials (hazmat) from enterprises, port chemical industrial parks face growing risks in hazardous material transportation. By using internal road network information of parks, this study investigates the hazmat vehicle routing problem (HVRP) under different road conditions, with a bi-objective of minimizing total transportation risk and cost. The two main innovations are as follows. First, according to the grid-like road conditions in parks, the research scope of transportation segments of hazmat vehicles is divided into straight segments and curved segments. Second, the potential affected area of an accident is defined as a type of geometric shape associated with a series of factors refined from transportation situations. Finally, the effectiveness of the proposed two-stage ant colony optimization (TSACO) algorithm is verified through one instance using field data from a real port chemical industry park, and twelve instances from the classical capacitated vehicle routing problem (CVRP) resource.

This paper presents a variant of vehicle routing problem, incorporating factors of transportation costs in conjunction with adverse situations. The effects of hazardous materials (HazMat) transportation are examined on air-pollution exposure levels, as well as the risk and damage in the case of accidents. In an urban network, the various weights that can be are assigned to each road of a route are associated to the following factors: time, cost, pollution exposure levels, and the risk of damage in HazMat transportation. These weights express the travel cost and the estimated provoked adverse consequences at each road of a vehicle transit route between two disparate points of the network concerning the pollution and risk of unforeseen accident during hazardous materials transportation. The sum of the weights assigned to every road of a route represents the route value according to the corresponding factors. We introduce an optimization criterion in order to select the optimal route among all vehicle transition routes joining any given pair of the network points that does not surpass a predefined threshold route value for each factor. The predefined weights for each factor are a percentage increment of its corresponding shortest route value. The optimal location of a central depot is determined where each vehicle serves a customer using one specific route with respect to the posed restrictions. Subsequently, a suitable partition into sub-networks is carried out in the case of large urban areas and a depot is assigned to each sub-network by applying a specific optimization criterion. A branch and bound tree search algorithm is developed for the determination of the optimal routes while the locations of the depots are investigated within the framework of graph theory. Finally, small numerical examples are given.

A mixed integer linear programming model applied in barge planning for Omya

It presents a practical modeling and solution approach for VMI cyclic inventory routing problem (IRP) under constant customer demand rates. In VMI, the supplier takes the responsibility for replenishing his customers' inventories based on their consumption data, with the aim of optimizing the overall distribution and inventory costs throughout the supply chain. The objective of this IRP problem is to determine a distribution plan that minimizes average distribution and inventory costs without causing any stockout at the customers. Deterministic constant customer demand rates are assumed and therefore, a long-term cyclical approach is adopted, integrating fleet sizing, vehicle routing, and inventory management. Further, realistic side-constraints such as limited storage capacities, driving time restrictions and constant replenishment intervals are taken into account. A heuristic solution approach is proposed, analyzed and evaluated against a comparable heuristic. The heuristic solution approach is well capable of finding the appropriate cost trade-off under varying circumstances. Furthermore, when fleet sizing is not considered, the heuristic outperforms an existing heuristic in finding the two-way trade-off between distribution and inventory costs.

This work is motivated by the need to solve the inventory routing problem when implementing a business practice called vendor managed inventory replenishment (VMI). With VMI, vendors monitor their customers′ inventories and decide when and how much inventory should be replenished at each customer. The inventory routing problem attempts to coordinate inventory replenishment and transportation in such a way that the cost is minimized over the long run. We formulate a Markov decision process model of the stochastic inventory routing problem and propose approximation methods to find good solutions with reasonable computational effort. We indicate how the proposed approach can be used for other Markov decision processes involving the control of multiple resources.

A variable MIP neighborhood descent for the multi-attribute inventory routing problem