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

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 .

A practical solution approach for the cyclic inventory routing problem

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

This work proposes a multi-objective extension of a real-world inventory routing problem (IRP), a generalisation of the classical vehicle routing problem (VRP) with vendor managed inventory (VMI) replenishment. While many mathematical formulations and solution models already exist, this study incorporates business-related and risk considerations that makes it unique. It is known that a significant volume of hazardous materials travels every day. Consideration of risks arising from the transportation of hazardous materials as a criterion for selecting distribution routes could potentially reduce the likelihood of accidents and/or the expected consequences of accidents.

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.

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.

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

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.

This paper presents a detailed study concerning the importance of the planning horizon when solving inventory routing problems (IRPs). We evaluate the quality of decisions obtained by solving a finite‐horizon IRP. We also discuss the relevance of explicitly considering profit maximization models rather than the traditional cost minimization variant. As a means to this end, we describe four classes of the IRP corresponding to different types of markets. Two of them lead to nonlinear models, which are linearized. Furthermore, we provide a deterministic simulator to evaluate the long‐term effects arising from using planning horizons of varying lengths when solving the IRP. A computational study is performed on cases generated from benchmark data instances. The results confirm that the long‐term performance of the IRP decisions is, in part, contingent on the length of the selected planning horizon. They also show that considering profit maximization instead of cost minimization leads to different decisions, generating considerably more revenue and profits, albeit not nearly as much as suggested by individual solutions to static IRPs with short planning horizons.

In This Issue

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

An assign-and-route matheuristic for the time-dependent inventory routing problem

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

This paper introduces the Cyclic Production Routing Problem (CPRP). The CPRP is an extension of the well-known NP-hard Production Routing Problem (PRP), which is a hard-to-solve combinatorial optimisation problem with numerous practical applications in the field of freight transportation, logistics and supply chain management. Under the PRP setting, a manufacturer is responsible for determining production decisions, as well as the timing and quantity of replenishment services offered to a set of geographically dispersed customers over a multi-period time horizon. The problem calls for jointly optimising the production, inventory, distribution and routing decisions. In this paper, the basic PRP model is modified to generate repeatable cyclic production and delivery schedules. A two-commodity flow formulation is proposed along with valid inequalities. Extensive comparisons between the basic PRP and the proposed cyclic variant on well-known benchmark instances are provided. The new variant is significantly harder to solve, especially when the vehicle fleet is limited. From a managerial perspective, the generation of cyclic production-routing schedules significantly increases all costs, whereas the number of vehicle routes required to implement a cyclic schedule is higher.

A variable neighborhood search heuristic algorithm for production routing problems