The effect of different mathematical formulations on a matheuristic algorithm for the production routing problem

We perform an experimental study to evaluate the performance of a matheuristic for the production routing problem (PRP). First, we develop a basic matheuristic that prescribes starting from a partial initial solution, completing it using a sequence of constructive heuristics, and improving it using a general-purpose mixed-integer programming heuristic. Next, we investigate the effect of three state-of-the-art mathematical formulations on the proposed matheuristic convergence. The formulations are implemented and tested with and without the use of valid inequalities. In addition, by suggesting different techniques to generate a feasible starting solution for our matheuristic, we assess the contribution of an initial solution to the matheuristic’s overall performance. We conduct extensive computational experiments on benchmark data instances for the PRP. The results show that a proper choice of an embedded mathematical formulation depends on the data instances’ features, such as the number of customers and the length of the planning horizon. The comparisons undertaken in this study indicate that having a better initial solution does not necessarily lead to finding a better final solution.publishe

Solving a Continent-Scale Inventory Routing Problem at Renault

This paper is the fruit of a partnership with Renault. Their backward logistic requires to solve a continent-scale multi-attribute inventory routing problem (IRP). With an average of 30 commodities, 16 depots, and 600 customers spread across a continent, our instances are orders of magnitude larger than those in the literature. Existing algorithms do not scale. We propose a large neighborhood search (LNS). To make it work, (1) we generalize existing split delivery vehicle routing problem and IRP neighborhoods to this context, (2) we turn a state-of-the art matheuristic for medium-scale IRP into a large neighborhood, and (3) we introduce two novel perturbations: the reinsertion of a customer and that of a commodity into the IRP solution. We also derive a new lower bound based on a flow relaxation. In order to stimulate the research on large-scale IRP, we introduce a library of industrial instances. We benchmark our algorithms on these instances and make our code open-source. Extensive numerical experiments highlight the relevance of each component of our LNS

The Deterministic Repeatable Inventory Routing Problem

The Deterministic Repeatable Inventory Routing Problem (DRIRP) is a combination of a Vehicle Routing Problem and an Inventory ManagementProblem. It is the problem of finding a set of vehicle routes and delivery/pickup amounts servicing customers with deterministic production rates. The customers have limited local storage and thus a visit must be scheduled before the stockout or overflow level is reached. The objective of the problem is to minimize the per unit cost of picking up the product.Moreover, the problem is constrained to finding solutions that are repeatable in a cyclic fashion. This means that, once established, an optimal routingstrategy can be implemented over a long planning horizon as long as the problem data remains the same, The DRIRP model can be applied to a number of real world problems including off-shore barge scheduling.Several models, ranging from a single-vehicle single-visit to a complex multi-vehicle multi-visit model are developed. Each of these models increases the complexity and range of the solutions that can be considered by an analyst while the basic problem instance remains the same.The DRIRP is in a general class of mathematically difficult problem that cannot be solved in polynomial time. However, this research examines several techniques to help solve particular instances and models of the problem. These include variable elimination techniques, continuous variable bounding logic, and a cutting plane approach based on polyhedral theory.The various techniques improve the lower bound of the LP relaxation, thus improving the efficiency and run-time of the branch-and-bound technique used to solve the Mixed Integer Program.The approaches are tested on sample test problems obtained from areal world industrial operation. Preliminary results show that the problem is indeed very difficult but the solution methodology developed in this dissertation can be applied to barge scheduling. Moreover, these models and solution techniques further expand the set of feasible solutions that can be considered and allow larger problems to be solved

An efficient two-phase iterative heuristic for Collection-Disassembly problem

Closing the loop in the supply chains is one of the mandatory conditions for more sustainable development. The Collection-Disassembly Problem appears in the reverse part of the closed-loop supply chains. Its aim is to coordinate the activities of collection of end-of-life products from collection centres and their subsequent disassembly. The disassembly step is required for efficient remanufacturing and recycling of returned products. The Collection-Disassembly problem integrates such optimization problems as dynamic lot-sizing and vehicle routing in general cases. In this paper, we develop a Two-Phase Iterative Heuristic to efficiently address large size instances. The numerical tests show that the heuristic provides good solutions under acceptable computational time

A concise guide to existing and emerging vehicle routing problem variants

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges

A concise guide to existing and emerging vehicle routing problem variants

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of modern supply chains. We organize the main problem attributes within this structured framework. We discuss recent research directions and pinpoint current shortcomings, recent successes, and emerging challenges.</p

Arc routing problems: A review of the past, present, and future

[EN] Arc routing problems (ARPs) are defined and introduced. Following a brief history of developments in this area of research, different types of ARPs are described that are currently relevant for study. In addition, particular features of ARPs that are important from a theoretical or practical point of view are discussed. A section on applications describes some of the changes that have occurred from early applications of ARP models to the present day and points the way to emerging topics for study. A final section provides information on libraries and instance repositories for ARPs. The review concludes with some perspectives on future research developments and opportunities for emerging applicationsThis research was supported by the Ministerio de Economia y Competitividad and Fondo Europeo de Desarrollo Regional, Grant/Award Number: PGC2018-099428-B-I00. The Research Council of Norway, Grant/Award Numbers: 246825/O70 (DynamITe), 263031/O70 (AXIOM).Corberán, Á.; Eglese, R.; Hasle, G.; Plana, I.; Sanchís Llopis, JM. (2021). Arc routing problems: A review of the past, present, and future. Networks. 77(1):88-115. https://doi.org/10.1002/net.21965S8811577