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The Inventory-Routing Problem (IRP) deals with the joint optimisation of inventory and the associated routing decisions. The IRP with time windows (IRPTW) considers time windows for the deliveries to the customers. Due to its importance and several real-world applications, in this paper, we develop an intricate solution algorithm for this problem. A combination of tools ranging from established groups of valid inequalities, pre-processing techniques, local search procedures, and a local branching algorithm is utilised to solve the IRPTW efficiently. We compare the performance of our algorithm on a benchmark set of instances and show how our solution algorithm provides promising results against a competing algorithm from the literature. Moreover, the results of our study provide an overview of the performance of several already proposed techniques and their integration in the literature. [ABSTRACT FROM AUTHOR]

Inventory-routing problems (IRPs) define a class of combinatorial optimization problems, encompassing inventory management and vehicle routing decisions into the same framework. In this article, we propose a new modular mechanism capable of recovering feasibility and improving even partial solutions by reorganizing delivery routes and optimizing inventory flows. It can be embedded into different optimization algorithms, either heuristic or exact ones. We exploit the use of this mechanism to improve a traditional branch-and-cut scheme and evaluate it by solving the multi-vehicle IRP (MIRP) and the multi-depot IRP (MDIRP). The results show that our method is very effective; outperforming other approaches on well-known benchmark instances from the literature. Regarding the MIRP, our algorithm obtains 417 optimal solutions for 638 small instances, the best result among all exact algorithms, with nine new ones. On a large data set, our method finds all optimal solutions for instances with up to 50 customers for the single-vehicle, besides providing 90% of new best-known solutions (BKS) for 100 customers. On the MDIRP, our approach finds 27 new optimal solutions and 73% of new BKS, improving previous BKS by more than 7% on average. [ABSTRACT FROM AUTHOR]

The vehicle routing problem (VRP) and its variants are a class of network problems that have attracted the attention of many researchers in recent years, owing to their pragmatic approach to solving issues in logistics management. Most surveys/reviews of the extant literature often focus on specific variants or aspects of the VRP. However, a few reviews of the overall VRP literature are available. The focus of these papers is to identify which VRP literature characteristics are the most popular in recent studies. To this end, we analyze 229 articles published between 2015 and 2017. We provide a systematic literature review evaluating the Scenario Characteristics and Problem Physical Characteristics that are most frequently addressed by VRP researchers, the Type of Study and Data Characteristics that they address, the most cited works that constitute the theoretical pillars of the field, and details of three specific problem variants that have been studied extensively in recent years and their opportunities for future research. [ABSTRACT FROM AUTHOR]

We propose a multivariate regression model to deal with multiple continuous bounded data. The proposed model is based on second-moment assumptions, only. We adopted the quasi-score and Pearson estimating functions for estimation of the regression and dispersion parameters, respectively. Thus, the proposed approach does not require a multivariate probability distribution for the variable response vector. The multivariate quasi-beta regression model can easily handle multiple continuous bounded outcomes taking into account the correlation between the response variables. Furthermore, the model allows us to analyze continuous bounded data on the interval [0, 1], including zeros and/or ones. Simulation studies were conducted to investigate the behavior of the NORmal To Anything (NORTA) algorithm and to check the properties of the estimating function estimators to deal with multiple correlated response variables generated from marginal beta distributions. The model was motivated by a data set concerning the body fat percentage, which was measured at five regions of the body and represent the response variables. We analyze each response variable separately and compare it with the fit of the multivariate proposed model. The multivariate quasi-beta regression model provides better fit than its univariate counterparts, as well as allows us to measure the correlation between response variables. Finally, we adapted diagnostic tools to the proposed model. In the supplementary material, we provide the data set and R code. [ABSTRACT FROM AUTHOR]

The Periodic Capacitated Arc Routing Problem is considered as a generalization of the Capacitated Arc Routing Problem (CARP) due to two characteristics: first for planning period larger than a time unity, as that vehicles make several travels and later by considering the frequency of associated visits to the arcs to be serviced over the planning horizon. In the literature involving periodic routing problems, not only in nodes, but also in arcs within a time horizon do not address the case of multiple tasks with the possibility of simultaneous execution. This paper consists in a modeling proposal which considers that in the passage through the arc more than one task must be developed. Those activities even have different periods that must also be regarded. In this way a new problem and its exact mathematical model is constructed, enounced as multiple tasks Periodic Capacitated Arc Routing Problem. A few new characteristics are presented, such as: multiple tasks to be performed on each edge or edges; different frequencies to accomplish each of the tasks; heterogeneous fleet; and flexibility for more than one vehicle passing through the same edge at the same day. The mathematical model was implemented and examples were generated randomly, in a way that the proposed model could be validated. [ABSTRACT FROM AUTHOR]

The Periodic Capacitated Arc Routing Problem is considered as a generalization of the Capacitated Arc Routing Problem (CARP) due to two characteristics: first for planning period larger than a time unity, as that vehicles make several travels and later by considering the frequency of associated visits to the arcs to be serviced over the planning horizon. In the literature involving periodic routing problems, not only in nodes, but also in arcs within a time horizon do not address the case of multiple tasks with the possibility of simultaneous execution. This paper consists in a modeling proposal which considers that in the passage through the arc more than one task must be developed. Those activities even have different periods that must also be regarded. In this way a new problem and its exact mathematical model is constructed, enounced as multiple tasks Periodic Capacitated Arc Routing Problem. A few new characteristics are presented, such as: multiple tasks to be performed on each edge or edges; different frequencies to accomplish each of the tasks; heterogeneous fleet; and flexibility for more than one vehicle passing through the same edge at the same day. The mathematical model was implemented and examples were generated randomly, in a way that the proposed model could be validated. [ABSTRACT FROM AUTHOR]