In horizontal collaborations, carriers form coalitions in order to perform parts of their logistics operations jointly. By exchanging transportation requests among each other, they can operate more efficiently and in a more sustainable way. Collaborative vehicle routing has been extensively discussed in the literature. We identify three major streams of research: (i) centralized collaborative planning, (ii) decentralized planning without auctions, and (ii) auction-based decentralized planning. For each of them we give a structured overview on the state of knowledge and discuss future research directions.

One of the principal ways nations are responding to the COVID-19 pandemic is by locking down portions of their economies to reduce infectious spread. This is expensive in terms of lost jobs, lost economic productivity, and lost freedoms. So it is of interest to ask: What is the optimal intensity with which to lockdown, and how should that intensity vary dynamically over the course of an epidemic? This paper explores such questions with an optimal control model that recognizes the particular risks when infection rates surge beyond the healthcare system’s capacity to deliver appropriate care. The analysis shows that four broad strategies emerge, ranging from brief lockdowns that only “smooth the curve” to sustained lockdowns that prevent infections from spiking beyond the healthcare system’s capacity. Within this model, it can be optimal to have two separate periods of locking down, so returning to a lockdown after initial restrictions have been lifted is not necessarily a sign of failure. Relatively small changes in judgments about how to balance health and economic harms can alter dramatically which strategy prevails. Indeed, there are constellations of parameters for which two or even three of these distinct strategies can all perform equally well for the same set of initial conditions; these correspond to so-called triple Skiba points. The performance of trajectories can be highly nonlinear in the state variables, such that for various times , the optimal unemployment rate could be low, medium, or high, but not anywhere in between. These complex dynamics emerge naturally from modeling the COVID-19 epidemic and suggest a degree of humility in policy debates. Even people who share a common understanding of the problem’s economics and epidemiology can prefer dramatically different policies. Conversely, favoring very different policies is not evidence that there are fundamental disagreements.

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature.However, there has been only limited discussion about how workload equity should be modelled in the context of VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences.This article addresses this gap by providing an analysis of classical and alternative equity functions for bi-objective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs.In the analysis, we identify a set of axiomatic properties which an ideal equity measure should satisfy, collect six common measures of equity, and point out important connections between their properties and the properties of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small bi-objective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with non-monotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP-optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be under-estimated. The results of our bi-objective analysis remain valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research on equity in logistics.

The logistics industry is known to suffer from inefficiencies. Recently published numbers on the percentage of trucks running idle or almost idle on European road networks are alarming. Collaborative transportation offers opportunities to share capacities and thus reduce inefficiencies and environmental pollution considerably. It is therefore a highly relevant topic for both researchers and practitioners. We survey up-to-date literature in the field of shared resources in collaborative vehicle routing. We report that, in the last 3 years alone, more than 40 relevant articles were published. These studies can be classified according to the underlying level of information sharing. If a fully informed decision maker exists, we refer to this as centrally planned collaboration. In decentralized collaborations coalition partners agree on mechanisms, where no or only a limited amount of information has to be revealed. We elaborate on recent findings and identify topical research gaps for both centralized and decentralized collaborations.

In horizontal collaborations, carriers form coalitions in order to perform parts of their logistics operations jointly. By exchanging transportation requests among each other, they can operate more efficiently and in a more sustainable way. This exchange of requests can be organized through combinatorial auctions, where collaborators submit requests for exchange to a common pool. The requests in the pool are grouped into bundles, and these are offered to participating carriers. From a practical point of view, offering all possible bundles is not manageable, since the number of bundles grows exponentially with the number of traded requests. We show how the complete set of bundles can be efficiently reduced to a subset of attractive ones. For this we define the Bundle Generation Problem (BuGP). The aim is to provide a reduced set of offered bundles that maximizes the total coalition profit, while a feasible assignment of bundles to carriers is guaranteed. The objective function, however, could only be evaluated whether carriers reveal sensitive information, which would be unrealistic. Thus, we develop a proxy for the objective function for assessing the attractiveness of bundles under incomplete information. This is used in a genetic algorithms-based framework that aims at producing attractive and feasible bundles, such that all requirements of the BuGP are met. We achieve very good solution quality, while reducing the computational time for the auction procedure significantly. This is an important step towards running combinatorial auctions of real-world size, which were previously intractable due to their computational complexity. The strengths but also the limitations of the proposed approach are discussed. B Margaretha Gansterer

The Ant System is a distributed metaheuristic that combines an adaptive memory with a local heuristic function to repeatedly construct solutions of hard combinatorial optimization problems. In this paper, we present an improved ant system algorithm for the Vehicle Routing Problem with one central depot and identical vehicles. Computational results on fourteen benchmark problems from the literature are reported and a comparison with five other metaheuristic approaches for solving Vehicle Routing Problems is given.

Collaboration has been one of the important trends in vehicle routing. A typical mechanism to enable carrier collaboration is to use combinatorial auctions, where requests are not traded individually but are combined into bundles. Previous literature on carrier collaboration has focused on issues such as bundle formation or winner determination, typically assuming truthfulness of all agents and absence of any strategic behavior. This article considers the interdependencies and problems that arise from bidders acting as buyers and sellers of requests at the same time. From standard auction theory, desirable properties of exchange mechanisms are identified as efficiency, incentive compatibility, individual rationality, and budget balance. It is shown that these desirable properties cannot be fulfilled at the same time. In particular, the properties efficiency and incentive compatibility induce that budget balance is violated, that is, an outside subsidy is required. We propose two incentive compatible exchange mechanisms. One is more closely related to the classical VCG approach, while the other one uses a more complicated concept for computing payments to participants. A numerical study investigates how frequently desired properties are violated. We show that both mechanisms can be acceptable in practical situations, but none of them can satisfy all desired properties.

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