Assignment constraints in shared transportation services.

Competitive markets, increased fuel costs, and underutilized vehicle fleets are characteristics that currently define the logistics sector. Given an increasing pressure to act in a manner that is economically and ecologically efficient, mechanisms that help to benefit from idle capacities are on the rise. In the Sharing Economy, collaborative usage is typically organized through platforms that facilitate the exchange of goods or services. Our study examines a collaborative pickup and delivery problem where carriers can exchange customer requests. The aim is to quantify the potential of horizontal collaborations under a centralized framework. An Adaptive Large Neighborhood Search is developed to solve yet unsolved test instances. A computational study confirms the results of past studies which have reported cost savings between 20 and 30%. In addition, the numerical results indicate an even greater potential for settings with a high degree of regional customer overlap. Unfortunately, these high collaborative gains typically come at the cost of an uneven customer distribution, which is known to be one of the main barriers that prevent companies from entering into horizontal collaborations. To generate acceptable solutions for all participants, several constraints are included in the model. The introduction of these constraints to single-vehicle instances, decreases the potential collaborative gain considerably. Surprisingly, this does not happen in more realistic settings of carriers operating multiple vehicles. Overall, the computational study shows that centralized collaborative frameworks have the potential to generate considerable cost savings, while at the same time limiting customer or profit share losses and enabling carriers to keep some of their most valued customers.

The optimal lockdown intensity for COVID-19.

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 t , 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 evident that there are fundamental disagreements.

The collaborative multi-level lot-sizing problem with cost synergies.

Collaborative operations planning is a key element of modern supply chains. We introduce the collaborative multi-level lot-sizing problem with cost synergies. This arises if producers can realise reductions of their costs by providing more than one product in a specific time horizon. Since producers are typically not willing to reveal critical information, we propose a decentralised mechanism, where producers do not have to reveal their individual items costs. Additionally, a Genetic Algorithms-based centralised approach is developed, which we use for benchmarking. Our study shows that this approach comes very close to the a central plan, while in the decentralised one no critical information has to be shared. We compare the results to a myopic upstream planning approach, and show that these results are almost 12% worse than the centralised ones. All solution approaches are assessed on available test instances for problems without cost synergies. For the biggest available instances, the proposed centralised mechanism improves the best known solutions on average by 10.8%. The proposed decentralised mechanism can be applied to other problem classes, where collaborative decision makers aim for good plans under incomplete information.

The cost of incentive compatibility in auction-based mechanisms for carrier collaboration.

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.

Exact solutions for the collaborative pickup and delivery problem.

In this study we investigate the decision problem of a central authority in pickup and delivery carrier collaborations. Customer requests are to be redistributed among participants, such that the total cost is minimized. We formulate the problem as multi-depot traveling salesman problem with pickups and deliveries. We apply three well-established exact solution approaches and compare their performance in terms of computational time. To avoid unrealistic solutions with unevenly distributed workload, we extend the problem by introducing minimum workload constraints. Our computational results show that, while for the original problem Benders decomposition is the method of choice, for the newly formulated problem this method is clearly dominated by the proposed column generation approach. The obtained results can be used as benchmarks for decentralized mechanisms in collaborative pickup and delivery problems.

Centralized bundle generation in auction-based collaborative transportation.

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.

The two-region multi-depot pickup and delivery problem.

Logistics networks are constantly evolving such that new and more varied structures arise and need to be studied. Carriers are aiming for opportunities to save costs by efficient planning. Motivated by this, we define the two-region multi-depot pickup and delivery problem. A region in this setting refers to an area where customers and depots are located. We differentiate two kinds of requests depending on whether their customers are located in the same region or not. Due to geographical characteristics, direct transportation between different regions is considered inefficient and a long-distance transportation mode needs to be used to connect them. Hence, we face a complex problem where interrelated decisions are to be made. We propose a decomposition into three subproblems, which relate to well-known problems in the literature. For solving the global problem, an adaptive large neighborhood search (ALNS) algorithm is developed. The algorithm mixes operators tailored to each of the different decisions of each subproblem. We demonstrate that these operators are efficient when applied to problems of their primal nature. In an extensive computational study, we show that the proposed ALNS dominates alternative ALNS schemes, where subproblems are treated sequentially. A detailed analysis of the solution convergence is provided. The proposed approach is a powerful tool to tackle complex decision problems in large distribution networks.

Leading bureaucracies to the tipping point: An alternative model of multiple stable equilibrium levels of corruption.

We present a novel model of corruption dynamics in the form of a nonlinear optimal dynamic control problem. It has a tipping point, but one whose origins and character are distinct from that in the classic Schelling (1978) model. The decision maker choosing a level of corruption is the chief or some other kind of authority figure who presides over a bureaucracy whose state of corruption is influenced by the authority figure's actions, and whose state in turn influences the pay-off for the authority figure. The policy interpretation is somewhat more optimistic than in other tipping models, and there are some surprising implications, notably that reforming the bureaucracy may be of limited value if the bureaucracy takes its cues from a corrupt leader.

Numerical solution of a conspicuous consumption model with constant control delay.

We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account.This non-standard optimal control problem is difficult to solve analytically, and solutions depend on the variable model parameters. Therefore, we use a numerical result-driven approach. We propose a structure-exploiting direct method for optimal control to solve this challenging optimization problem. In particular, we discretize the uncertainties in the model formulation by using scenario trees and target the control delays by introduction of slack control functions.Numerical results illustrate the validity of our approach and show the impact of uncertainties and delay effects on optimal economic strategies. During the recession, delayed optimal prices are higher than the non-delayed ones. In the normal economic period, however, this effect is reversed and optimal prices with a delayed impact are smaller compared to the non-delayed case.