In this study, we formulate positive and negative externalities caused by changes in the supply of shared vehicles as ride sharing games. The study aims to understand the price of anarchy (PoA) and its improvement via a coordination technique in ride sharing games. A critical question is whether ride sharing games exhibit a pure Nash equilibrium (pNE) since the PoA bound assumes it. Our result shows a sufficient condition for a ride sharing game to have a finite improvement property and a pNE similar to potential games. This is the first step to analyze PoA bound and its improvement by coordination in ride sharing games. We also show an example of coordinating players in ride sharing games using signaling and evaluate the improvement in the PoA.
According to a review of sharing studies in transportation areas @cite_14 , there are few game theory studies on externalities and coordination of players' moves in vehicle sharing problems. Traditional studies on sharing include the optimization of vehicle routes for picking up all passengers (the Dial-a-ride problem ), problems of splitting passengers' fares according to their riding distances, optimization of locations of carpool stations, and problems of relocation of carpool vehicles among stations. Those studies mainly focus on optimization problems under given moves (origins and destinations) of passengers and fixed drivers of vehicles, and therefore, do not analyze the PoA when passengers strategically choose their moves in response to the moves of other passengers and vehicles. The review states that there are no studies on coordination of players' moves to improve the efficiency of sharing or reduce the PoA.
@cite_14
2614461528 2565919573 1817264369 2364071307 1982002004 2051358678 2031128290 2032251915 2072113937 2153344215 2145569785 1998816621 2810102121 1984648987 2073588680 1971759877 2068957801 2037992565 1999587457 2156767060
Optimizing shared vehicle systems (bike-sharing car-sharing ride-sharing) is more challenging compared to traditional resource allocation settings due to the presence of complex network externalities. In particular, changes in the demand supply at any location (via dynamic pricing, rebalancing of empty vehicles, etc.) affect future supply throughout the system within short timescales. Such externalities are well captured by steady-state Markovian models, which are therefore widely used to analyze and design shared vehicle systems. However, using such models to design pricing control policies is computationally difficult since the resulting optimization problems are high-dimensional and non-convex. To this end, we develop a general approximation framework for designing pricing policies in shared vehicle systems, based on a novel convex relaxation which we term elevated flow relaxation. Our approach provides the first efficient algorithms with rigorous approximation guarantees for a wide range of objective functions (throughput, revenue, welfare). For any shared vehicle system with @math stations and m vehicles, our framework provides a pricing policy with an approximation ratio of 1+(n-1) m. This guarantee is particularly meaningful when m n, the average number of vehicles per station is large, as is often the case in practice. Further, the simplicity of our approach allows us to extend it to more complex settings. Apart from pricing, shared vehicle systems enable other control levers for modulating demand and supply, e.g. rebalancing empty vehicles, redirecting riders to nearby vehicles, etc. Our approach yields efficient algorithms with the same approximation guarantees for all these problems, and in the process, obtains as special cases several existing heuristics and asymptotic guarantees. We also extend our approach to obtain bi-criterion guarantees in multi-objective settings; we illustrate this with the example of Ramsey pricing. From a technical perspective, our work develops a new approach for obtaining control policies with approximation guarantees in steady-state Markovian models. Our approach can be distilled into the following three-step program: (i) construct an upper bound via a relaxation to the original problem that encodes essential conservation laws of the system, (ii) identify a family of control policies inducing known steady-state distributions that achieve the value of the relaxed solution in an appropriate scaling limit (in our case, state-independent policies in the limit m++), and (iii) characterize the performance loss between the finite system (i.e. fixed m) and the scaling limit. This technique may be of independent interest for other settings. Ride-sharing services are transforming urban mobility by providing timely and convenient transportation to anybody, anywhere, and anytime. These services present enormous potential for positive societ al impacts with respect to pollution, energy consumption, congestion, etc. Current mathematical models, however, do not fully address the potential of ride-sharing. Recently, a large-scale study highlighted some of the benefits of car pooling but was limited to static routes with two riders per vehicle (optimally) or three (with heuristics). We present a more general mathematical model for real-time high-capacity ride-sharing that ( i ) scales to large numbers of passengers and trips and ( ii ) dynamically generates optimal routes with respect to online demand and vehicle locations. The algorithm starts from a greedy assignment and improves it through a constrained optimization, quickly returning solutions of good quality and converging to the optimal assignment over time. We quantify experimentally the tradeoff between fleet size, capacity, waiting time, travel delay, and operational costs for low- to medium-capacity vehicles, such as taxis and van shuttles. The algorithm is validated with ∼3 million rides extracted from the New York City taxicab public dataset. Our experimental study considers ride-sharing with rider capacity of up to 10 simultaneous passengers per vehicle. The algorithm applies to fleets of autonomous vehicles and also incorporates rebalancing of idling vehicles to areas of high demand. This framework is general and can be used for many real-time multivehicle, multitask assignment problems. Dynamic ride-sharing systems enable people to share rides and increase the efficiency of urban transportation by connecting riders and drivers on short notice. Automated systems that establish ride-share matches with minimal input from participants provide the most convenience and the most potential for system-wide performance improvement, such as reduction in total vehicle-miles traveled. Indeed, such systems may be designed to match riders and drivers to maximize system performance improvement. However, system-optimal matches may not provide the maximum benefit to each individual participant. In this paper we consider a notion of stability for ride-share matches and present several mathematical programming methods to establish stable or nearly-stable matches, where we note that ride-share matching optimization is performed over time with incomplete information. Our numerical experiments using travel demand data for the metropolitan Atlanta region show that we can significantly increase the stability of ride-share matching solutions at the cost of only a small degradation in system-wide performance. The ubiquitous deployment of mobile and sensor technologies has led to both the capacity to observe human behavior in physical (offline) settings as well as to record it. This provides researchers with a new lens to study and better understand the individual decision processes that were previously unobserved. In this paper, we study decision making behavior of 11,196 taxi drivers in a large Asian city using a rich data set consisting of 10.6 million fine-grained GPS trip records. These records include detailed taxi GPS trajectories, taxi occupancy data (i.e., whether a taxi was occupied with a passenger or was vacant) and taxi drivers’ daily incomes. This capacity to use data where occupancy of the taxi is known is a distinctive feature of our data set and sets this work apart from prior work which has attempted to study driver behavior. The specific decision we focus on pertains to actions drivers take to find new passengers after they have dropped off their current passengers. In particular, we study the role of information derivable from the GPS trace data (e.g., where passengers are dropped off, where passengers are picked up, longitudinal taxicab travel history with fine-grained time stamps) observable by or made available to drivers in enabling them to learn the distribution of demand for their services over space and time. We conduct our study using a heterogeneous Bayesian learning model. We find strong heterogeneity in individual learning behavior and driving decisions, which is significantly associated with individual economic outcomes. Drivers with higher incomes benefit significantly from their ability to learn from not only demand information directly observable in the local market, but also aggregate information on demand flows across markets. Interestingly, our policy simulations indicate information that is noisy at the individual level becomes valuable after being aggregated across various spatial and temporal dimensions. Moreover, the value of information does not increase monotonically with the scale and frequency of information sharing. Finally, our study has important welfare implications in that efficient information sharing leads to an income increase among all drivers, instead of a redistribution of income between different types of drivers. Our work allows us not only to explain driver decision making behavior using these detailed behavioral traces, but also to prescribe information sharing strategy for the firm in order to improve the overall market efficiency. Smartphone technology enables dynamic ride-sharing systems that bring together people with similar itineraries and time schedules to share rides on short-notice. This paper considers the problem of matching drivers and riders in this dynamic setting. We develop optimization-based approaches that aim at minimizing the total system-wide vehicle miles incurred by system users, and their individual travel costs. To assess the merits of our methods we present a simulation study based on 2008 travel demand data from metropolitan Atlanta. The simulation results indicate that the use of sophisticated optimization methods instead of simple greedy matching rules substantially improve the performance of ride-sharing systems. Furthermore, even with relatively low participation rates, it appears that sustainable populations of dynamic ride-sharing participants may be possible even in relatively sprawling urban areas with many employment centers. In the dial-a-ride problem, users formulate requests for transportation from a specific origin to a specific destination. Transportation is carried out by vehicles providing a shared service. The problem consists of designing a set of minimum-cost vehicle routes satisfying capacity, duration, time window, pairing, precedence, and ride-time constraints. This paper introduces a mixed-integer programming formulation of the problem and a branch-and-cut algorithm. The algorithm uses new valid inequalities for the dial-a-ride problem as well as known valid inequalities for the traveling salesman, the vehicle routing, and the pick-up and delivery problems. Computational experiments performed on randomly generated instances show that the proposed approach can be used to solve small to medium-size instances. Dynamic ride-share systems aim to bring together travelers with similar itineraries and time schedules on short-notice. These systems may provide significant societ al and environmental benefits by reducing the number of cars used for personal travel and improving the utilization of available seat capacity. Effective and efficient optimization technology that matches drivers and riders in real-time is one of the necessary components for a successful dynamic ride-share system. We systematically outline the optimization challenges that arise when developing technology to support ride-sharing and survey the related operations research models in the academic literature. We hope that this paper will encourage more research by the transportation science and logistics community in this exciting, emerging area of public transportation. Bike-sharing systems allow people to rent a bicycle at one of many automatic rental stations scattered around the city, use them for a short journey and return them at any station in the city. A crucial factor for the success of a bike-sharing system is its ability to meet the fluctuating demand for bicycles and for vacant lockers at each station. This is achieved by means of a repositioning operation, which consists of removing bicycles from some stations and transferring them to other stations, using a dedicated fleet of trucks. Operating such a fleet in a large bike-sharing system is an intricate problem consisting of decisions regarding the routes that the vehicles should follow and the number of bicycles that should be removed or placed at each station on each visit of the vehicles. In this paper, we present our modeling approach to the problem that generalizes existing routing models in the literature. This is done by introducing a unique convex objective function as well as time-related considerations. We present two mixed integer linear program formulations, discuss the assumptions associated with each, strengthen them by several valid inequalities and dominance rules, and compare their performances through an extensive numerical study. The results indicate that one of the formulations is very effective in obtaining high quality solutions to real life instances of the problem consisting of up to 104 stations and two vehicles. Finally, we draw insights on the characteristics of good solutions. In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. We study a spectrum sharing problem in an unlicensed band where multiple systems coexist and interfere with each other. We first analyze a cooperative setting where all the systems collaborate to achieve a common goal. Under the assumptions that the systems communicate with Gaussian signals and treat interference as noise, we study the structure of the optimal power allocations. We show that any Pareto efficient vector of rates can be achieved with piece-wise constant power allocations. Moreover, if a strong interference condition among all the systems is satisfied, we show that frequency division multiplexing is optimal. We then consider a non-cooperative situation, where the systems act in a selfish and rational way, and investigate how the lack of cooperation can affect performance. Using game theory, we first analyze the possible outcomes of a one shot game, and observe that in many cases an inefficient solution results. We show that by extending the game definition to that of a repeated game, the possibility of building reputations and applying punishments allows to enlarge the set of achievable rates. We present examples that show that in many cases, the performance loss due to lack of cooperation is small. We also provide a converse theorem that proves that our results are tight and quantify the best achievable performance in a non-cooperative scenario Car pooling is a transportation service organized by a large company which encourages its employees to pick up colleagues while driving to from work to minimize the number of private cars travelling to from the company site. The car pooling problem consists of defining the subsets of employees that will share each car and the paths the drivers should follow, so that sharing is maximized and the sum of the path costs is minimized. The special case of the car pooling problem where all cars are identical can be modeled as a Dial-a-Ride Problem. In this paper, we propose both an exact and a heuristic method for the car pooling problem, based on two integer programming formulations of the problem. The exact method is based on a bounding procedure that combines three lower bounds derived from different relaxations of the problem. A valid upper bound is obtained by the heuristic method, which transforms the solution of a Lagrangean lower bound into a feasible solution. The computational results show the effectiveness of the proposed methods. The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15 . Moreover, improvements of up to 41 can be achieved for some test instances. We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion. In this paper, we consider a class of dynamic vehicle routing problems, in which a number of mobile agents in the plane must visit target points generated over time by a stochastic process. It is desired to design motion coordination strategies in order to minimize the expected time between the appearance of a target point and the time it is visited by one of the agents. We propose control strategies that, while making minimal or no assumptions on communications between agents, provide the same level of steady-state performance achieved by the best-known decentralized strategies. In other words, we demonstrate that inter-agent communication does not improve the efficiency of such systems, but merely affects the rate of convergence to the steady state. Furthermore, the proposed strategies do not rely on the knowledge of the details of the underlying stochastic process. Copyright © 2007 John Wiley & Sons, Ltd. Vehicle Routing Problems have been extensively analyzed to reduce transportation costs. More particularly, the Vehicle Routing Problem with Time Windows (VRPTW) imposes the period of time of customer availability as a constraint, a common characteristic in real world situations. Using minimization of the total distance as the main objective to be fulfilled, this work implements an efficient algorithm which associates non-monotonic Simulated Annealing to Hill-Climbing and Random Restart. The algorithm is compared to the best results published in the literature for the 56 Solomon instances and it is shown how statistical methods can be used to boost the performance of the method. We consider several vehicle routing problems (VRP) with profits, which seek to select a subset of customers, each one being associated with a profit, and to design service itineraries. When the sum of profits is maximized under distance constraints, the problem is usually called the team orienteering problem. The capacitated profitable tour problem seeks to maximize profits minus travel costs under capacity constraints. Finally, in the VRP with a private fleet and common carrier, some customers can be delegated to an external carrier subject to a cost. Three families of combined decisions must be taken: customer’s selection, assignment to vehicles, and sequencing of deliveries for each route.We propose a new neighborhood search for these problems, which explores an exponential number of solutions in pseudo-polynomial time. The search is conducted with standard VRP neighborhoods on an exhaustive solution representation, visiting all customers. Since visiting all customers is usually infeasible or suboptimal, an efficient select algorithm, based on resource constrained shortest paths, is repeatedly used on any new route to find the optimal subsequence of visits to customers. The good performance of these neighborhood structures is demonstrated by extensive computational experiments with a local search, an iterated local search, and a hybrid genetic algorithm. Intriguingly, even a local-improvement method to the first local optimum of this neighborhood achieves an average gap of 0.09 on classic team orienteering benchmark instances, rivaling with the current state-of-the-art metaheuristics. Promising research avenues on hybridizations with more standard routing neighborhoods are also open. The classic optimal transportation problem consists in finding the most cost-effective way of moving masses from one set of locations to another, minimizing its transportation cost. The formulation of this problem and its solution have been useful to understand various mathematical, economical, and control theory phenomena, such as, e.g., Witsenhausen's counterexample in stochastic control theory, the principal-agent problem in microeconomic theory, location and planning problems, etc. In this work, we incorporate the effect of network congestion to the optimal transportation problem and we are able to find a closed form expression for its solution. As an application of our work, we focus on the mobile association problem in cellular networks (the determination of the cells corresponding to each base station). In the continuum setting, this problem corresponds to the determination of the locations at which mobile terminals prefer to connect (by also considering the congestion they generate) to a given base station rather than to other base stations. Two types of problems have been addressed: a global optimization problem for minimizing the total power needed by the mobile terminals over the whole network (global optimum), and a user optimization problem, in which each mobile terminal chooses to which base station to connect in order to minimize its own cost (user equilibrium). This work combines optimal transportation with strategic decision making to characterize both solutions. SYNOPTIC ABSTRACTThe single-vehicle dial-a-ride problem with time window constraints for both pick-up and delivery locations, and precedence and capacity constraints, is solved using a forward dynamic programming algorithm. The total distance is minimized. The development of criteria for the elimination of infeasible states results in solution times which increase linearly with problem size. This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved.Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players.This interplay between optimisation and allocation is the main subject of the area of operations research games.It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory. Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network, which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40 or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting toward a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low.