Air taxis are poised to be an additional mode of transportation in major cities suffering from ground transportation congestion. Among several potential applications of air taxis, we focus on their use within a city to transport passengers to nearby airports. Specifically, we consider the problem of determining optimal locations for skyports (enabling pick-up of passengers to airport) within a city. Our approach is inspired from hub location problems, and our proposed method optimizes for aggregate travel time to multiple airports while satisfying the demand (trips to airports) either via (i) ground transportation to skyport followed by an air taxi to the airport, or (ii) direct ground transportation to the airport. The number of skyports is a constraint, and the decision to go via the skyport versus direct ground transportation is a variable in the optimization problem. Extensive experiments on publicly available airport trips data from New York City (NYC) show the efficacy of our optimization method implemented using Gurobi. In addition, we share insightful results based on the NYC data set on how ground transportation congestion can impact the demand and service efficiency in such skyports; this emerges as yet another factor in deciding the optimal number of skyports and their locations for a given city.
The first mathematical formulations of HLP were proposed by O'Kelly @cite_4 while focusing on a study based on airline passenger networks. In the HLP literature, this formulation is referred to as a single allocation @math -hub median problem. The first linear integer programming formulation of this quadratic model was proposed by Campbell @cite_15 . Various linear models for HLP were later proposed by Ernst and Krishnamoorty @cite_25 , and Skorin Kapov @cite_24 . In addition to selection of hub locations, the allocation of demand is an important decision criterion in HLP. In this context, there are two major allocation strategies for hub location: (i) single allocation where each non hub node (, origin point in a network) is allocated to one hub, and (ii) multiple allocation where O-D flows can be transferred via different pairs of hubs ( @cite_15 @cite_33 @cite_23 ). The hub facilities can be further categorized as uncapacitated (where there is no capacity restriction), and capacitated (where there is a limit to the maximum flow passing through a hub) ( @cite_13 @cite_17 ). Farahani @cite_2 , Alumur and Kara @cite_37 provide brief review and classification of various models and approaches to HLP.
@cite_37 @cite_4 @cite_33 @cite_24 @cite_23 @cite_2 @cite_15 @cite_13 @cite_25 @cite_17
2015462215 2013064914 2059060883 2103363383
Abstract The problem of locating hub facilities and allocating non-hub nodes to those hubs arises frequently in the design of communication networks, airline passenger flow and parcel delivery networks. In this paper we consider uncapacitated multiple and single allocation p -hub median problems. We develop new mixed 0 1 linear formulations with tight linear programming relaxations. The approach is tested on a well known and heavily used benchmark data set of real-world problems with resulting LP relaxations ranging from 10010 to 391 250 variables and from 2 101 to 31 901 constraints, which proved to be difficult linear programs. Yet, this approach proved to be very effective: in almost all instances the linear programming solution was integer. In cases with fractional solutions, the integrality was achieved by adding a small partial set of integrality constraints. Therefore, we extended the range of optimally solvable instances of these NP-hard hub location problems, which have defied researchers for the last ten years. As an additional result for the single allocation case we were able to establish optimality of all heuristic solutions obtained via tabu search algorithm from a previous study. For the more difficult single allocation p -hub median problem we also used the best known heuristic solution as a guidance in adding integrality constraints. This novel linkage between optimal and heuristic solutions has a potential impact in a number of other problem settings, where efficient heuristic solutions exist and are probably, but not provably optimal. Abstract The main purpose of this paper is to introduce the capacitated hub-and-spoke network design problem in which hubs have limited capacity for channelling flows between the nodes served by the system. The problem is formulated under a networking policy allowing both direct (nonstop) and hub connected (one-hub-stop and two-hub-stop) services between the nodes. A branch and bound algorithm and a heuristic procedure partitioning the set of solutions on the basis of hub locations are presented. In both algorithms, after identifying a set of hub locations, the problem is reduced into a smaller routing problem. Subgradient optimization is then applied to a Lagrangian relaxation of the reduced problem. The model and the proposed algorithms were applied to the air transportation system using data on passenger flows between the top forty US cities in 1989 (accounting for 73.32 of the surveyed passenger flow). Computational results from 141 problems suggest that both algorithms are effective at finding good solutions to this problem. .We consider a class of stochastic processing networks. Assume that the networks satisfy a complete resource pooling condition. We prove that each maximum pressure policy asymptotically minimizes the workload process in a stochastic processing network in heavy traffic. We also show that, under each quadratic holding cost structure, there is a maximum pressure policy that asymptotically minimizes the holding cost. A key to the optimality proofs is to prove a state space collapse result and a heavy traffic limit theorem for the network processes under a maximum pressure policy. We extend a framework of Bramson [Queueing Systems Theory Appl. 30 (1998) 89–148] and Williams [Queueing Systems Theory Appl. 30 (1998b) 5–25] from the multiclass queueing network setting to the stochastic processing network setting to prove the state space collapse result and the heavy traffic limit theorem. The extension can be adapted to other studies of stochastic processing networks. 1. Introduction. This paper is a continuation of Dai and Lin (2005), in which maximum pressure policies are shown to be throughput optimal for a class of stochastic processing networks. Throughput optimality is an important, first-order objective for many networks, but it ignores some key secondary performance measures like queueing delays experienced by jobs in these networks. In this paper we show that maximum pressure policies enjoy additional optimality properties; they are asymptotically optimal in minimizing a certain workload or holding cost of a stochastic processing network. Stochastic processing networks have been introduced in a series of three papers by Harrison (2000, 2002, 2003). In Dai and Lin (2005) and this paper we consider a special class of Harrison’s model. This class of stochastic processing networks is much more general than multiclass queueing networks that have been a subject of intensive study in the last 20 years; see, for example, Harrison (1988), Williams We consider the unsplittable flow problem (UFP) and the closely related column-restricted packing integer programs (CPIPs). In UFP we are given an edge-capacitated graph G = (V ,E ) and k request pairs R 1 , ..., R k , where each R i consists of a source-destination pair (s i ,t i ), a demand d i and a weight w i . The goal is to find a maximum weight subset of requests that can be routed unsplittably in G . Most previous work on UFP has focused on the no-bottleneck case in which the maximum demand of the requests is at most the smallest edge capacity. Inspired by the recent work of . [3] on UFP on a path without the above assumption, we consider UFP on paths as well as trees. We give a simple O (logn ) approximation for UFP on trees when all weights are identical; this yields an O (log2 n ) approximation for the weighted case. These are the first non-trivial approximations for UFP on trees. We develop an LP relaxation for UFP on paths that has an integrality gap of O (log2 n ); previously there was no relaxation with o (n ) gap. We also consider UFP in general graphs and CPIPs without the no-bottleneck assumption and obtain new and useful results.