Distributionally Robust Hub Location

2020 ◽  
Vol 54 (5) ◽  
pp. 1189-1210 ◽  
Author(s):  
Shuming Wang ◽  
Zhi Chen ◽  
Tianqi Liu
Keyword(s):  
Convex Hull ◽  
Mixed Integer ◽  
Hub Location ◽  
Hub Location Problem ◽  
Mixed Integer Linear Program ◽  
Worst Case ◽  
Data Set ◽  
Second Stage ◽  
Robust Model ◽  
Distributionally Robust

We study the adaptive distributionally robust hub location problem with multiple commodities under demand and cost uncertainty in both uncapacitated and capacitated cases. The hub location decision anticipates the worst-case expected cost over an ambiguity set of possible distributions of the uncertain demand and cost, and the routing policy, being adaptive to the uncertainty realization, ships commodities through selected hubs. We investigate the adaptivity and tractability of the distributionally robust model under different distributional information about uncertainty. In the uncapacitated case in which demand and cost are independent and costs of different commodities are also mutually independent, the adaptive distributionally robust model is equivalent to a nonadaptive classical robust model and the second-stage routing decision follows an optimal static policy. We then relax the independence assumption and show that the second-stage routing decision follows an optimal scenario-wise policy if either the demand or the cost is supported on a convex hull of given scenarios. We extend our analysis to the capacitated case and show that the second-stage routing decision still follows an optimal scenario-wise policy if the demand is supported on the convex hull of given scenarios. In terms of tractability, for all mentioned cases, we reformulate the distributionally robust model as a moderate-sized mixed-integer linear program, and we recover the associated worst-case distribution by solving a collection of linear programs. Through numerical studies using the Civil Aeronautics Board data set, we demonstrate the advantages of the distributionally robust model by examining its superior out-of-sample performance against the classical robust model and the stochastic model.

scholarly journals Location of regional and international hub ports in liner shipping

2017 ◽  
Vol 2 (2) ◽  
pp. 114-125 ◽  
Author(s):  
Jianfeng Zheng ◽  
Cong Fu ◽  
Haibo Kuang
Keyword(s):  
Design Methodology ◽  
Location Problem ◽  
Programming Model ◽  
Liner Shipping ◽  
Mixed Integer ◽  
Eastern Asia ◽  
Hub Location ◽  
Hub Location Problem ◽  
Content Type ◽  
Western Asia

Purpose This paper aims to investigate the location of regional and international hub ports in liner shipping by proposing a hierarchical hub location problem. Design/methodology/approach This paper develops a mixed-integer linear programming model for the authors’ proposed problem. Numerical experiments based on a realistic Asia-Europe-Oceania liner shipping network are carried out to account for the effectiveness of this model. Findings The results show that one international hub port (i.e. Rotterdam) and one regional hub port (i.e. Zeebrugge) are opened in Europe. Two international hub ports (i.e. Sokhna and Salalah) are located in Western Asia, where no regional hub port is established. One international hub port (i.e. Colombo) and one regional hub port (i.e. Cochin) are opened in Southern Asia. One international hub port (i.e. Singapore) and one regional hub port (i.e. Jakarta) are opened in Southeastern Asia and Australia. Three international hub ports (i.e. Hong Kong, Shanghai and Yokohama) and two regional hub ports (i.e. Qingdao and Kwangyang) are opened in Eastern Asia. Originality/value This paper proposes a hierarchical hub location problem, in which the authors distinguish between regional and international hub ports in liner shipping. Moreover, scale economies in ship size are considered. Furthermore, the proposed problem introduces the main ports.

scholarly journals Hub location problem in round-trip service applications

2020 ◽  
Author(s):  
Omar Kemmar ◽  
Karim Bouamrane ◽  
Shahin Gelareh
Keyword(s):  
Economies Of Scale ◽  
Location Problem ◽  
Service Providers ◽  
Real Life ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Hub Location ◽  
Service Networks ◽  
Hub Location Problem ◽  
Hub And Spoke

In this paper, we introduce a new hub-and-spoke structure for service networks based on round-trips as practiced by some transport service providers. This problem is a variant of Uncapacitated Hub Location Problem wherein the spoke nodes allocated to a hub node form round-trips (cycles) starting from and ending to the hub node. This problem is motivated by two real-life practices in logistics wherein  runaway  nodes and  runaway  connections with their associated economies of scale were foreseen to increase redundancy in the network. We propose a mixed integer linear programming mathematical model with exponential number of constraints. In addition to the separation routines for separating from among exponential constraints, we propose a hyper-heuristic based on reinforcement learning and its comparable counterpart as a variable neighborhood search. Our extensive computational experiments confirm efficiency of the proposed approaches.In this paper, we introduce a new hub-and-spoke structure for service networks based on round-trips as practiced by some transport service providers. This problem is a variant of Uncapacitated Hub Location Problem wherein the spoke nodes allocated to a hub node form round-trips (cycles) starting from and ending to the hub node. This problem is motivated by two real-life practices in logistics wherein  runaway  nodes and  runaway  connections with their associated economies of scale were foreseen to increase redundancy in the network. We propose a mixed integer linear programming mathematical model with exponential number of constraints. In addition to the separation routines for separating from among exponential constraints, we propose a hyper-heuristic based on reinforcement learning and its comparable counterpart as a variable neighborhood search. Our extensive computational experiments confirm efficiency of the proposed approaches.

scholarly journals Robust Day-Ahead Dispatch for Integrated Power-Heat-Gas Microgrid considering Wind Power Uncertainty

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Yang Liu ◽  
Yanli Ye ◽  
Xianbang Chen ◽  
Huaqiang Li ◽  
Yuan Huang
Keyword(s):  
Wind Power ◽  
Deterministic Model ◽  
Economic Dispatch ◽  
Two Stage ◽  
Worst Case ◽  
Constraint Generation ◽  
Second Stage ◽  
Robust Model ◽  
Operation Cost ◽  
Made In

Wind power generation has been widely deployed in the modern power system due to the issues of energy crisis and environment pollution. Meanwhile, the microgrid is gradually regarded as a feasible way to connect and accommodate the distributed wind power generations. Recently, more research studies also focus on incorporating various energy systems, for example, heat and gas into the microgrid in terms of satisfying different types of load demands. However, the uncertainty of wind power significantly impacts the economy of the integrated power-heat-gas microgrid. To deal with this issue, this paper presents a two-stage robust model to achieve the optimal day-ahead economic dispatch strategy considering the worst-case wind power scenarios. The first stage makes the initial day-ahead dispatch decision before the observation of uncertain wind power. The additional adjustment action is made in the second stage once the wind power uncertainty is observed. Based on the duality theory and Big-M approach, the original second-stage problem can be dualized and linearized. Therefore, the column-and-constraint generation algorithm can be further implemented to achieve the optimal day-ahead economic dispatch strategy for the integrated power-heat-gas microgrid. The experimental results indicate the effectiveness of the presented approach for achieving operation cost reduction and promoting wind power utilization. The robustness and the economy of the two-stage robust model can be balanced, of which the performances significantly outperform those of the single-stage robust model and the deterministic model.

scholarly journals A Biobjective and Trilevel Programming Model for Hub Location Problem in Design of a Resilient Power Projection Network

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Hai-Ling Bi ◽  
Kai Kang ◽  
Xu-Tao Zhang
Keyword(s):  
Programming Model ◽  
Multiple Criteria Decision Making ◽  
Complex Model ◽  
Hub Location ◽  
Hub Location Problem ◽  
Worst Case ◽  
Power Projection ◽  
Network Cost ◽  
The Cost ◽  
Projection Network

Hubs disruptions are taken into account in design of a resilient power projection network. The problem is tackled from a multiple criteria decision-making (MCDM) perspective. Not only the network cost in normal state is considered, but also the cost in the worst-case situation is taken into account. A biobjective and trilevel integer programming model is proposed using game theory. Moreover, we develop a metaheuristic based on tabu search and shortest path algorithm for the resolution of the complex model. Computational example indicates that making tradeoffs between the performances of the network in different situations is helpful for designing a resilient network.

scholarly journals Sampling Based Approaches for Minimizing Regret in Uncertain Markov Decision Processes (MDPs)

2017 ◽  
Vol 59 ◽  
pp. 229-264 ◽  
Author(s):  
Asrar Ahmed ◽  
Pradeep Varakantham ◽  
Meghna Lowalekar ◽  
Yossiri Adulyasak ◽  
Patrick Jaillet
Keyword(s):  
Markov Decision Processes ◽  
Decision Processes ◽  
Mixed Integer ◽  
Benchmark Problems ◽  
Minimax Regret ◽  
Mixed Integer Linear Program ◽  
Worst Case ◽  
Integer Linear Program Formulation ◽  
Markov Decision ◽  
Reward Functions

Markov Decision Processes (MDPs) are an effective model to represent decision processes in the presence of transitional uncertainty and reward tradeoffs. However, due to the difficulty in exactly specifying the transition and reward functions in MDPs, researchers have proposed uncertain MDP models and robustness objectives in solving those models. Most approaches for computing robust policies have focused on the computation of maximin policies which maximize the value in the worst case amongst all realisations of uncertainty. Given the overly conservative nature of maximin policies, recent work has proposed minimax regret as an ideal alternative to the maximin objective for robust optimization. However, existing algorithms for handling minimax regret are restricted to models with uncertainty over rewards only and they are also limited in their scalability. Therefore, we provide a general model of uncertain MDPs that considers uncertainty over both transition and reward functions. Furthermore, we also consider dependence of the uncertainty across different states and decision epochs. We also provide a mixed integer linear program formulation for minimizing regret given a set of samples of the transition and reward functions in the uncertain MDP. In addition, we provide two myopic variants of regret, namely Cumulative Expected Myopic Regret (CEMR) and One Step Regret (OSR) that can be optimized in a scalable manner. Specifically, we provide dynamic programming and policy iteration based algorithms to optimize CEMR and OSR respectively. Finally, to demonstrate the effectiveness of our approaches, we provide comparisons on two benchmark problems from literature. We observe that optimizing the myopic variants of regret, OSR and CEMR are better than directly optimizing the regret.

scholarly journals Optimization of the Collaborative Hub Location Problem with Metaheuristics

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2759
Author(s):  
Gargouri Mohamed Amine ◽  
Hamani Nadia ◽  
Mrabti Nassim ◽  
Kermad Lyes
Keyword(s):  
Distribution Network ◽  
Ghg Emissions ◽  
Three Dimensions ◽  
Mixed Integer ◽  
Particle Swarm Algorithm ◽  
Hub Location ◽  
Hub Location Problem ◽  
Health Crisis ◽  
Job Opportunities ◽  
The Social

By creating new job opportunities and developing the regional economy, the transport of goods generates significant costs, environmental and sanitary nuisances, and high greenhouse gas (GHG) emissions. In this context, collaboration is an interesting solution that can be used to enable companies to overcome some problems such as globalization, economic crisis, health crisis, issues related to sustainability, etc. This study deals with the design of a multiperiod multiproduct three-echelon collaborative distribution network with a heterogeneous fleet. By applying the mixed integer linear problem (MILP) formulations, it was possible to study the three dimensions of sustainability (economic, environmental, and social/societal). Since the examined problem was NP-hard, it was solved using four metaheuristic approaches to minimize the different logistics costs or CO2 emissions. The social/societal aspect evaluated the accident rate and the noise level generated by the freight transport. Four algorithms were developed to achieve our objectives: a genetic algorithm, a simulated annealing, a particle swarm algorithm, and a vibration damping optimization algorithm. Considering a French distribution network, these algorithms overcame the limits of the exact solution method by obtaining optimal solutions with reasonable execution time.

scholarly journals Megaregional Passenger Transportation Hub Location Problem Considering Congestion Effects

2021 ◽  
Vol 33 (4) ◽  
pp. 551-563
Author(s):  
Huang Yan ◽  
Xiaoning Zhang
Keyword(s):  
Location Problem ◽  
Travel Demand ◽  
Programming Model ◽  
Transportation Network ◽  
Network Capacity ◽  
Mixed Integer ◽  
Hub Location ◽  
Hub Location Problem ◽  
Passenger Transportation ◽  
Congestion Effects

The need to make effective plans for locating transportation hubs is of increasing importance in the megaregional area, as recent research suggests that the growing intercity travel demand affects the efficiency of a megaregional transportation system. This paper investigates a hierarchical facility location problem in a megaregional passenger transportation network. The aim of the study is to determine the locations of hub facilities at different hierarchical levels and distribute the demands to these facilities with minimum total cost, including investment, transportation, and congestion costs. The problem is formulated as a mixed-integer nonlinear programming model considering the service availability structure and hub congestion effects. A case study is designed to demonstrate the effectiveness of the proposed model in the Wuhan metropolitan area. The results show that the congestion effects can be addressed by reallocating the demand to balance the hub utilisation or constructing new hubs to increase the network capacity. The methods of appropriately locating hubs and distributing traffic flows are proposed to optimise the megaregional passenger transportation networks, which has important implications for decision makers.

scholarly journals Distribution-Free Inventory Risk Pooling in a Multilocation Newsvendor

2020 ◽  
Author(s):  
Aravind Govindarajan ◽  
Amitabh Sinha ◽  
Joline Uichanco
Keyword(s):  
Upper Bound ◽  
Stochastic Approach ◽  
Distribution Networks ◽  
Semidefinite Program ◽  
Worst Case ◽  
Expected Cost ◽  
Demand Distribution ◽  
Cost Structures ◽  
Robust Model ◽  
Distributionally Robust

We study a multilocation newsvendor network when the only information available on the joint distribution of demands are the values of its mean vector and covariance matrix. We adopt a distributionally robust model to find inventory levels that minimize the worst-case expected cost among the distributions consistent with this information. This problem is NP-hard. We find a closed-form tight bound on the expected cost when there are only two locations. This bound is tight under a family of joint demand distributions with six support points. For the general case, we develop a computationally tractable upper bound on the worst-case expected cost if the costs of fulfilling demands have a nested structure. This upper bound is the optimal value of a semidefinite program whose dimensions are polynomial in the number of locations. We propose an algorithm that can approximate general fulfillment cost structures by nested structures, yielding a computationally tractable heuristic for distributionally robust inventory optimization on general newsvendor networks. We conduct experiments on networks resembling U.S. e-commerce distribution networks to show the value of a distributionally robust approach over a stochastic approach that assumes an incorrect demand distribution. This paper was accepted by Chung Piaw Teo, optimization.

scholarly journals Learning-‘N-Flying: A Learning-Based, Decentralized Mission-Aware UAS Collision Avoidance Scheme

2021 ◽  
Vol 5 (4) ◽  
pp. 1-26
Author(s):  
Alëna Rodionova ◽  
Yash Vardhan Pant ◽  
Connor Kurtz ◽  
Kuk Jang ◽  
Houssam Abbas ◽  
...  
Keyword(s):  
Collision Avoidance ◽  
Computation Time ◽  
Unmanned Aircraft ◽  
Mixed Integer ◽  
Mixed Integer Linear Program ◽  
Worst Case ◽  
Online Computation ◽  
Multiple Case ◽  
Aircraft System ◽  
The City

Urban Air Mobility, the scenario where hundreds of manned and Unmanned Aircraft Systems (UASs) carry out a wide variety of missions (e.g., moving humans and goods within the city), is gaining acceptance as a transportation solution of the future. One of the key requirements for this to happen is safely managing the air traffic in these urban airspaces. Due to the expected density of the airspace, this requires fast autonomous solutions that can be deployed online. We propose Learning-‘N-Flying (LNF), a multi-UAS Collision Avoidance (CA) framework. It is decentralized, works on the fly, and allows autonomous Unmanned Aircraft System (UAS)s managed by different operators to safely carry out complex missions, represented using Signal Temporal Logic, in a shared airspace. We initially formulate the problem of predictive collision avoidance for two UASs as a mixed-integer linear program, and show that it is intractable to solve online. Instead, we first develop Learning-to-Fly (L2F) by combining (1) learning-based decision-making and (2) decentralized convex optimization-based control. LNF extends L2F to cases where there are more than two UASs on a collision path. Through extensive simulations, we show that our method can run online (computation time in the order of milliseconds) and under certain assumptions has failure rates of less than 1% in the worst case, improving to near 0% in more relaxed operations. We show the applicability of our scheme to a wide variety of settings through multiple case studies.

scholarly journals Distributionally Robust Model of Energy and Reserve Dispatch Based on Kullback–Leibler Divergence

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1454 ◽  
Author(s):  
Ce Yang ◽  
Dong Han ◽  
Weiqing Sun ◽  
Kunpeng Tian
Keyword(s):  
Robust Optimization ◽  
Benders Decomposition ◽  
Mixed Integer ◽  
Worst Case ◽  
Total Cost ◽  
Kl Divergence ◽  
Leibler Divergence ◽  
Expected Total Cost ◽  
Distributionally Robust ◽  
Bus System

This paper proposes a distance-based distributionally robust energy and reserve (DB-DRER) dispatch model via Kullback–Leibler (KL) divergence, considering the volatile of renewable energy generation. Firstly, a two-stage optimization model is formulated to minimize the expected total cost of energy and reserve (ER) dispatch. Then, KL divergence is adopted to establish the ambiguity set. Distinguished from conventional robust optimization methodology, the volatile output of renewable power generation is assumed to follow the unknown probability distribution that is restricted in the ambiguity set. DB-DRER aims at minimizing the expected total cost in the worst-case probability distributions of renewables. Combining with the designed empirical distribution function, the proposed DB-DRER model can be reformulated into a mixed integer nonlinear programming (MINLP) problem. Furthermore, using the generalized Benders decomposition, a decomposition method is proposed and sample average approximation (SAA) method is applied to solve this problem. Finally, simulation result of the proposed method is compared with those of stochastic optimization and conventional robust optimization methods on the 6-bus system and IEEE 118-bus system, which demonstrates the effectiveness and advantages of the method proposed.

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