Demand Nodes Research Articles

Multi-modal and multi-product hierarchical hub location problem with fuzzy demands

The hub location is a major problem in the systems with high dependence on the transportation of goods, information, and passengers between the constituent parts. The present study is aimed to introduce a multi-commodity multi-model hierarchical hub location problem with uncertain demand. Thus, it is estimated by intuitionistic fuzzy variables. The objective function in the present problem is to minimize the total transportation costs in the network to determine the optimal hub location, allocate non-hub nodes to the hubs and the ground hubs to the air hubs, and identify the type of vehicles required in each route. The model has a hierarchical structure consisting of a three-echelon network (i.e., central hubs, non-central hubs, and demand nodes) connected in the star-tour-star form. A four-index mathematical model was presented and solved by GAMS optimization software. The results indicated that the objective function (cost) has a descending trend with increasing the number of hubs which can be assigned to the decline in the transportation costs. The costs increased by a decrease in the maximum delivery time which could be due to the selection method of the transportation mode. In the multi-product case, the costs declined by increasing the number of hubs as these hubs decremented the network complexity. Regarding the NP-Hard nature of the hub problems, a genetic meta-heuristic algorithm was proposed in the MATLAB software to solve the large-scale problem. According to the results, this algorithm offered close-optimal solutions. Noteworthy, this study employed known AP datasets.

Adaptive distributionally robust hub location and routing problem with a third-party logistics strategy

In this paper, we study an essential and more realistic variant of the hub location-routing problem in which third-party logistics (3PL) are incorporated into a self-built distribution hub network. A two-stage mixed-integer programming model is developed to address the proposed hub location-routing problem with mixed logistical strategies. In the strategic stage, the hub location and allocation decisions are made before the realization of uncertain demands to minimize the total construction and transportation costs. In the operational stage, the managers make vehicle routing decisions with and without the 3PL strategy, and route planning is considered for multiple owned and 3PL vehicles on the basis of simultaneous pickup and delivery. We investigate the effects of uncertain factors on the network design of this framework, as the node demands are often unobservable or difficult to obtain accurately in practice. To address the inherent uncertainty of the problem, we propose an adaptive distributionally robust model by limiting uncertain demands to a specified ambiguity set. Moreover, we reformulate the proposed model into tractable robust counterpart forms under the ambiguity set with information about the support, mean and upper bounds on the dispersion. We design a genetic algorithm with local search to solve the reformulated model on a large scale. Finally, we conduct a case study for a leading retail enterprise in the Beijing–Tianjin–Hebei region to demonstrate the effectiveness and applicability of our model.

Optimal design and cost analysis of water distribution networks based on pressure-dependent leakage using NSGA-II

Leakage from water distribution networks (WDNs) is inevitable. Therefore, during design a WDN, engineers add a percentage of each nodal water demand as leakage discharge to total node demand. The amount of leakage depends on the pressure, which is not known at the design stage. Considering a constant percentage of node demand in lieu of its leakage makes the problem worse. In this study, the effect of leakage on the optimal WDN design was investigated by developing the matrix form of the gradient algorithm while accounting for leakage using the pressure-dependent model. Non-dominated genetic algorithm version II (NSGA-II) was used as the optimization engine with two objectives which includes minimizing the network construction cost and minimizing the total network pressure deficiency. Two well-known two- and three-loop WDNs in literature were studied. The results indicated that the pressure-dependent leakage varies between 12.9 and 29.44% of the node demand while the network construction cost stays the same if compared with the fixed percentage leakage model, and the construction cost would increase by 17–31%, if leakage is not accounted for. This is expected the optimized diameters and hydraulic characteristics of the networks being affected by the leakage calculation method.

Routing and resource allocation in non-profit settings with equity and efficiency measures under demand uncertainty

Motivated by food distribution operations for non-profit organizations, we study a variant of the stochastic routing-allocation problem under demand uncertainty, in which one decides the assignment of trucks for demand nodes, the sequence of demand nodes to visit (i.e., truck route), and the allocation of food supply to each demand node. We propose three stochastic mixed-integer programming (SMIP) models representing different performance measures important to food banks, namely maximizing efficiency, maximizing equity, and maximizing efficiency and equity simultaneously. To solve practical large-scale instances, we develop an original matheuristic based on adaptive large-scale neighborhood search. Using real-world data based on real-life instances, we conduct an extensive numerical experiment to assess the computational performance of our approach and derive insights relevant to food banks. The proposed matheuristic produces high-quality solutions quickly with an optimality gap never exceeding 4.11% on tested instances. We also demonstrate the performance of the three models in terms of service levels, food waste, and equity.

A parallel adaptive memory algorithm for the capacitated modular hub location problem

The capacitated modular hub location problem is a realistic variant of the popular hub location problem arising from the design of telecommunications networks. Given a set of demand nodes, the problem consists in selecting a subset of nodes to represent hubs and assigning the rest of the nodes to the hub nodes, such that the transportation cost is minimized while satisfying the capacity constraints. The adaptive memory algorithm is a hybrid evolutionary heuristic that uses a central memory to store blocks of solutions. At each iteration, the recombination operator uses these solution blocks to create an offspring solution. In this paper, we present a parallel adaptive memory algorithm for the capacitated modular hub location problem that stores both solution blocks and complete solutions in a shared memory for the creation of an offspring. Other distinguishing features of our proposed algorithm include specially designed recombination and mutation operators for search diversification, an effective tabu search procedure for search intensification, and parallel computing for global optimization. Extensive computational results on three well-known data sets of 170 benchmark instances show that the proposed algorithm competes very favorably with the state-of-the-art heuristics from the literature. In particular, it finds 115 improved best-known solutions (for more than 67% of the cases). Furthermore, we analyze the key algorithmic components and shed lights on their impact on the proposed algorithm.

Research on leakage area detection method in water distribution network based on gray wolf optimization

Abstract Leakage in a water distribution network (WDN) leads to a large amount of water loss and water pipe pollution and affects residents’ domestic water supply. Therefore, network leakage detection significantly saves water resources. The traditional model approach has ample search space in solving large distribution network applications, a challenging and complex leakage detection process and a low detection accuracy. For the above problems, this study proposes a new method of leakage area detection based on gray wolf optimization (GWO). First, the extensive WDN is divided into several virtual areas. Then, the leakage is simulated by the additional water demand of nodes, and the node demand of the distribution network is calibrated based on the GWO algorithm. Finally, the leakage area is identified, and the size of the leakage in that area is estimated. The method was experimented on in two cases, simulating single-point leakage and multi-point simultaneous leakage, respectively. The results show that the method estimates the size of leakage in the corresponding area based on accurate identification of leakage areas, and the detection error of leakage is within 17.14%. The method provides water workers with guidance on leak detection, significantly reducing staff time to repair pipes.

Efficient Day-Ahead Dispatch of Photovoltaic Sources in Monopolar DC Networks via an Iterative Convex Approximation

The objective of this research is to propose an efficient energy management system for photovoltaic (PV) generation units connected to monopolar DC distribution networks via convex optimization while considering a day-ahead dispatch operation scenario. A convex approximation is used which is based on linearization via Taylor’s series expansion to the hyperbolic relations between voltages and powers in the demand nodes. A recursive solution methodology is introduced via sequential convex programming to minimize the errors introduced by the linear approximation in the power balance constraints. Numerical results in the DC version of the IEEE 33-bus grid demonstrate the effectiveness of the proposed convex model when compared to different combinatorial optimization methods, with the main advantage that the optimal global solution is found thanks to the convexity of the solution space and the reduction of the error via an iterative solution approach. Different objective functions are analyzed to validate the effectiveness of the proposed iterative convex methodology (ICM), which corresponds to technical (energy losses reduction), economic (energy purchasing and maintenance costs), and environmental (equivalent emissions of CO2 to the atmosphere in conventional sources) factors. The proposed ICM finds reductions of about 43.9754% in daily energy losses, 26.9957% in energy purchasing and operating costs, and 27.3771% in CO2 emissions when compared to the benchmark case in the DC version of the IEEE 33-bus grid. All numerical validations were carried out in the MATLAB programming environment using the SEDUMI and SDPT3 tools for convex programming and our own scripts for metaheuristic methods.

A [formula omitted]-level [formula omitted]-facility network design problem in the presence of congestion

In this paper, we propose a bi-level model for a p-facility network design problem in a transportation network in which the effect of congestion is also considered. In order to cope with the traffic burden imposed by the clients of demand nodes, the possibility of rerouting the previously existing origin–destination flows is allowed. In addition, the network designers consider a limited budget for constructing new facilities as well as applying some operational enhancements on network links to alleviate the increased traffic congestion caused by the clients of facilities and avoid inordinate growth in network travel time and corresponding cost. The upper level is dedicated to selecting the location of facilities and link enhancements with the purpose of minimizing the total travel cost, while at the lower level, a pseudo-traffic assignment problem is applied to determine the user-equilibrium path flows. By analyzing the characteristics of the model, the near-optimal solutions are given by an online supervised machine learning algorithm. Finally, the validity of the proposed model and used method is evaluated through some numerical examples.

Multimodal Fuzzy Downstream Petroleum Supply Chain: A Novel Pentagonal Fuzzy Optimization

The petroleum industry has a complex, inflexible and challenging supply chain (SC) that impacts both the national economy as well as people’s daily lives with a range of services, including transportation, heating, electricity, lubricants, as well as chemicals and petrochemicals. In the petroleum industry, supply chain management presents several challenges, especially in the logistics sector, that are not found in other industries. In addition, logistical challenges contribute significantly to the cost of oil. Uncertainty regarding customer demand and supply significantly affects SC networks. Hence, SC flexibility can be maintained by addressing uncertainty. On the other hand, in the real world, decision-making challenges are often ambiguous or vague. In some cases, measurements are incorrect owing to measurement errors, instrument faults, etc., which lead to a pentagonal fuzzy number (PFN) which is the extension of a fuzzy number. Therefore, it is necessary to develop quantitative models to optimize logistics operations and supply chain networks. This study proposed a linear programming model under an uncertain environment. The model minimizes the cost along the refineries, depots, multimode transport and demand nodes. Further developed pentagonal fuzzy optimization, an alternative approach is developed to solve the downstream supply chain using the mixed-integer linear programming (MILP) model to obtain a feasible solution to the fuzzy transportation cost problem. In this model, the coefficient of the transportation costs and parameters is assumed to be a pentagonal fuzzy number. Furthermore, defuzzification is performed using an accuracy function. To validate the model and technique and feasibility solution, an illustrative example of the oil and gas SC is considered, providing improved results compared with existing techniques and demonstrating its ability to benefit petroleum companies is the objective of this study.

Harnessing the Power of Metaheuristic Algorithms for Optimal Logistics Management in Epidemic Response

This paper investigates the use of metaheuristics as computational tools for managing epidemic logistics. Epidemics pose severe risks to world health, necessitating coordinated, effective, and prompt response plans. Effective logistics management is a critical component of this, requiring, among other things, timely distribution of vaccinations and the efficient deployment of workers and resources. Such logistical difficulties are frequently dynamic and complex, demanding more sophisticated computational techniques. The complex logistic optimization problems are addressed by metaheuristics, which offer higher-level problem-solving techniques. The Multi-Depot Vehicle Routing Problem (MD- VRP), a common metaheuristic, and its solution in the context of epidemic logistics are the specific topic of this paper. The objective of MDVRP, which is categorized as an NP-Hard issue, is to efficiently distribute supplies from many depots to numerous demand nodes (hospitals, clinics). Due to this problem’s complexity, time-sensitivity, scalability concerns, and dynamic and uncertain situations, traditional methods frequently fail to solve it effectively. However, the genetic algorithm can potentially improve the MDVRP inside epidemic logis- tics, delivering effective and adaptable solutions in a fair amount of time. This work advances knowledge of the function of metaheuristics in improving epidemic response logistics through a thorough literature analysis, potential applications discussion, and case study illustration. We acknowledge the necessity for additional study in customizing these algorithms considering the many uncertainties and dynamic aspects in the real-world application as we come to a close.

A greedy heuristic and a lower bound on a nonlinear stochastic TSP with partially satisfied node demand coverage constraint

A greedy heuristic and a lower bound on a nonlinear stochastic TSP with partially satisfied node demand coverage constraint

Effect of variation of empirical exponent coefficient values in water distribution network analysis

The water distribution network supplies water to consumer to fulfill demands at desired pressure. Due to pressure deficient conditions pressure fall below minimum required which ultimately lead to reduction in flow supplied to consumer. The water distribution network is said to be pressure deficient, if the pressure head in each node is less than the required head. Adding artificial element approach for predicting partial flow at demand node in pressure deficient condition is used by many researchers. The objective of study is to investigate effect of variation in empirical exponent coefficient on emitter exponent, pressure and actual demand at demand node. The steady state simulation is carried out for case study network with pressure deficient node as emitter node using Fictitious component free – Pressure Deficient Network Algorithm. The emitter coefficient formula, derived from Wagner’s equation is used for predicting actual demand under pressure deficient condition. The value of emitter coefficient depends on emitter exponent coefficient value, which is calculated using empirical exponent coefficient. The study is carried out for three different values of empirical exponent coefficient 0.5, 1, 1.5, 1.852, 2 and 2.5 respectively. The simulation analysis shows that as empirical exponent increases emitter exponent decreases, pressure decreases and actual demand at nodes increases. This study can be useful in calculating resilience index, which is measure of average efficiency of water distribution network under pressure deficient condition.

Distributionally robust day-ahead scheduling for power-traffic network under a potential game framework

Widespread utilization of electric vehicles (EVs) incurs more uncertainties and impacts on the scheduling of the power-transportation coupled network. This paper investigates optimal power scheduling for a power-transportation coupled network in the day-ahead energy market considering multiple uncertainties related to photovoltaic (PV) generation and the traffic demand of vehicles. The crux of this problem is to model the coupling relation between the two networks in the day-ahead scheduling stage and consider the intra-day spatial uncertainties of the source and load. Meanwhile, the flexible load with a certain adjustment margin is introduced to ensure the balance of supply and demand of power nodes and consume the renewable energy better. Furthermore, we show the interactions between the power system and EV users from a potential game-theoretic perspective, where the uncertainties are characterized by an ambiguity set. In order to ensure the individual optimality of the two networks in a unified framework in day-ahead power scheduling, a two-stage distributionally robust centralized optimization model is established to carry out the equilibrium of power-transportation coupled network. On this basis, a combination of the duality theory and the Benders decomposition is developed to solve the distributionally robust optimization (DRO) model. Simulations demonstrate that the proposed approach can obtain individual optimal and less conservative strategies.

Exact and Heuristics Algorithms for Screen Line Problem in Large Size Networks: Shortest Path-Based Column Generation Approach

In this study, we present exact and heuristics algorithms for a traffic sensors location problem called the screen line problem. It is a problem of how to locate traffic sensors on a transportation network where all the origin/destination node pairs are fully separated. The problem experiences two main complexity dimensions that obstruct finding an efficient solution algorithm for large-scale networks: its mathematical formulation, which is proved in the literature to be NP-hard, and an inherent combinatorial complexity due to the need for a network complete path enumeration. In this study, the problem is reformulated as a set covering problem. Thereafter, the dual formulation is recalled showing that the shortest path-based column generation method would yield as many paths as necessary and hence circumvent the intractability of the full path enumeration task. This path generation technique enables applying both the proposed heuristics and exact methods to the problem. In addition, the gap value between the heuristics and the exact algorithms is set to be examined statistically. For evaluation, three networks of different sizes were used to track the scalability of proposed algorithms. The methodology showed high efficiency to deal with up to 10,000 demand node pairs in addition to the capability of producing practical solutions with respect to normal traffic flow conditions. The proposed heuristics algorithm stipulates a gap value of less than 25% with more than 99% confidence.

Multi-type maximal covering location problems: Hybridizing discrete and continuous problems

This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different normed spaces are simultaneously decided to maximize the demand generated by a set of points. From the need of intertwining location decisions in discrete and in continuous sets, a general hybridized problem is considered in which some types of facilities are to be located in finite sets and the others in continuous normed spaces. A natural non-linear model is proposed for which an integer linear programming reformulation is derived. A branch-and-cut algorithm is developed for better tackling the problem. The study proceeds considering the particular case in which the continuous facilities are to be located in the Euclidean plane. In this case, by taking advantage from some geometrical properties it is possible to propose an alternative integer linear programming model. The results of an extensive battery of computational experiments performed to assess the methodological contribution of this work is reported. Apart from a synthetic dataset, the different approaches are tested on a real geographical and demographic data with up to 920 demand nodes.

Recursive Convex Model for Optimal Power Flow Solution in Monopolar DC Networks

This paper presents a new optimal power flow (OPF) formulation for monopolar DC networks using a recursive convex representation. The hyperbolic relation between the voltages and power at each constant power terminal (generator or demand) is represented as a linear constraint for the demand nodes and generators. To reach the solution for the OPF problem a recursive evaluation of the model that determines the voltage variables at the iteration t+1 (vt+1) by using the information of the voltages at the iteration t (vt) is proposed. To finish the recursive solution process of the OPF problem via the convex relaxation, the difference between the voltage magnitudes in two consecutive iterations less than the predefined tolerance is considered as a stopping criterion. The numerical results in the 85-bus grid demonstrate that the proposed recursive convex model can solve the classical power flow problem in monopolar DC networks, and it also solves the OPF problem efficiently with a reduced convergence error when compared with semidefinite programming and combinatorial optimization methods. In addition, the proposed approach can deal with radial and meshed monopolar DC networks without modifications in its formulation. All the numerical implementations were in the MATLAB programming environment and the convex models were solved with the CVX and the Gurobi solver.

Optimization of installation and energy costs in water distribution systems with unknown flow directions

Abstract Water distribution networks (WDNs) are an important part of water distribution systems and are responsible for water transportation from the reservoirs to the demand nodes at adequate pressure and velocity. In the present paper, the synthesis of WDN is treated as an optimization problem with a mixed integer nonlinear programming formulation. The objective function to be minimized is the total network cost, considering installation and energy costs, with unknown flow directions, which is the novelty in the paper. Disjunctive programming and linearization techniques are used in the model formulation to avoid nonlinear and nonconvex problems. Two case studies are used to test the model's applicability. Results show that operational costs can represent a significant part of the total cost in sustainable networks. In the first case study, the total cost was better than the literature results (US$ 2,272,538.85 vs. US$ 2,272,387.49) and the operational costs represent ¼ of the total WDN costs. In the second case study, the operation cost corresponds to almost 2/3 of the total WDN cost. These results show the importance of considering operational costs in the WDN design. Also, the consideration of unknown flow directions can lead to better results for the network topology.

Integrated and coordinated relief logistics and road recovery planning problem

Sudden onset disasters can block roads and hinder relief logistics. With the objective of facilitating access to critical locations in the disaster-stricken area, we propose a new mathematical model that determines the schedule and routes of a relief distribution team and a road restoration team. The road restoration team restores some of the blocked roads to provide faster access to critical nodes for the relief distribution team. We study the case in which the restoration times are stochastic, and our goal is to minimize the time by which the last demand node is met by the relief distribution team. We provide a detailed case study of our model with real data from Harris County in Texas, which was impacted by Hurricane Harvey during 2017. The results obtained from testing our model show that the objective function is decreased by up to 15% using the proposed non-myopic policy.

Power Flow Solution in Bipolar DC Networks Considering a Neutral Wire and Unbalanced Loads: A Hyperbolic Approximation

This paper addresses the problem of the power flow analysis of bipolar direct current (DC) networks considering unbalanced loads and the effect of a neutral wire, which may be solidly grounded or non-grounded. The power flow problem is formulated using the nodal admittance representation of the system and the hyperbolic relations between power loads and voltages in the demand nodes. Using Taylor series expansion with linear terms, a recursive power flow method with quadratic convergence is proposed. The main advantage of the hyperbolic approximation in dealing with power flow problems in DC bipolar networks is that this method can analyze radial and meshed configurations without any modifications to the power flow formula. The numerical results in three test feeders composed of 4, 21, and 85 bus systems show the efficiency of the proposed power flow method. All of the simulations were conducted in MATLAB for a comparison of the proposed approach with the well-established successive approximation method for power flow studies in distribution networks.

Transit facility allocation: Hybrid quantum-classical optimization.

An essential consideration in urban transit facility planning is service efficiency and accessibility. Previous research has shown that reducing the number of facilities along a route may increase efficiency but decrease accessibility. Striking a balance between these two is a critical consideration in transit planning. Transit facility consolidation is a cost-effective way to improve the quality of service by strategically determining the desirable allocation of a limited number of facilities. This paper develops an optimization framework that integrates Geographical Information systems (GIS), decision-making analysis, and quantum technologies for addressing the problem of facility consolidation. Our proposed framework includes a novel mathematical model that captures non-linear interactions between facilities and surrounding demand nodes, inter-facility competition, ridership demand and spatial coverage. The developed model can harness the power of quantum effects such as superposition and quantum tunnelling and enables transportation planners to utilize the most recent hardware solutions such as quantum and digital annealers, coherent Ising Machines and gate-based universal quantum computers. This study presents a real-world application of the framework to the public transit facility redundancy problem in the British Columbia Vancouver metropolitan area. We demonstrate the effectiveness of our framework by reducing the number of facilities by 40% while maintaining the same service accessibility. Additionally, we showcase the ability of the proposed mathematical model to take advantage of quantum annealing and classical optimization techniques.