Network Flow Programming Research Articles

Modeling and mitigating supply chain disruptions as a bilevel network flow problem

Years of globalization, outsourcing and cost cutting have increased supply chain vulnerability calling for more effective risk mitigation strategies. In our research, we analyze supply chain disruptions in a production setting. Using a bilevel optimization framework, we minimize the total production cost for a manufacturer interested in finding optimal disruption mitigation strategies. The problem constitutes a convex network flow program under a chance constraint bounding the manufacturer’s regrets in disrupted scenarios. Thus, in contrast to standard bilevel optimization schemes with two decision-makers, a leader and a follower, our model searches for the optimal production plan of a manufacturer in view of a reduction in the sequence of his own scenario-specific regrets. Defined as the difference in costs of a reactive plan, which considers the disruption as unknown until it occurs, and a benchmark anticipative plan, which predicts the disruption in the beginning of the planning horizon, the regrets allow measurement of the impact of scenario-specific production strategies on the manufacturer’s total cost. For an efficient solution of the problem, we employ generalized Benders decomposition and develop customized feasibility cuts. In the managerial section, we discuss the implications for the risk-adjusted production and observe that the regrets of long disruptions are reduced in our mitigation strategy at the cost of shorter disruptions, whose regrets typically stay far below the risk threshold. This allows a decrease of the production cost under rare but high-impact disruption scenarios.

Tracking-by-Counting: Using Network Flows on Crowd Density Maps for Tracking Multiple Targets.

State-of-the-art multi-object tracking (MOT) methods follow the tracking-by-detection paradigm, where object trajectories are obtained by associating per-frame outputs of object detectors. In crowded scenes, however, detectors often fail to obtain accurate detections due to heavy occlusions and high crowd density. In this paper, we propose a new MOT paradigm, tracking-by-counting, tailored for crowded scenes. Using crowd density maps, we jointly model detection, counting, and tracking of multiple targets as a network flow program, which simultaneously finds the global optimal detections and trajectories of multiple targets over the whole video. This is in contrast to prior MOT methods that either ignore the crowd density and thus are prone to errors in crowded scenes, or rely on a suboptimal two-step process using heuristic density-aware point-tracks for matching targets. Our approach yields promising results on public benchmarks of various domains including people tracking, cell tracking, and fish tracking.

Green logistics location-routing problem with eco-packages

Optimization of the green logistics location-routing problem with eco-packages involves solving a two-echelon location-routing problem and the pickup and delivery problem with time windows. The first echelon consists of large eco-package transport, which is modeled by a time-discretized transport-concentrated network flow programming in the resource sharing state–space–time (SST) network. The second echelon focuses on small eco-package pickups and deliveries, established by the cost-minimized synchronization-oriented location routing model that minimizes the total generalized cost, which includes internal transportation cost, value of eco-packages, short-term benefits and environmental externalities. In addition, the Gaussian mixture clustering algorithm is utilized to assign customers to their respective service providers in the pickup and delivery process, and a Clarke–Wright saving method-based non-dominated sorting genetic algorithm II is designed to optimize pickup and delivery routes, and improve their cost-effectiveness and degree of synchronization. Different strategy testing results are used in the service phase as input data to calculate the cost of the transport phase, which is solved through a Lagrangian relaxation approach. The 3D SST network representation innovatively captures the eco-package route sequence and state transition constraints over the shortest path in the pickup and delivery at any given moment of the transport phase. A large-scale logistics network in Chengdu, China, is used to demonstrate the proposed model and algorithm, and undertake sensitivity analysis considering the life cycle of green eco-packages.

Optimally locating electric scooter battery swapping stations and battery deployment

ABSTRACT In the past, several studies have focused on planning for the deployment of charging stations for electric vehicles, with fewer studies being conducted on electric scooters. These works, however, did not consider the characteristics of electric scooters with regard to tourism activities. Therefore, in this study the authors adopt network flow and mathematical programming techniques to develop a model to find the optimal location for electric scooter battery swapping stations and battery deployment. This model is formulated as an integer network flow problem with side constraints and is characterized as NP hard. To efficiently and effectively solve the model for large-scale problems faced in practice, a solution algorithm is also developed. Finally, numerical tests are conducted using real data for Taichung City, Taiwan. The results demonstrate that the proposed model and solution algorithm are potentially useful for locating battery swapping stations and battery deployment in actual practice.

Machine Learning, Urban Water Resources Management and Operating Policy

Meticulously analyzing all contemporaneous conditions and available options before taking operations decisions regarding the management of the urban water resources is a necessary step owing to water scarcity. More often than not, this analysis is challenging because of the uncertainty regarding inflows to the system. The most common approach to account for this uncertainty is to combine the Bayesian decision theory with the dynamic programming optimization method. However, dynamic programming is plagued by the curse of dimensionality, that is, the complexity of the method is proportional to the number of discretized possible system states raised to the power of the number of reservoirs. Furthermore, classical statistics does not consistently represent the stochastic structure of the inflows (see persistence). To avoid these problems, this study will employ an appropriate stochastic model to produce synthetic time-series with long-term persistence, optimize the system employing a network flow programming modelling, and use the optimization results for training a feedforward neural network (FFN). This trained FFN alone can serve as a decision support tool that describes not only reservoir releases but also how to operate the entire water supply system. This methodology is applied in a simplified representation of the Athens water supply system, and the results suggest that the FFN is capable of successfully operating the system according to a predefined operating policy.

Performance Assessment of a Coupled Particle Swarm Optimization and Network Flow Programming Model for Optimum Water Allocation

Water resources allocation problems are mainly categorized in two classes of simulation and optimization. In most cases, optimization problems due to the number of variables, constraints and nonlinear feasible search space are known as a challenging subject in the literature. In this research, by coupling particle swarm optimization (PSO) algorithm and a network flow programming (NFP) based river basin simulation model, a PSO-NFP hybrid structure is constructed for optimum water allocation planning. In the PSO-NFP model, the NFP core roles as the fast inner simulation engine for finding optimum values for a large number of water discharges in the network links (rivers and canals) and nodes (reservoirs and demands) while the heuristic PSO algorithm forms the outer optimization cover to search for the optimum values of reservoirs capacities and their storage priorities. In order to assess the performance of the PSO-NFP model, three hypothetical test problems are defined, and their equivalent nonlinear mathematical programs are developed in LINGO and the results are compared. Finally, the PSO-NFP model is applied in solving a real river basin water allocation problem. Results indicate that the applied method of coupling PSO and NFP has an efficient ability for handling river basin-scale water resources optimization problems.

A Demand Management Based Crop and Irrigation Planning Using the Simulation-Optimization Approach

Coupled simulation-optimization models are useful tools for solving optimum water allocation and crop planning problems. In this study, the optimum crops pattern in the Arayez plain in the Karkheh river basin in Iran is determined by integration of a network flow programming (NFP) based simulation model and the shuffle frog leaping optimization algorithm (SFLA) in the form of a simulation-optimization approach. MODSIM applies NFP for finding water allocations which by use of its customization ability, the benefit of water supply for the agricultural crops is calculated based on the agronomic equations. The objective function is to maximize the total net benefit gained from crops production where the decision variables which are the irrigation depths and the cultivation areas are optimized by SFLA. Results show that by use of the coupled SFLA-NFP model, the net benefit increases 12% comparing the present situation in the plain. Also, the sensitivity analyses on effective parameters indicate that the potential maximum yield and the net price of the crops yield in the market have a direct impact on the crops optimum cultivation area.

Applying the Network Flow Programming to Cropping Plan Decision for FSC with Time Flexibility

Applying the Network Flow Programming to Cropping Plan Decision for FSC with Time Flexibility

Optimal Control of Technological Innovations in Post-conflict Regions by Minimization of Admissible Network Investments and Risks

The problem for planning and control of technological investments is considered, in regions with increased risks for the investments being applied. A network flow approach for solving such problem is proposed which is adapted to innovation networks keeping in mind the risks. The capacity of such a network is determined as the minimal admissible risks are considered on its separate sections, as well as other possible constraints. The optimal decisions for implementation of technological innovations through minimal possible investments and admissible risks are found by solving problems of network flow programming. Two numerical examples are given for solving such type of problems that demonstrate the good opportunities using the method which is being suggested.

Optimal Control of Mobile Agents for Monitoring of Points on a Network

Abstract This paper concerns the problems of finding optimal trajectories between nodes on a network, which must be periodically surveyed, and probably serviced. It is shown, that such trajectories may be generated if optimal Hamiltonian cycles are used between the separate network nodes under inspection. It is known that the Hamiltonian path problem is NP-complete, but an edge decomposition of the network is proposed. This is performed by reducing in a particular way to network flow circulations. The requirements and the equations for describing such circulation are pointed out. Defining of the optimal circulations of the mobile agents is reduced to network flow programming problems. A numerical example is presented for solving a similar class of monitoring problems by mobile agents.

Determination of cost coefficients of a priority-based water allocation linear programming model – a network flow approach

Abstract. This paper presents a method to establish the objective function of a network flow programming model for simulating river–reservoir system operations and associated water allocation, with an emphasis on situations when the links other than demand or storage have to be assigned with nonzero cost coefficients. The method preserves the priorities defined by rule curves of reservoir, operational preferences for conveying water, allocation of storage among multiple reservoirs, and transbasin water diversions. Path enumeration analysis transforms these water allocation rules into linear constraints that can be solved to determine link cost coefficients. An approach to prune the original system into a reduced network is proposed to establish the precise constraints of nonzero cost coefficients, which can then be efficiently solved. The cost coefficients for the water allocation in the Feitsui and Shihmen reservoirs' joint operating system of northern Taiwan was adequately assigned by the proposed method. This case study demonstrates how practitioners can correctly utilize network-flow-based models to allocate water supply throughout complex systems that are subject to strict operating rules.

Special Issue Dedicated to the Memory of Paul A. Jensen

As theory and practice merge, we have seen dramatic advances in the design and use of analytic methods across all subdisciplines of operations research, industrial engineering and business-related fields. This has been accompanied by an explosive growth in computer power, which has allowed for ever-wider implementation and the solution of very large-scale problems. Nevertheless, much analysis in industry, government, and academia occurs with commonly available software such as spreadsheets running on personal computers with limited processing speeds. Because of the pervasiveness of spreadsheets, if we succeed in embedding our analytical tools available in them and in making our success stories known, we can reach a wider audience. For similar reasons, spreadsheet computation can strengthen the teaching of mathematical models and methods, particularly because it can provide a standard interface across topics ranging from optimization and decision analysis to queueing, simulation, and statistics. During his 39-year career at The University of Texas in the Cockrell School of Engineering, Paul Jensen was in the vanguard of developing and implementing computer-based tools to flatten the learning curve for those wishing to solve problems arising in operations research, industrial engineering, operations management, and engineering economics. His first of several co-authored textbooks, Network Flow Programming, broke new ground in its comprehensive coverage of single-commodity network models and algorithms, including all pure and generalized formulations with both convex and concave costs. What was unique about this award-winning book was its algorithmic details, computational flowcharts, and packaged software written in Basic for minicomputers. At the dawning of microcomputers in the early 1980s, Paul published Microsolve/Operations Research, the first compendium of OR computer programs specifically adapted for PCs. Soon after, the Student’s Guide to Operations Research appeared, surveying OR topics and related computational methods in an easyto-read style. For the remainder of his career, Paul designed, programmed and distributed a vast collection of Microsoft Excel add-ins for every aspect of OR, IE, MS, OM and more. These add-ins have been used by hundreds of thousands of analysts, and are freely available at http://www.me.utexas.edu/ ~jensen/ORMM/. This site was originally created to support the text Operations Research Models and Methods but has grown in content much beyond its initial scope. In early 2005, Paul was asked to undertake a full revision of the required undergraduate course, Engineering Economic Analysis, offered by the Mechanical Engineering Department at The University of Texas. Although just retired, he relished the challenge and jumped into the project with the enthusiasm of a new faculty member. Because he had taught the course in the traditional manner for 30 years, he understood what worked and what the potential was for engaging the students in a more interconnected way. Rather than digitizing his notes and problem sets, he set out to develop a comprehensive online course using a variety of media including videos, Excel addins, interactive quizzes, embedded calculators, and flash presentations. What emerged was a completely new course renamed Engineering Finance, along with the website http://www.me.utexas.edu/~me353/ to house the material. Paul was passionate about OR education, and in 2007 he received the INFORMS Prize for the Teaching of ORMS Practice for his work highlighted here. The breadth and scope of his contributions continue to resonate deeply within the INFORMS community

A Model for Solving the Optimal Water Allocation Problem in River Basins with Network Flow Programming When Introducing Non-Linearities

The allocation of water resources between different users is a traditional problem in many river basins. The objective is to obtain the optimal resource distribution and the associated circulating flows through the system. Network flow programming is a common technique for solving this problem. This optimisation procedure has been used many times for developing applications for concrete water systems, as well as for developing complete decision support systems. As long as many aspects of a river basin are not purely linear, the study of non-linearities will also be of great importance in water resources systems optimisation. This paper presents a generalised model for solving the optimal allocation of water resources in schemes where the objectives are minimising the demand deficits, complying with the required flows in the river and storing water in reservoirs. Evaporation from reservoirs and returns from demands are considered, and an iterative methodology is followed to solve these two non-network constraints. The model was applied to the Duero River basin (Spain). Three different network flow algorithms (Out-of-Kilter, RELAX-IV and NETFLO) were used to solve the allocation problem. Certain convergence issues were detected during the iterative process. There is a need to relate the data from the studied systems with the convergence criterion to be able to find the convergence criterion which yields the best results possible without requiring a long calculation time.

Multiobjective evolutionary algorithm for long-term planning of the national energy and transportation systems

The transportation and electric sectors are by far the largest producers of greenhouse emissions in the United States while they consume a significant amount of the national energy. The ever rising demand for these systems, the growing public concern on issues like global warming or national security, along with emerging technologies that promise great synergies between both (plug-in hybrid vehicles or electrified rail), creates the necessity for a new framework for long-term planning. This paper presents a comprehensive methodology to investigate long-term investment portfolios of these two infrastructures and their interdependencies. Its multiobjective nature, based on the NSGA-II evolutionary algorithm, assures the discovery of the Pareto front of solutions in terms of cost, sustainability and resiliency. The optimization is driven by a cost-minimization network flow program which is modified in order to explore the solution space. The modular design enables the use of metrics to evaluate sustainability and resiliency and better characterize the objectives that the systems must meet. An index is presented to robustly meet long-term emission reduction goals. An example of a high level representation of the continental United States through 2050 is presented and analyzed using the present methodology.

On generating maximal nondominated Benders cuts

In this paper, we explore certain algorithmic strategies for accelerating the con- vergence of Benders decomposition method via the generation of maximal nondominated cuts. Based on interpreting the seminal work of Magnanti and Wong (Operations Research, 29(3), 464-484, 1981) for generating nondominated cuts within a multiobjective frame- work, we propose an algorithmic strategy that utilizes a preemptively small perturbation of the right-hand-side of the Benders subproblem to generate maximal nondominated Benders cuts, as well as a complimentary strategy that generates an additional cut in each iteration via an alternative emphasis on decision variable weights. We also examine the computa- tional effectiveness of solving a secondary subproblem using an objective cut as proposed by Magnanti and Wong versus identifying the Pareto-optimality region for cut generation by utilizing complementary slackness conditions. In addition, we exhibit how a standard fea- sibility cut can be extracted from the solution of subproblems that generate only optimality cuts through the use of artificial variables. With Magnanti and Wong's baseline procedure approximated during implementation via the use of a core point estimation technique (Pa- padakos in Computers and Operations Research, 36(1), 176-195, 2009), these algorithmic strategies are tested on instances from the literature concerning the fixed charge network flow program.

Efficient Mining of Multiple Partial Near-Duplicate Alignments by Temporal Network

This paper considers the mining and localization of near-duplicate segments at arbitrary positions of partial near-duplicate videos in a corpus. Temporal network is proposed to model the visual-temporal consistency between video sequence by embedding temporal constraints as directed edges in the network. Partial alignment is then achieved through network flow programming. To handle multiple alignments, we consider two properties of network structure: conciseness and divisibility, to ensure that the mining is efficient and effective. Frame-level matching is further integrated in the temporal network for alignment verification. This results in an iterative alignment-verification procedure to fine tune the localization of near-duplicate segments. The scalability of frame-level matching is enhanced by exploring visual keyword matching algorithms. We demonstrate the proposed work for mining partial alignments from two months of broadcast videos and across six TV sources.

A min–max theorem for plane bipartite graphs

We consider a partitioning problem, defined for bipartite and 2-connected plane graphs, where each node should be covered exactly once by either an edge or by a cycle surrounding a face. The objective is to maximize the number of face boundaries in the partition. This problem arises in mathematical chemistry in the computation of the Clar number of hexagonal systems. In this paper we establish that a certain minimum weight covering problem of faces by cuts is a strong dual of the partitioning problem. Our proof relies on network flow and linear programming duality arguments, and settles a conjecture formulated by Hansen and Zheng in the context of hexagonal systems [P. Hansen, M. Zheng, Upper Bounds for the Clar Number of Benzenoid Hydrocarbons, Journal of the Chemical Society, Faraday Transactions 88 (1992) 1621–1625].

A Novel EP Approach for Multi-area Economic Dispatch with Multiple Fuel Options

This paper presents a novel approach to multi-area economic dispatch problems with multiple fuel options using a hybrid evolutionary programming method. The objective is to minimize the operation cost of the entire system while satisfying the tie line constraints. In this paper, EP-LMO (Evolutionary Programming with Levenberg-Marquardt Optimization) technique is proposed to solve multi-area economic dispatch problems with multiple fuel options. The EP-LMO is developed in such a way that a simple evolutionary programming (EP) is applied as a base level search to find the direction of the optimal global region. And Levenberg-Marquardt Optimization (LMO) method is used as a fine tuning to determine the optimal solution. The applicability and validity of the proposed approach on multi-area economic dispatch problems are presented in two parts. In Part I, two multi-area bench mark problems without fuel options are considered. In Part II, 10 unit system with both multi-area and multi-fuel options is considered. The proposed approach is compared with the results of Incremental Network Flow Programming, Spatial Dynamic Programming and Evolutionary Programming approaches. The results show that the EP-LMO gives the optimum generation cost than any other methods.

On Achieving Fairness in the Allocation of Scarce Resources: Measurable Principles and Multiple Objective Optimization Approaches

Equity principles are embedded within a multiple objective framework for obtaining optimal solutions to a generic allocation problem, such as the fair distribution of water, energy, or other types of key resources among users in society. Because of the great import of fresh water as a scarce and diminishing resource within and among many nations of the world, the equity concepts are used in the allocation of water rights and subsequent water transfers or trades among users to improve the economic efficiency of water utilization. More specifically, water allocation is formulated as a generalized multiple objective problem and then the measurable fairness principles are used in the development of two approaches for equitable water rights allocation. In particular, the proposed priority-based maximal multiperiod network flow programming method has a social aggregation function satisfying the monotonicity and priority principles, and thus is a priority equitable allocation approach. The lexicographic minimax water shortage ratios method, which satisfies the principles of monotonicity, impartiality, and equitability, generates perfectly equitable solutions. The priority ranks and weights used in the two proposed approaches, respectively, are designed to achieve fair treatment of all the competitors for access to limited water resources and constitute important parameters. The capabilities of the approaches are tested and demonstrated in applications to the Aral Sea Basin in Central Asia and the South Saskatchewan River Basin in Western Canada.

A procedure for distribution system planning of a large-scale agricultural project

Different mathematical techniques adapting linear, nonlinear, mixed-integer, and network flow programming have been developed over the past decades to solve the distribution planning optimization problem. The high dimensionality of the problem made it in some of practical cases unmanageable by such classical optimization techniques. This gave rise to the application of knowledge based, heuristics, artificial intelligence, and approximate iterative techniques to search for the optimal solution. The problem also was typically perceived from the distribution companies’ perspectives with the objective being to supply sustainable yet cost effective power to multi-objective multi-interest consumers with different damage functions and relatively uncertain data. This paper presents a value-based distribution system planning procedure for large-scale agricultural real life project. This type of distribution planning is characterized not only by high load demand but also with a huge distribution network covering the vast agricultural area. Yet it is a planning for single type of customers who has a consistent developing policy, interest, cost damage function, together with a realistic and less uncertain data. The planning is also perceived from the consumer perspective who may even question the connection to the power utility unless it is proved as cost effective way of power supply. Macro and micro-levels planning is suggested for both overall project and farm modules, respectively. The proposed planning procedure evaluates different feasible alternatives based on life cycle cost while reliability indices and cost of interruption are taken into consideration. The procedure is illustrated on the micro-level for a real life agricultural problem.