Service providers usually offer different pricing schemes to consumers, which can simultaneously influence consumers' tariff choices and their usage of the service and thus greatly affect the profits of the servic...
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Service providers usually offer different pricing schemes to consumers, which can simultaneously influence consumers' tariff choices and their usage of the service and thus greatly affect the profits of the service providers or the utilization of the service system. However, little is known about the optimal design and management of three-part tariff pricing schemes because the models are generally not analytically tractable since the arbitrary population of heterogeneous consumers can yield an extremely complex profit function with multiple local optima. This study investigates how to design three-part tariffs, which are pricing plans that are widely used in transportation or telecommunications industries, by formulating a mixed-integer nonlinear programming optimization model. In particular, numerical analyses using GAMS/BARON and metaheuristic approaches including genetic algorithm, particle swarm optimization algorithm, and sine cosine algorithm were conducted to derive the optimal three-part tariffs under specific conditions and to compare several common tariff structures (e.g., the menus of the three-part tariff, single three-part tariff, two-part tariff, and flat rate). This study successfully identified key factors affecting the performance of the different pricing structures. Guidelines for determining the best timing of the use of different pricing structures were also derived.
Chemical process data is usually not directly valorized in pure machine learning predictive models due to limited data availability. This limitation often caused from high sensor costs, data variety, and veracity issu...
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Planning and scheduling are crucial components of enterprise-wide optimization (EWO). For the successful execution of EWO, it is vital to view the enterprise operations as a holistic decision-making problem, composed ...
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Planning and scheduling are crucial components of enterprise-wide optimization (EWO). For the successful execution of EWO, it is vital to view the enterprise operations as a holistic decision-making problem, composed of different interconnected elements or layers, to make the most efficient use of resources in process industries. Among different layers of the operating decisions, planning and scheduling are often treated sequentially, leading to impractical solutions. To tackle this problem, integrated approaches, such as bi-level programming are utilized to optimize these two layers simultaneously. Nonetheless, the bi-level optimization of such interdependent and holistic formulations is still difficult, particularly when dealing with mixed-integer nonlinear programming (MINLP) problems, due to a lack of effective algorithms. In this study, we employ the Data-driven Optimization of bi-level mixed-integernonlinear problems (DOMINO) framework, a data- driven algorithm developed to handle single-leader single-follower bi-level mixed-integer problems, to solve single-leader multi-follower planning and scheduling problems subject to MINLP scheduling formulations. We apply DOMINO to the continuous production of multi-product methyl methacrylate polymerization process formulated as a Traveling Salesman Problem and demonstrate its capability in achieving near-optimal guaranteed feasible solutions. Building on this foundation, we extend this strategy to solve a high-dimensional and highly constrained nonlinear crude oil refinery operation problem that has not been previously tackled in this context. Our study further evaluates the efficacy of using local, NOMAD (nonlinear Optimization by Mesh Adaptive Direct Search), and a global data-driven optimizer, ARGONAUT (AlgoRithms for Global Optimization of coNstrAined grey-box compUTational), within the DOMINO framework and characterize their performance both in terms of solution quality and computational expense. The results ind
Increasing online retail has resulted in increased automation in order picking systems, leading to new challenges and opportunities in task scheduling. The job-shop scheduling problem is an optimization problem essent...
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Increasing online retail has resulted in increased automation in order picking systems, leading to new challenges and opportunities in task scheduling. The job-shop scheduling problem is an optimization problem essential in such systems, but existing JSP literature often overlooks workplace fatigue, which harms employees' well-being and costs U.S. employers up to 127 billion annually. In this work, we propose fatigue consideration in the job-shop scheduling problem in a cobotic order picking system to mitigate its negative effects. We present a new bi-objective mixedintegernonlinearprogramming problem formulation that considers worker fatigue and productivity during schedule optimisation. To put the results of simulated optimisation in perspective, we experimentally validate the fatigue model and scheduling results in a real operation. The mathematical model finds solutions that conventional single-objective optimisation cannot, allowing fractional fatigue distribution improvements more than 4x larger than the decrease in productivity they require in 53% of the considered virtual cases. The experiments show that our predictive fatigue model has an average RMSE of 2.20 kcal/min in estimating energy expenditure rates compared to heart rate measurements. It also shows a low correlation, meaning it is unfit for application. On the other hand, fatigue-conscious schedules show no clear benefit regarding measured and perceived fatigue. However, the scheduling model could also use heart rate measurements that do not show these inaccuracies. Our study highlights the need to further develop and validate the mathematical formulation and fatigue model and extend to other human factors and indirect fatigue effects. (C) 2024 The Authors. Published by Elsevier B.V.
Microgrids have become valuable assets because they improve the reliability of consumers while integrating renewables via distributed energy resources (DERs). Thus, making them cost-efficient is essential to secure th...
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Microgrids have become valuable assets because they improve the reliability of consumers while integrating renewables via distributed energy resources (DERs). Thus, making them cost-efficient is essential to secure their proliferation. This paper proposes a new method for the optimal design of microgrids. The proposed two-stage method optimizes the size and the location of the DERs, i.e., the renewable energy sources (RESs), distributed generation (DG) units, and battery energy storage systems (BESSs). Furthermore, the overall operation of the microgrid is optimized using a stochastic scenario-based approach, considering grid-connected and unintentional islanded modes. The proposed method also considers internal network reinforcements. Thus, the first stage is an energy-based approach, formulated as a mixed-integer linear programming (MILP) problem, and it is used to size the DERs, whereas the second stage uses an optimal AC power flow (AC-OPF) to formulate a mixed-integer nonlinear programming (MINLP) model that allocates the DERs and selects the best conductor for each circuit. The multi-objective nature of the problem is addressed via Pareto optimization to analyze the trade-off between operational and capital costs. The MINLP model is linearized through piece-wise approximations and solved using commercial solvers. Furthermore, the impact of battery degradation is analyzed through a simple adaptation of the Stage 1 model. Results were obtained with data from the real university campus microgrid CampusGrid, located at the State University of Campinas (UNICAMP), in São Paulo, Brazil.
The solution to the capacitated vehicle routing problem (CVRP) is vital for optimizing logistics. However, the transformation of real-world logistics problems into the CVRP involves diverse constraints, interactions b...
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The solution to the capacitated vehicle routing problem (CVRP) is vital for optimizing logistics. However, the transformation of real-world logistics problems into the CVRP involves diverse constraints, interactions between various routes, and a balance between optimization performance and computation load. In this study, we propose a systematic model originating from the part logistic routing problem (PLRP), which is a two-dimensional loading capacitated pickup-and-delivery problem that considers time windows, multiple uses of vehicles, queuing, transit, and heterogeneous vehicles. The newly introduced queuing and transit complicate the problem, and to the best of our knowledge, it cannot be solved using existing methods or the standard commercial optimizer. Hence, this problem has caused the existing research to develop, generalize, and extend into the two-dimensional CVRP (2L-CVRP). To solve this problem, we provide a framework that decouples the combination of 2L-CVRP and global optimization engineering and derives an efficient and realistic solver that integrates diverse types of intelligent algorithms. These algorithms include: (1) a heuristic algorithm for initializing feasible solutions by imitating manual planning, (2) asynchronous simulated annealing (SA) and Tabu search (TS) algorithms to accelerate the optimization of global routes based on novel bundling mechanics, (3) dynamic programming for routing, (4) heuristic algorithms for packing, (5) simulators to review associated time-related constraints, and (6) truck-saving processes to promote the optimal solution and reduce the number of trucks. Moreover, the performances of the SA and TS solver algorithms are compared in terms of various size scales of data to obtain an empirical recommendation for selection. The proposed model successfully established an intelligent management system that can provide systematic solutions for logistics planning, resulting in higher performance and lower costs compared to
This paper addresses the problem of coordinating the operation of electricity and natural gas (NG) transmission systems with green hydrogen (H2) production and injection into existing NG networks. In particular, the o...
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This paper addresses the problem of coordinating the operation of electricity and natural gas (NG) transmission systems with green hydrogen (H2) production and injection into existing NG networks. In particular, the operation of the two systems consists of a two-stage optimization framework that solves a network-constrained unit commitment (UC) problem with transmission power losses to obtain the profiles of gas energy demands from gas-powered generators and the maximum allowable H2 injection flow rates from power-to-gas (PtG), which are then used as inputs to an optimal transient NG-H2 flow problem with H2 concentration tracking. The nonlinearities introduced by the discretization of the H2 concentration tracking equations are particularly challenging to solve using second-order nonlinearprogramming (NLP) methods. Moreover, the nonlinear constraints capturing transmission line losses make the electricity operational problem intractable if solved with mixed-integer NLP methods. Therefore, this work leverages the reliability and scalability of linear programming (LP) by designing two novel and distinct sequential LP (SLP) methods that exploit the particular structures of the two problems to find feasible, possibly optimal solutions, using only first-order information. The algorithmic framework is demonstrated on the IEEE 24-bus RTS connected to the 22-node Belgian gas network. This paper is the first to demonstrate H2 concentration tracking under transient gas flow in a multi-energy optimization framework on a realistic gas transmission network with multiple H2 injection locations.
In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The...
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In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an iterative MILP-based method and the second is an iterative LP-based method with an elaborate procedure for ensuring an integral solution. The convergence of the two approaches is founded on two key features. The first is a penalty term with a single, automatically tuned, parameter for controlling the step size of the gas network iterates. The second is a sequence of supporting hyperplanes and halfspaces for controlling the convergence of the electricity network iterates. Moreover, the two proposed algorithms use as a warm start the solution from a novel polyhedral relaxation of the MOEGF problem, for a noticeable improvement in computation time as compared to a cold start. Unlike the first method, which invokes a branch-and-bound algorithm to find an integral solution, the second method implements an elaborate steering procedure that guides the continuous variables to take integral values at the solution. Numerical evaluation demonstrates that the two proposed methods can converge to high-quality feasible solutions in computation times at least two orders of magnitude faster than both a state-of-the-art nonlinear branch-and-bound (NLBB) MINLP solver and a mixed-integer convex programming (MICP) relaxation of the MOEGF problem. The experimental setup consists of five test cases, three of which involve the real electricity and gas transmission networks of the state of Victoria with actual linepack and demand profiles.
This paper concentrates on the formulation of a large-scale nonconvex mixed-integer nonlinear programming model and the application of robust optimization for the multi-period operational planning of realworld integra...
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This paper concentrates on the formulation of a large-scale nonconvex mixed-integer nonlinear programming model and the application of robust optimization for the multi-period operational planning of realworld integrated refinery-petrochemical site in China under uncertain product demands and crude oil price. To avoid excessive conservativeness resulting from classical static robust optimization, an adjustable robust counterpart incorporating resource decisions via an affinely adjustable linear decision rule is first derived. On the basis of a proposed polyhedral dynamic uncertainty set that mimics the dynamic behavior of the product demand over time, an adjustable robust counterpart with a dynamic uncertainty set is further formulated. Classical static robust optimization, adjustable robust optimization, and adjustable robust optimization with dynamic uncertainty sets are systematically compared for case studies. The results clearly illustrate the advantages of the affinely adjustable robust optimization with a dynamic uncertainty set over the classic robust optimization in decision making.
Urban public transportation agencies sometimes have to operate mixing vehicles of different sizes on their routes, due to resource limitations or historical reasons. Services with different passenger-carrying capaciti...
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Urban public transportation agencies sometimes have to operate mixing vehicles of different sizes on their routes, due to resource limitations or historical reasons. Services with different passenger-carrying capacities are provided to passengers during a mixed-fleet operation. A fundamental question arising here is how to optimally deploy a given fleet of different bus sizes to provide services that minimize passenger waiting time. We formulate a mixed-fleet vehicle dispatching problem as a mixed-integer nonlinear programming (MINLP) model to optimize dispatching schemes (dispatching orders and times) when a given set of buses of different sizes are available to serve demand along a route. The objective is to minimize the average passenger waiting time under time-dependent demand volumes. Stochastic travel times between stops and vehicle capacity constraints (i.e., introducing extra waiting time due to denied boarding) are explicitly modeled. A Simulated Annealing (SA) algorithm coupled with a Monte Carlo simulation framework is developed to solve large real-world instances in the presence of stochastic travel times. Results show that, in addition to dispatching headway, bus dispatching sequence can strongly affect waiting times under a mixed-fleet operation. Indeed, with an optimal dispatching sequence, a more accurate adjustment of supply to demand is possible in accordance with time-dependent demand conditions, and the total savings in waiting time are mainly driven by a further reduction in the number of passengers left behind. The optimality of uneven dispatching headways stems from two elements: having a mixed fleet and having localized peaks on demand that make buses run full. (c) 2021 Elsevier B.V. All rights reserved.
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