The objective of the proposed article is to minimize the transportation costs of foods and medicines from different source points to different hospitals by applying stochastic mathematical programming model to a trans...
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The objective of the proposed article is to minimize the transportation costs of foods and medicines from different source points to different hospitals by applying stochastic mathematical programming model to a transportation problem in a multi-choice environment containing the parameters in all constraints which follow the Logistic distribution and cost coefficients of objective function are also multiplicative terms of binary variables. Using the stochastic programming approach, the stochastic constraints are converted into an equivalent deterministic one. A transformation technique is introduced to manipulate cost coefficients of objective function involving multi-choice or goals for binary variables with auxiliary constraints. The auxiliary constraints depends upon the consecutive terms of multi-choice type cost coefficient of aspiration levels. A numerical example is presented to illustrate the whole idea.
A bi-level approach is presented for the optimal design of batch and steady-state recycling (SSR) chromatography. On the first level, an efficient formulation as mixed-integer problem (MIP) is applied to obtain optima...
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A bi-level approach is presented for the optimal design of batch and steady-state recycling (SSR) chromatography. On the first level, an efficient formulation as mixed-integer problem (MIP) is applied to obtain optimal fractionation times for chromatograms simulated by the equilibrium model. On the second level, the optima are evaluated against a parametrized objective function. The combination of model and optimization method provides a computationally very efficient tool. A comprehensive example study demonstrates that batch chromatography achieves the highest productivities at the cost of limited yields, which is optimal only for vanishing feed costs. In other instances, the more flexible SSR concept provides larger profits. The results reveal also new optimal operating policies for SSR processes with segmented product fractions and waste streams. (C) 2019 Published by Elsevier Ltd.
Cardinality constraints enforce an upper bound on the number of variables that can be nonzero. This article investigates linear programs with cardinality constraints that mutually overlap, i.e., share variables. We pr...
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Cardinality constraints enforce an upper bound on the number of variables that can be nonzero. This article investigates linear programs with cardinality constraints that mutually overlap, i.e., share variables. We present the components of a branch-and-cut solution approach, including new branching rules that exploit the structure of the corresponding conflict hypergraph. We also investigate valid or facet defining cutting planes for the convex hull of the feasible solution set. Our approach can be seen as a continuous analogue of independence system polytopes. We study three different classes of cutting planes: hyperclique bound cuts, implied bound cuts, and flow cover cuts. In a computational study, we examine the effectiveness of an implementation based on the presented concepts. (C) 2019 Elsevier B.V. All rights reserved.
As renewable technology advances and decreases in cost, microgrids are becoming an appealing means of distributed generation both for isolated communities and integrated with existing electrical grid systems. Due to t...
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As renewable technology advances and decreases in cost, microgrids are becoming an appealing means of distributed generation both for isolated communities and integrated with existing electrical grid systems. Due to their small size, however, microgrids may have financial limitations which preclude them from using commercial software to optimize control of their assets. Open-source optimization solvers are a viable alternative, but increase computation time. This work expands on a rolling horizon optimization framework for economic dispatch within an existing residential microgrid located in Hoover, Alabama. The microgrid has an open-source solver requirement and a need for quick solution time on a rolling horizon as opposed to a day-ahead commitment. We present a method of reducing integer variables by relaxation which completes two goals: reduction in computation time for real-time operations, and reduction in daily operational cost for the microgrid. Seasonal data for load and photovoltaic (PV) power was also collected from the microgrid to facilitate simulation testing. Computation time was successfully reduced using multiple variations of the relaxation method, while obtaining solution quality with operational cost similar to or better than the original model.
Procurement for forest companies with pulp and paper mills aims to ensure that a sufficient volume of wood supply enters the production process. Numerous suppliers and contract types are available;however, their selec...
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Procurement for forest companies with pulp and paper mills aims to ensure that a sufficient volume of wood supply enters the production process. Numerous suppliers and contract types are available;however, their selection is a complex decision for procurement managers. In addition, managers typically dedicate a portion of their wood fiber demand to each group of suppliers, which is referred to as a portfolio strategy. Despite the available literature in contract selection, the consideration of contract types and their characteristics have not been addressed for the complex procurement process. In this study, a mixed-integer optimization model is proposed to best select contracts for pulp and paper procurement. The challenge was to plan deliveries in each time period to satisfy the demand of raw material at the mills. The potential of this model is demonstrated with a case study based on characteristics from a forest company in Quebec, Canada. A comparison between traditional fixed and flexible contracts is presented. Different portfolio strategies are also evaluated for groups of suppliers to investigate potential improvements.
We model and solve an order acceptance and scheduling problem in an identical parallel machine setting. The goal is to maximize profit by making four decisions: (i) accept or reject an order, (ii) assign accepted orde...
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We model and solve an order acceptance and scheduling problem in an identical parallel machine setting. The goal is to maximize profit by making four decisions: (i) accept or reject an order, (ii) assign accepted orders to identical parallel machines, (iii) sequence accepted orders, and (iv) schedule order starting times. First, we develop a mixed-integer model that simultaneously optimizes the above four decisions. We enhance the model with pre-processing techniques, valid inequalities, and dominance rules. Second, we show that the model has a special structure that allows us to develop both classical and combinatorial Benders decomposition. We thus develop a classical Benders decomposition approach and two combinatorial Benders variants: (i) logic-based Benders decomposition and (ii) Branch-Relax-and-Check (BRC). The BRC, as the primary contribution of this paper, extends the literature in three ways: (1) it incorporates novel sequencing sub-problem relaxations that expedite convergence, (2) it employs a novel cutting-plane partitioning procedure that allows these sub-problem relaxations to be separately optimized outside the master problem, and (3) it uses temporary Benders cuts that communicate sub-problem relaxation solutions to the master problem. Third, we demonstrate that the BRC outperforms significantly other methods and finds integer feasible solutions for 100% of instances, guarantees optimality in 50% of instances, and achieves an average optimality gap of 3.20% within our time limit. (C) 2019 Elsevier B.V. All rights reserved.
Many engineering and scientific applications, e.g. resource allocation, control of hybrid systems, scheduling, etc., require the solution of mixed-integer non-linear problems (MINLPs). Problems of such class combine t...
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Many engineering and scientific applications, e.g. resource allocation, control of hybrid systems, scheduling, etc., require the solution of mixed-integer non-linear problems (MINLPs). Problems of such class combine the high computational burden arising from considering discrete variables with the complexity of non-linear functions. As a consequence, the development of algorithms able to efficiently solve medium-large MINLPs is still an interesting field of research. In the last decades, several approaches to tackle MINLPs have been developed. Some of such approaches, usually defined as exact methods, aim at finding a globally optimal solution for a given MINLP at expense of a long execution time, while others, generally defined as heuristics, aim at discovering suboptimal feasible solutions in the shortest time possible. Among the various proposed paradigms, outer approximation (OA) and feasibility pump (FP), respectively as exact method and as heuristic, deserve a special mention for the number of relevant publications and successful implementations related to them. In this paper we present a new exact method for convex mixed-integer non-linear programming called proximal outer approximation (POA). POA blends the fundamental ideas behind FP into the general OA scheme that attepts to yield faster and more robust convergence with respect to OA while retaining the good performances in terms of fast generation of feasible solutions of FP.
One of the main challenges in applying optimization-based scheduling techniques in process industries stems from the different process characteristics and constraints that need to be taken into account when generating...
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One of the main challenges in applying optimization-based scheduling techniques in process industries stems from the different process characteristics and constraints that need to be taken into account when generating a schedule. For instance, consideration of sequence-dependent changeovers may easily make the resulting optimization model computationally expensive. Accordingly, building upon the recently pro-posed Discrete-Continuous Algorithm (Lee and Maravelias, 2018), we propose generalized algorithm that enables accurate and fast solution of difficult instances while efficiently handling a wide range of process characteristics. The algorithm combines modeling versatility with computational tractability while guar-anteeing the feasibility and accuracy of the final solution. Through a case study inspired by a real-world brewing process, we show that our algorithm provides accurate and high quality solutions to industrial-scale instances in reasonable time. (C) 2020 Elsevier Ltd. All rights reserved.
While passenger-only ferries can be an effective instrument in mitigating road congestion in urban areas, they are among the most polluting modes of transportation. This paper studies technical and economic feasibilit...
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While passenger-only ferries can be an effective instrument in mitigating road congestion in urban areas, they are among the most polluting modes of transportation. This paper studies technical and economic feasibilities of a battery-powered high-speed ferry service in Oslo, Norway. An urban ferry planner problem that minimizes ferry operator and passenger costs and external costs of road transport subject to strategic (fleet selection and infrastructure location), tactical (service frequency) and operational (vessel speed) decisions is proposed. While the results show that zero emission technologies can pass the cost-benefit test for a short-range service, competitiveness hinges on energy costs and capacities and on the performance of the existing service. Counterfactual scenarios show substantial cost reductions from altering the current ferry route. Anticipated increase in external costs of road transport from closing the ferry service is also much smaller than the system costs of maintaining the urban ferry connection.
Some extreme weather events, such as the hurricane, pass through an area sequentially and thus are called sequential extreme weather events (SEWEs). This paper proposes a data-based robust optimization (RO) model to e...
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Some extreme weather events, such as the hurricane, pass through an area sequentially and thus are called sequential extreme weather events (SEWEs). This paper proposes a data-based robust optimization (RO) model to enhance the resilience of the integrated electricity and gas system (IEGS) against SEWEs. Specifically, the SEWE strikes the IEGS sequentially. After each attack, the system state is adjusted immediately to minimize the maximized expected system cost caused by the SEWE. The attack-defense procedures are repeated alternatively during the SEWE. Preventive measures, hardening, are made in advance to reduce the impact of sequential attacks. The entire process is formulated as a multi-period RO model. It is proved that the most effective resilience enhancement strategies for this model are the same as those for a two-stage RO model, which can be solved by the nested column-and-constraint generation (C&CG) algorithm. In addition, the property of SEWEs, sequentially endangering limited regions of the IEGS, is incorporated to build a data-based uncertainty set and reduce its conservativeness. Simulation results on two IEGSs validate the effectiveness of the proposed model.
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