In this paper, we consider the optimal meeting scheduling problem in a commercial building over a fixed period of time, with the objectives of minimizing the cost of energy consumption by the air-conditioning system a...
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In this paper, we consider the optimal meeting scheduling problem in a commercial building over a fixed period of time, with the objectives of minimizing the cost of energy consumption by the air-conditioning system and possibly achieving more balanced power distribution. By considering a set of realistic factors, including the eligible time slots of attendees and energy consumption characteristics of meeting rooms, this problem is formulated as a constrained mixed-integerlinear program, which then can be solved by an optimization solver, e.g., CPLEX. However, because the computation complexity increases dramatically with the problem size, a fast heuristic algorithm is proposed. The numerical simulations verify that the heuristic algorithm produces a near-optimal result.
The United States (US) military plans to acquire drop-in biofuels (renewable diesel and biojet fuel) to reduce carbon emissions and diversify military energy portfolio. To expedite this endeavor, the military provided...
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The United States (US) military plans to acquire drop-in biofuels (renewable diesel and biojet fuel) to reduce carbon emissions and diversify military energy portfolio. To expedite this endeavor, the military provided direct financial incentives to offset investment costs of selected drop-in biofuel demonstration facilities. It is not known if investment incentives alone will stimulate the creation of a full-scale advanced biofuel supply chain capable of meeting US military demands, given limited availability of low-cost sustainable biomass feedstocks in some areas and considering the uncertainty in global oil prices. The objective of this work is to determine 1) whether a state in the US can meet its share of military biofuel targets from local biomass resources, and 2) if direct financial incentives can expedite the development of the military biofuel supply chain, under two different oil price scenarios. The Biofuel supply chain GeoSpatial and Temporal Optimizer (BioGeSTO), was developed for that purpose and applied to the state of California, USA from 2020 to 2040. The BioGeSTO model determined that biomass resources in California can meet 12-19% of its annual military targets between 2020 and 2040 of renewable diesel and biojet fuel using the Fischer-Tropsch (FT) and Hydro-Treatment of Esters and Fatty Acids (HEFA) conversion technologies. However, under the reference oil price scenario, only HEFA conversion facilities introduced at 2027 in Kings County were found feasible. Under the high oil price scenario, both the HEFA and FT technologies were financially feasible and the supply chain production approaches the theoretical production limit by 2032. In both scenarios, providing investment incentives has a modest impact on expediting the supply chain, as facilities are introduced only 1-3 years earlier when receiving direct investment incentives. Sensitivity analysis shows that biomass availability has the greatest impact on the supply chain performance such th
Alarm identification refers to selecting a set of measurements to be configured to the alarm system. Contrary to prior literature which uses qualitative cause-effect based techniques, the present work incorporates qua...
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Alarm identification refers to selecting a set of measurements to be configured to the alarm system. Contrary to prior literature which uses qualitative cause-effect based techniques, the present work incorporates quantitative aspects such as the time taken by measurements for deviation, to make alarm identification more reliable. The present work proposes a systematic approach to alarm identification through an optimization formulation, as a mixed-integer linear programming (MILP) problem, for the time. The proposed formulation maximizes the time available for operators to respond to faults while keeping the number of alarms triggered at a minimum. Subsequently, a linear multi-objective optimization formulation reduces the number of optimal solutions taking into account additional criteria, such as order of priority of potential faults. The proposed formulation is applied to the Tennessee Eastman (TE) Challenge problem. A closed-loop simulator was used for fault propagation, to obtain quantitative information required to apply the formulation, and CPLEX solver in GAMS was used to solve this case study problem.
In designing energy supply systems, designers should consider the robustness in performance criteria against the uncertainty in energy demands. In this paper, a robust optimal design method of energy supply systems un...
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In designing energy supply systems, designers should consider the robustness in performance criteria against the uncertainty in energy demands. In this paper, a robust optimal design method of energy supply systems under uncertain energy demands is proposed using a mixed-integerlinear model so that it can consider discrete characteristics for selection and on/off status of operation and piecewise linear approximations for nonlinear performance characteristics of constituent equipment. First, a robust optimal design problem is formulated as a three-level min-max-min optimization one by expressing uncertain energy demands by intervals based on the interval programming, evaluating the robustness in a performance criterion based on the minimax regret criterion, and considering hierarchical relationships among design variables, uncertain energy demands, and operation variables. Then, a special solution method of the problem is proposed especially in consideration of the existence of integer operation variables. In a case study, the proposed method is applied to the robust optimal design of a cogeneration system with a simple configuration. Through the study, the validity and effectiveness of the method is ascertained, and some features of the obtained solutions are clarified. (C) 2018 Elsevier Ltd. All rights reserved.
A mixed-integer linear programming model is proposed to determine the optimal number, location and capacity of the warehouses required to support a long-term forecast with seasonal demand. Discrete transportation cost...
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A mixed-integer linear programming model is proposed to determine the optimal number, location and capacity of the warehouses required to support a long-term forecast with seasonal demand. Discrete transportation costs, dynamic warehouse contracting, and the handling of safety stock are the three main distinctive features of the problem. Four alternatives for addressing discrete transportation costs are compared. The most efficient formulation is obtained using integer variables to account for the number of units used of each transportation mode. Contracting policies constraints are derived to ensure use of warehouses for continuous periods. Similar constraints are included for the case when a warehouse is closed. Safety stock with risk-pooling effect is considered using a piecewise-linear representation. To solve large-scale problems, tightening constraints, and simplified formulations are proposed. These formulations are based on single-sourcing assumptions and yield near-optimal results with large reduction in the solution time. (c) 2017 Elsevier Ltd. All rights reserved.
Large-scale mixed-integer linear programming (MILP) problems, such as those from two-stage stochastic programming, usually have a decomposable structure that can be exploited to design efficient optimization methods. ...
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Large-scale mixed-integer linear programming (MILP) problems, such as those from two-stage stochastic programming, usually have a decomposable structure that can be exploited to design efficient optimization methods. Classical Benders decomposition can solve MILPs with weak linking constraints (which are decomposable when linking variables are fixed) but not strong linking constraints (which are not decomposable even when linking variables are fixed). In this paper, we first propose a new rigorous bilevel decomposition strategy for solving MILPs with strong and weak linking constraints, then extend a recently developed cross decomposition method based on this strategy. We also show how to apply the extended cross decomposition method to two-stage stochastic programming problems with conditional-value-at-risk (CVaR) constraints. In the case studies, we demonstrate the significant computational advantage of the proposed extended cross decomposition method as well as the benefit of including CVaR constraints in stochastic programming. (C) 2018 Elsevier Ltd. All rights reserved.
We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied...
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We consider the embedding of piecewise-linear deep neural networks (ReLU networks) as surrogate models in mixed-integer linear programming (MILP) problems. A MILP formulation of ReLU networks has recently been applied by many authors to probe for various model properties subject to input bounds. The formulation is obtained by programming each ReLU operator with a binary variable and applying the big-M method. The efficiency of the formulation hinges on the tightness of the bounds defined by the big-M values. When ReLU networks are embedded in a larger optimization problem, the presence of output bounds can be exploited in bound tightening. To this end, we devise and study several bound tightening procedures that consider both input and output bounds. Our numerical results show that bound tightening may reduce solution times considerably, and that small-sized ReLU networks are suitable as surrogate models in mixed-integerlinear programs. (C) 2019 Elsevier Ltd. All rights reserved.
Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, which are iteratively solved to produce useful information. One such approach is the Lagrangian relaxation (L...
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Solving very-large-scale optimization problems frequently require to decompose them in smaller subproblems, which are iteratively solved to produce useful information. One such approach is the Lagrangian relaxation (LR), a general technique that leads to many different decomposition schemes. The LR produces a lower bound of the objective function and useful information for heuristics aimed at constructing feasible primal solutions. In this paper, we compare the main LR strategies used so far for stochastic hydrothermal unit commitment problems, where uncertainty mainly concerns water availability in reservoirs and demand (weather conditions). The problem is customarily modeled as a two-stage mixed-integer optimization problem. We compare different decomposition strategies (unit and scenario schemes) in terms of quality of produced lower bound and running time. The schemes are assessed with various hydrothermal systems, considering different configuration of power plants, in terms of capacity and number of units.
This paper studies the cyclic jobshop hoist scheduling with multi-capacity reentrant tanks and time-window constraints. Parts of different types are processed in a series of tanks with bounded processing times. Multi ...
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This paper studies the cyclic jobshop hoist scheduling with multi-capacity reentrant tanks and time-window constraints. Parts of different types are processed in a series of tanks with bounded processing times. Multi capacity tanks are used to handle stages with long processing times. Tanks can be reentrant so that a part visits them more than once. A hoist is responsible for the transportation of parts between tanks. We consider the cyclic scheduling where multiple parts enter and leave the production line during a cycle. The difficulty to deal with the problem lies in how to effectively handle the constraints related to multi-capacity reentrant tanks and their relations with time windows. To this end, a mixed-integer linear programming model is developed by addressing the time-window constraints and tank capacity constraints in a novel way. Computational experiments are conducted to demonstrate the effectiveness of the proposed model.
Flexible ramping products (flexiramp), provided by entitled resources to meet net demand forecast error, are the underpinning for the accommodation of the substantial uncertainties associated with variable wind power....
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Flexible ramping products (flexiramp), provided by entitled resources to meet net demand forecast error, are the underpinning for the accommodation of the substantial uncertainties associated with variable wind power. This paper proposes an enhanced flexiramp modeling approach, cast in a hybrid stochastic/deterministic multi-timescale framework. The framework employs a chance-constrained day-ahead scheduling method, as well as deterministic scheduling on intra-hourly basis (real-time scheduling), to allow optimal procurement planning of the flexiramp products in both timescales. A stepwise and piecewise demand price curve is also proposed to calculate the flexiramp surplus procurement price. Non-generation resource (NGR), referring to energy storage, is implemented to provide extra flexibility. Additionally, cycling ramping cost (cycliramp), introduced to model operational and maintenance costs and reduce the wear and tear of generators, is also included as a penalty. Numerical tests are conducted on 6-bus and 118-bus systems. Results demonstrate the merits of the proposed scheduling model as well as the effects of flexiramp and cycliramp costs in the multi-timescale scheduling.
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