The development of optimization models for planning and scheduling is one of the most useful tools for improving productivity of a large number of manufacturing companies. This paper presents a mixed-integer programmi...
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The development of optimization models for planning and scheduling is one of the most useful tools for improving productivity of a large number of manufacturing companies. This paper presents a mixed-integer programming model for scheduling steelmaking-continuous casting production. We first review the recent works in continuous casting planning. We focus on a model inspired from an application of steelmaking-continuous casting by Arcelor Group in Liege, Belgium. The process scheduling is characterized by several constraints: job grouping, technological interdependence, no dead time inside the same group of jobs and dynamic processing time of jobs. We present a formulation with mixed-integer linear programming which can be solved using standard software packages. Finally, we treat a few examples to illustrate this application and we conclude this paper with some comments and directions for future extensions. (c) 2004 Elsevier B.V. All rights reserved.
This technical note concerns the predictive control of discrete-time linear models subject to state, input and avoidance polyhedral constraints. Owing to the presence of avoidance constraints, the optimization associa...
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This technical note concerns the predictive control of discrete-time linear models subject to state, input and avoidance polyhedral constraints. Owing to the presence of avoidance constraints, the optimization associated with the predictive control law is non-convex, even though the constraints themselves are convex. The inclusion of the avoidance constraints in the predictive control law is achieved by the use of a modified version of a mixed-integer programming approach previously derived in the literature. The proposed modification consists of adding constraints to ensure that linear segments of the system trajectories between consecutive sampling times do not cross existing obstacles. This avoids the significant extra computation that would be incurred if the sampling time was reduced to prevent these crossings. Simulation results show that the inclusion of these additional constraints successfully prevents obstacle collisions that would otherwise occur. Copyright (C) 2008 John Wiley & Sons, Ltd.
At Kawasaki Steel Mizushima Works, a new energy control system has been established in order to deal with energy and utilities in the steelworks. The system consists of the works' central computer, online computer...
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At Kawasaki Steel Mizushima Works, a new energy control system has been established in order to deal with energy and utilities in the steelworks. The system consists of the works' central computer, online computer, process computer and digital instrumentation system. The software system is divided into the planning system, execution system and evaluation system. As the representative topic of the execution system, an optimal gas supply amount for the joint electric power plant is determined. An optimal guidance for the gas supply amount is given to operators by solving a mixed-integer program by a decomposition method in process computer online realtime. This new energy control system has brought a satisfactory energy saving effect.
This paper addresses a scheduling problem with a continuously divisible, cumulative and renewable resource with limited capacity. During its processing, each task consumes a part of this resource, which lies between a...
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This paper addresses a scheduling problem with a continuously divisible, cumulative and renewable resource with limited capacity. During its processing, each task consumes a part of this resource, which lies between a minimum and a maximum requirement. A task is finished when a certain amount of energy is received by it within its time window. This energy is received via the resource and an amount of resource is converted into an amount of energy with a non-decreasing and continuous function. The goal is to find a feasible schedule, which is already NP-complete, and then to minimize the resource consumption. For the case where all functions are linear, we present two new mixed-integer linear programs (MILP), as well as improvements of an existing formulation. We also present a detailed version of the adaptation of the well-known "left-shift/right-shift" satisfiability test for the cumulative constraint and the associated time-window adjustments to our problem. For this test, three ways of computing relevant intervals are described. Finally, a hybrid branch-and-bound using both the satisfiability test and the MILP is presented with a new heuristic for choosing the variable on which the branching is done. Computational experiments on randomly generated instances are reported in order to compare all of these solution methods.
In classical regression analysis, the ordinary least-squares estimation is the best strategy when the essential assumptions such as normality and independency to the error terms as well as ignorable multicollinearity ...
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In classical regression analysis, the ordinary least-squares estimation is the best strategy when the essential assumptions such as normality and independency to the error terms as well as ignorable multicollinearity in the covariates are met. However, if one of these assumptions is violated, then the results may be misleading. Especially, outliers violate the assumption of normally distributed residuals in the least-squares regression. In this situation, robust estimators are widely used because of their lack of sensitivity to outlying data points. Multicollinearity is another common problem in multiple regression models with inappropriate effects on the least-squares estimators. So, it is of great importance to use the estimation methods provided to tackle the mentioned problems. As known, robust regressions are among the popular methods for analyzing the data that are contaminated with outliers. In this guideline, here we suggest two mixed-integer nonlinear optimization models which their solutions can be considered as appropriate estimators when the outliers and multicollinearity simultaneously appear in the data set. Capable to be effectively solved by metaheuristic algorithms, the models are designed based on penalization schemes with the ability of down-weighting or ignoring unusual data and multicollinearity effects. We establish that our models are computationally advantageous in the perspective of the flop count. We also deal with a robust ridge methodology. Finally, three real data sets are analyzed to examine performance of the proposed methods.
The future of power systems known as smart grids is expected to involve an increasing level of intelligence and incorporation of new information and communication technologies in every aspect of the power grid. Demand...
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The future of power systems known as smart grids is expected to involve an increasing level of intelligence and incorporation of new information and communication technologies in every aspect of the power grid. Demand response resources and gridable vehicle are two interesting programs which can be utilized in the smart grid environment. Demand response resources can be used as a demand side virtual power plant (resource) to enhance the security and reliability of utility and have the potential to offer substantial benefits in the form of improved economic efficiency in wholesale electricity markets. An economic model of incentive responsive loads is modelled based on price elasticity of demand and customers' benefit function. On the other hand, a gridable vehicle can be used as a small portable power plant to improve the reliability as well as security of the power system. This paper formulates a mixed-integer programming approach to solve the unit commitment problem with demand response resources and gridable vehicles. The objective function of the unit commitment problem has been modified to incorporate demand response resources and gridable vehicles. The proposed method is conducted on the conventional 10-unit test system to illustrate the impacts of smart grid environment on the unit commitment problem. Moreover the benefits of implementing demand response resources and gridable vehicle in electricity markets are demonstrated.
Background: In treatment planning for intensity-modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. mixed-integer programming (MIP) ha...
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Background: In treatment planning for intensity-modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. mixed-integer programming (MIP) has been applied in radiation therapy to generate treatment plans. However, MIP has not been used effectively for IMPT treatment planning with dose-volume constraints. In this study, we incorporated dose-volume constraints in an MIP model to generate treatment plans for IMPT. Methods: We created a new MIP model for IMPT with dose volume constraints. Two groups of IMPT treatment plans were generated for each of three patients by using MIP models for a total of six plans: one plan was derived with the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method while the other plan was derived with our MIP model with dose-volume constraints. We then compared these two plans by dose-volume histogram (DVH) indices to evaluate the performance of the new MIP model with dose-volume constraints. In addition, we developed a model to more efficiently find the best balance between tumor coverage and normal tissue protection. Results: The MIP model with dose-volume constraints generates IMPT treatment plans with comparable target dose coverage, target dose homogeneity, and the maximum dose to organs at risk (OARs) compared to treatment plans from the conventional quadratic programming method without any tedious trial-and-error process. Some notable reduction in the mean doses of OARs is observed. Conclusions: The treatment plans from our MIP model with dose-volume constraints can meetall dose-volume constraints for OARs and targets without any tedious trial-and-error process. This model has the potential to automatically generate IMPT plans with consistent plan quality among different treatment planners and across institutions and better protection for important parallel OARs in an effective way.
This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutti...
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This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.
This paper presents a hybrid refinery scheduling system combining mathematical programming model and expert system. mixed-integer linear programming models for crude oil movement between units are merged into the expe...
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This paper presents a hybrid refinery scheduling system combining mathematical programming model and expert system. mixed-integer linear programming models for crude oil movement between units are merged into the expert system that is for qualitative issues concerning crude vessel unloading operations. The target problem ranging from the crude unloading to the crude charging to distillation towers is decomposed into several module problems for efficiency. Compared with existing scheduling approaches for oil movement, the proposed hybrid refinery scheduling system is very effective in dealing with timing decisions involving vessel unloading operations due to the advantages of an expert system. Since the proposed scheduling system can generate solutions so fast, it is expected to play a key role in the real processes.
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