We address the problem of scheduling a flowshop plant with uncertain processing times described by discrete probability distributions. The objective is to find a sequence of batches that minimizes the expected makespa...
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We address the problem of scheduling a flowshop plant with uncertain processing times described by discrete probability distributions. The objective is to find a sequence of batches that minimizes the expected makespan. To circumvent the problem of combinatorially explosive state spaces, we propose a novel and rigorous branch and bound algorithm that provides the optimal solution and is based on the result that a lower bound to the expected makespan can be obtained by evaluating over an aggregated probability model. Numerical results for a number of example problems show that the solution times for the proposed method are several orders of magnitude smaller than those for a multiperiod model. In addition, an important extension of this method is proposed for the case of continuous probability distributions of certain forms, using discretization schemes that give excellent approximations. (C) 2002 Elsevier Science Ltd. All rights reserved.
Very Large and/or computationally complex optimization problems sometimes require parallel or high-performance computing for achieving a reasonable time for computation. One of the most popular and most complicate pro...
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ISBN:
(纸本)9759845857
Very Large and/or computationally complex optimization problems sometimes require parallel or high-performance computing for achieving a reasonable time for computation. One of the most popular and most complicate problems of this family is "Traveling Salesman Problem". In this paper we have introduced a branch & bound based algorithm for the solution of such complicated problems. The main focus of the algorithm is to solve the "symmetric traveling salesman problem". We reviewed some of already available algorithms and felt that there is need of new algorithm which should give optimal solution or near to the optimal solution. On the basis of the use of logarithmic sampling, it was found that the proposed algorithm produced a relatively optimal solution for the problem and results excellent performance as compared with the traditional algorithms of this series.
Yard cranes are the most popular container handling equipment for loading containers onto or unloading containers from trucks in container yards of land scarce port container terminals. However, such equipment is bulk...
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Yard cranes are the most popular container handling equipment for loading containers onto or unloading containers from trucks in container yards of land scarce port container terminals. However, such equipment is bulky, and very often generates bottlenecks in the container flow in a terminal because of their slow operations. Hence, it is essential to develop good yard crane work schedules to ensure a high terminal throughput. This paper studies the problem of scheduling a yard crane to perform a given set of loading/unloading jobs with different ready times. The objective is to minimize the sum of job waiting times. A branch and bound algorithm is proposed to solve the scheduling problem optimally. Efficient and effective algorithms are proposed to find lower bounds and upper bounds. The performance of the proposed branch and bound algorithm is evaluated by a set of test problems generated based on real life data. The results show that the algorithm can find the optimal sequence for most problems of realistic sizes. (C) 2004 Elsevier Inc. All rights reserved.
This paper considers the constrained redundancy optimization problem in series systems. This problem can be formulated as a nonlinear integer programming problem of maximizing the overall systems reliability under lim...
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This paper considers the constrained redundancy optimization problem in series systems. This problem can be formulated as a nonlinear integer programming problem of maximizing the overall systems reliability under limited resource constraints. By exploiting special features of the problem, we derive a new necessary condition for optimal redundancy assignments. This condition leads to a new fathoming condition in the branch and bound method that may result in a significant reduction of computational efforts, as evidenced in our numerical calculation for linearly constrained redundancy optimization problems.
The intent of this Note is to show that the piecewise linear control allocation problem can be solved fast enough to be implemented in a digital flight-control system. The approach taken here differs from the authors&...
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The intent of this Note is to show that the piecewise linear control allocation problem can be solved fast enough to be implemented in a digital flight-control system. The approach taken here differs from the authors' initial paper on this subject in two ways. The first difference is a move away from the mixed-integer linear programming form of the optimization problem and to a linear programming formulation. The linear programming problem will be solved using a modified simplex algorithm where a rule-based approach is employed to enforce the necessary adjacency constraints on the interpolating coefficients. The second difference is that we solve a mixed optimization problem2 as opposed to the solution of the multibranch control allocation problem.' This allows us to achieve the same objective as before, but only having to solve one optimization problem instead of two. We will compare the performance of the simplex method with restricted basis entry rules to the mixed-integer formulation and show that the two approaches give equivalent solutions to the same set of control allocation problems. To perform this comparison, we will look at both closed-loop and open-loop control allocation problems. In the latter case, a set of control allocation problems are randomly selected and solved by each approach. For the former, we compare the algorithms in a digital simulation of a reentry vehicle on approach and landing.
The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long-short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on ...
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The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long-short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on the variables. We will show that this algorithm can solve a problem of practical size and that the long-short strategy leads to a portfolio with significantly better risk-return structure compared with standard purchase only portfolio both in terms of ex-ante and ex-post performance.
Lagrangian bounds, i.e. bounds computed by Lagrangian relaxation, have been used successfully in branch and boundbound methods for solving certain classes of nonconvex optimization problems by reducing the duality ga...
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Lagrangian bounds, i.e. bounds computed by Lagrangian relaxation, have been used successfully in branch and boundbound methods for solving certain classes of nonconvex optimization problems by reducing the duality gap. We discuss this method for the class of partly linear and partly convex optimization problems and, incidentally, point out incorrect results in the recent literature on this subject.
This paper considers a new class of scheduling problems arising in logistics systems in which two different transportation modes are available at the stage of product delivery. The mode with the shorter transportation...
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This paper considers a new class of scheduling problems arising in logistics systems in which two different transportation modes are available at the stage of product delivery. The mode with the shorter transportation time charges a higher cost. Each job ordered by the customer is first processed in the manufacturing facility and then transported to the customer. There is a due date for each job to arrive to the customer. Our approach integrates the machine scheduling problem in the manufacturing stage with the transportation mode selection problem in the delivery stage to achieve the global maximum benefit. In addition to studying the NP-hard special case in which no tardy job is allowed, we consider in detail the problem when minimizing the sum of the total transportation cost and the total weighted tardiness cost is the objective. We provide a branch and bound algorithm with two different lower bounds. The effectiveness of the two lower bounds is discussed and compared. We also provide a mathematical model that is solvable by CPLEX. Computational results show that our branch and bound algorithm is more efficient than CPLEX. (C) 2005 Wiley Periodicals, Inc.
Generalizations of the branch and bound method and of the Piyavskii method for solution of stochastic global optimization problems are considered. These methods employ the concept of a tangent minorant of an objective...
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Generalizations of the branch and bound method and of the Piyavskii method for solution of stochastic global optimization problems are considered. These methods employ the concept of a tangent minorant of an objective function as a source of global information about the function. Calculus of tangent minorants is developed.
This paper is concerned with a portfolio optimization problem under concave and piecewise constant transaction cost. We formulate the problem as nonconcave maximization problem under linear constraints using absolute ...
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This paper is concerned with a portfolio optimization problem under concave and piecewise constant transaction cost. We formulate the problem as nonconcave maximization problem under linear constraints using absolute deviation as a measure of risk and solve it by a branch and bound algorithm developed in the field of global optimization. Also, we compare it with a more standard 0-1 integer programming approach. We will show that a branch and bound method elaborating the special structure of the problem can solve the problem much faster than the state-of-the integer programming code.
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