This paper presents new mixed integer programming formulations for scheduling of a flexible flow line with blocking. The flexible flow line consists of several processing stages in series, separated by finite intermed...
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This paper presents new mixed integer programming formulations for scheduling of a flexible flow line with blocking. The flexible flow line consists of several processing stages in series, separated by finite intermediate buffers, where each stage has one or more identical parallel machines. The line produces several different product types and each product must be processed by, at most, one machine in each stage. A product which has completed processing on a machine may remain there and block the machine until a downstream machine becomes available for processing. The objective is to determine a production schedule for all products so as to complete the products in a minimum time. The basic mixed integer programming formulations have been enhanced to model blocking scheduling with alternative processing routes where for each product a set of routes is available for processing. A reentrant flow line where a product visits a set of stages more than once is also considered. Numerical examples are presented to illustrate applications of the various models proposed. (C) 2000 Elsevier Science Ltd. All rights reserved.
In this paper we study the 0-1 maximum probability model that consists in maximizing the probability that a certain quantity c(T)x is greater than a prescribed constant t, where c and x are n vectors. c(1),..., c(n), ...
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In this paper we study the 0-1 maximum probability model that consists in maximizing the probability that a certain quantity c(T)x is greater than a prescribed constant t, where c and x are n vectors. c(1),..., c(n), are mutually independent and normally distributed random variables and x is a vector of n binary variables such that Ax less than or equal to b, where b is an m vector and A is an m x n matrix. It is known that this problem can be formulated as a nonlinear fractional program. We show how to solve it exactly using mixed integer programming. The advantage of the approach is that it requires only standard, commercially available software. The computational results which we present show that this technique makes it possible to treat instances with up to 100 random variables in a few seconds of CPU time. (C) 2003 Elsevier B.V. All rights reserved.
mixed integer programming models and computational strategies developed for treatment planning optimization in brachytherapy are described. The problem involves the designation of optimal placement of radioactive sour...
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mixed integer programming models and computational strategies developed for treatment planning optimization in brachytherapy are described. The problem involves the designation of optimal placement of radioactive sources (seeds) inside a tumor site. Two MIP models are described. The resulting MIP instances are difficult to solve, due in large part to dense constraint matrices with large disparities in the magnitudes of the nonzero entries. A matrix reduction and approximation scheme is presented as a computational strategy for dealing with the dense matrices. Penalty-based primal heuristic and branching strategies to assist in the solution process are also described. Numerical results are presented for 20 MIP instances associated with prostate cancer cases. Compared to currently used computer-aided planning methods, plans derived via the MIP approach use fewer seeds (20-30 fewer) and needles, and provide better coverage and conformity-measures commonly used to assess the quality of treatment plans. Good treatment plans are returned in 15 CPU minutes, suggesting that incorporation of this MIP-based optimization module into a real-time comprehensive treatment planning system is feasible.
Facility location optimization is very important for many retail industries, such as banking network, chain stores, and so on. Maximal covering location problem (MCLP) is one of the well-known models for these facilit...
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ISBN:
(纸本)9781424420124
Facility location optimization is very important for many retail industries, such as banking network, chain stores, and so on. Maximal covering location problem (MCLP) is one of the well-known models for these facility location optimization problems, which has earned extensive research interests. However, various practical requirements limit the application of the traditional formulation of MCLP, and the NP-hard characteristic makes effective approaches for large scale problems extremely difficult. This paper focuses on a facility location problem motivated by a practical project of bank branching. The traditional MCLP formulation is generalized as a mixed integer programming (MIP) with considerations of various costs and revenues, multi-type of facilities, and flexible coverage functions. A CPLEX-based hybrid nested partition algorithm is developed for large scale problems, and heuristic-based extensions are introduced to deal with extremely large problems. Our formulation and algorithm are embedded into an asset called IFAO-SIMO. Numerical results demonstrate the effectiveness and efficiency of our approach.
This study targets an examination proctor assignment problem where faculties and academic staffs are assigned to examinations as proctors in the regular examination period at our university. In previous work, the auth...
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This study targets an examination proctor assignment problem where faculties and academic staffs are assigned to examinations as proctors in the regular examination period at our university. In previous work, the author formulated fundamental mathematical model for the assignment task in a mixed integer programming form and developed a prototype system based on spreadsheet software to derive an optimal assignment. In this study, the proposed mathematical model is extended and revised to deal with the conditions in the assignment task. Some solutions are discussed to improve practicality for system users. (C) 2015 The Authors. Published by Elsevier B.V.
In this paper, we propose a mixed-integerprogramming model for an integrated flexible job shop and operators shift-based scheduling in a Flexible Manufacturing System (FMS). The objective is to schedule a given set o...
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In this paper, we propose a mixed-integerprogramming model for an integrated flexible job shop and operators shift-based scheduling in a Flexible Manufacturing System (FMS). The objective is to schedule a given set of jobs while taking operators schedule into account. Operators are qualified to operate a set of machines, and thus are only able to execute operations scheduled on these machines during their active shifts. An operation can be executed on a qualified machine in presence of a qualified operator. Furthermore, we tested the proposed MIP model on a set of generated instances to evaluate its performances. The MIP model provides optimal solutions for small scale instances. For larger instance the computational time and solutions gaps are still quite high. We are currently investigating how to reduce the computation time and improve the gaps for industrial size problems.
A graph is an interval graph if its vertex set corresponds to a family of intervals on the real line, called a model, such that two distinct vertices are adjacent in the graph if and only if their corresponding interv...
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A graph is an interval graph if its vertex set corresponds to a family of intervals on the real line, called a model, such that two distinct vertices are adjacent in the graph if and only if their corresponding intervals intersect each other. The minimum number of interval lengths that suffices to represent a model of a given interval graph is its interval count. The use of mathematical optimization techniques for solving interval count problems was first explored by Joos et al.[1]. In more detail, given a bipartition of vertices into classes of lengths, the authors propose an efficient linear programming based algorithm for solving the interval count two problem. However, so far, no mathematical formulation exists in the literature for general interval count. As a contribution in that direction, we introduce a mixed integer programming formulation for the exact value of interval count, parameterized by the largest interval length. Additionally, we also propose a quadratic formulation for a valid upper bound on interval count. Solution algorithms for these formulations were tested on interval count instances found in the literature. As an outcome of these experiments, the algorithm for the upper bound formulation was shown to run much faster than its exact solution counterpart. Furthermore, the upper bounds thus obtained were frequently certified as optimal by the exact algorithm. (C) 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0)
In this paper, a set of mixed integer programming (MIP) models to optimize the location of a set of resources when fighting fire is proposed. The MIP model integrates fire spread and the decisions relative to the reso...
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ISBN:
(纸本)9783319951652;9783319951645
In this paper, a set of mixed integer programming (MIP) models to optimize the location of a set of resources when fighting fire is proposed. The MIP model integrates fire spread and the decisions relative to the resources location. Four problems are considered: protecting specific areas, minimizing the total burned area, and two problems of fire containment (depending on the definition of fire containment: no new ignitions in a given time interval or resources located in all the fire perimeter). A small example is used to illustrate the solutions to these problems. A transformation of the optimization problem of determining fire arrival times in a feasibility problem, based on linear programming duality, is also proposed. This transformation is used in all the MIP models, assuring the correctness of the fire arrival times in all the areas of the landscape.
A mixedinteger approach for the least cost design of structural masonry walls with high eccentricities is developed. The integer variables in the approach are used to select the optimum values from a range of discret...
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In this paper, a rescheduling problem involving annealing welding in a quartz glass factory is studied. Two different mixed integer programming (MIP) formulations for the problem are presented first, and the NP-hardne...
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ISBN:
(纸本)9781467397148
In this paper, a rescheduling problem involving annealing welding in a quartz glass factory is studied. Two different mixed integer programming (MIP) formulations for the problem are presented first, and the NP-hardness of this rescheduling problem is analyzed. Then the computational performance of two different MIP is analysised. Further, based on the comparison results, we discuss which MIP formulation might work better for the problem and propose the future work.
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