The order selection process for firms operating in markets characterized by standard products as well as strong product customization, is directly tied to the customer and to the associated production costs. This orde...
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The order selection process for firms operating in markets characterized by standard products as well as strong product customization, is directly tied to the customer and to the associated production costs. This order selection process must be inter-functional with marketing and manufacturing in deciding which orders to accept, specially since the selection criteria used by marketing and manufacturing tend to differ. This paper develops a methodology/mathematical programming model for improving this coordination through an optimal selection of sales orders, such that die total financial contribution of selected orders is maximized. Based on an actual case study in the pigment manufacturing industry, the methodology provides for a user interface that addresses both the manufacturing and marketing department. More importantly, such a marketing/production coordination allows for improved performance in increasingly segmented (customized) markets, while continuing standard product lines as well.
In spite of the remarkable improvements in the quality of general purpose mixed-integer programming software, the effective solution of a variety of lot-sizing problems depends crucially on the development of tight fo...
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In spite of the remarkable improvements in the quality of general purpose mixed-integer programming software, the effective solution of a variety of lot-sizing problems depends crucially on the development of tight formulations for the special problem features occurring in practice. After reviewing some of the basic preprocessing techniques for handling safety stocks and multilevel problems, we discuss a variety of aspects arising particularly in small and large bucket (time period) models such as start-ups, changeovers, minimum batch sizes, choice of one or two set-ups per period, etc. A set of applications is described that contains one or more of these special features, and some indicative computational results are presented. Finally, to show another technique that is useful, a slightly different (supply chain) application is presented, for which the a priori addition of some simple mixed-integer inequalities, based on aggregation, leads to important improvements in the results.
We present a nontrivial family of facet-defining inequalities for the uncapacitated p-median polytope. We incorporate the inequalities in a branch-and-cut scheme, and we report computational results that demonstrate t...
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We present a nontrivial family of facet-defining inequalities for the uncapacitated p-median polytope. We incorporate the inequalities in a branch-and-cut scheme, and we report computational results that demonstrate their effectiveness. (C) 2001 Elsevier Science B.V. All rights reserved.
We study an integrated logistics model for locating production and distribution facilities in a multi-echelon environment. Designing such logistics systems requires two essential decisions, one strategic (e.g., where ...
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We study an integrated logistics model for locating production and distribution facilities in a multi-echelon environment. Designing such logistics systems requires two essential decisions, one strategic (e.g., where to locate plants and warehouses) and the other operational (distribution strategy from plants to customer outlets through warehouses). The distribution strategy is influenced by the product mix at each plant, the shipments of raw material from vendors to manufacturing plants and the distribution of finished products from the plants to the different customer zones through a set of warehouses. First we provide a mixedintegerprogramming formulation to the integrated model. Then, we present an efficient heuristic solution procedure that utilizes the solution generated from a Lagrangian relaxation of the problem. We use this heuristic procedure to evaluate the performance of the model with respect to solution quality and algorithm performance. Results of extensive tests on the solution procedure indicate that the solution method is both efficient and effective. Finally a 'real-world' example is solved to explore the implications of the model. (C) 2001 Elsevier Science B.V. All rights reserved.
The paper discusses a framework for modeling, analyzing and controlling systems whose behavior is governed by interdependent physical laws, logic rules, and operating constraints, denoted as mixed Logical Dynamical (M...
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The paper discusses a framework for modeling, analyzing and controlling systems whose behavior is governed by interdependent physical laws, logic rules, and operating constraints, denoted as mixed Logical Dynamical (MLD) systems. They are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD models are equivalent to various other system descriptions like Piece Wise Affine (PWA) systems and Linear Complementarity (LC) systems. They have the advantage, however, that all problems of system analysis (like controllability, observability, stability and verification) and all problems of synthesis (like controller design and filter design) can be readily expressed as mixedinteger linear or quadratic programs, for which many commercial software packages exist. In this paper we first recall how to derive MLD models and then illustrate their use in predictive control. Subsequently we define “verification” and show how verification algorithms can be used to solve a variety of practical problems like checking the correctness of an emergency shutdown procedure implemented on a PLC, or assessing the performance of a constrained MPC controller. The eventual practical success of these methods will depend on progress in the development of the various optimization packages so that problems of realistic size can be tackled.
We develop a technique for refining the unit commitment solution obtained from solving the Lagrangian. Our model is an integer program with nonlinear constraints. It can be solved to optimality using branch-and-bound....
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We develop a technique for refining the unit commitment solution obtained from solving the Lagrangian. Our model is an integer program with nonlinear constraints. It can be solved to optimality using branch-and-bound. Numerical results indicate a significant improvement in the quality of the solution obtained.
This paper discusses a simple procedure to derive network inequalities for capacitated fixed charge network problems. Properties of the fractional extreme points of the LP relaxation are used to construct a class of i...
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This paper discusses a simple procedure to derive network inequalities for capacitated fixed charge network problems. Properties of the fractional extreme points of the LP relaxation are used to construct a class of inequalities and to construct a computational heuristic procedure for generating violated cutting planes. Computational results confirm the usefulness of the procedure. (C) 2000 Elsevier Science B.V. All rights reserved.
The three-dimensional orthogonal packing problem consists of filling a big rectangular box with as many small rectangular boxes as possible. In a recent paper G. Fasano (Alenia Aerospazio, Turin) has given a mixed-int...
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The three-dimensional orthogonal packing problem consists of filling a big rectangular box with as many small rectangular boxes as possible. In a recent paper G. Fasano (Alenia Aerospazio, Turin) has given a mixed-integer programming formulation of this problem. Here we extend Fasano's formulation and subject it to polyhedral analysis. The result is a more general formulation whose linear programming relaxation is a tighter approximation of the convex hull of the mixed-integer solutions to the problem than the original model.
作者：
Padberg, MNYU
Operat Management Dept New York NY 10003 USA
We discuss two models from the literature that have been developed to formulate piecewise linear approximations of separable nonlinear functions by way of mixed-integer programs. We show that the most commonly propose...
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We discuss two models from the literature that have been developed to formulate piecewise linear approximations of separable nonlinear functions by way of mixed-integer programs. We show that the most commonly proposed method is computationally inferior to a lesser known technique by comparing analytically the linear programming relaxations of the two formulations. A third way of formulating the problem, that shares the advantages of the better of the two known methods, is also proposed. (C) 2000 Elsevier Science B.V. All rights reserved.
In this paper, we present a unified decommitment method to solve the unit commitment problem. This method starts with a solution having all available units online at all hours in the planning horizon and determines an...
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In this paper, we present a unified decommitment method to solve the unit commitment problem. This method starts with a solution having all available units online at all hours in the planning horizon and determines an optimal strategy for decommitting units one at a time. We show that the proposed method may be viewed as an approximate implementation of the Lagrangian relaxation approach and that the number of iterations is bounded by the number of units. Numerical tests suggest that the proposed method is a reliable, efficient, and robust approach for solving the unit commitment problem.
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