To optimize revenue, service firms must integrate within their pricing policies the rational reaction of customers to their price schedules. In the airline or telecommunication industry, this process is all the more c...
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To optimize revenue, service firms must integrate within their pricing policies the rational reaction of customers to their price schedules. In the airline or telecommunication industry, this process is all the more complex due to interactions resulting from the structure of the supply network. In this paper, we consider a streamlined version of this situation where a firm's decision variables involve both prices and investments. We model this situation as a joint design and pricing problem that we formulate as a mixed-integer bilevel program, and whose properties are investigated. In particular, we take advantage of a feature of the model that allows the development of an algorithmic framework based on Lagrangean relaxation. This approach is entirely novel, and numerical results show that it is capable of solving problems of significant sizes.
In this article, the author recalls his involvement in the early development of linear programming. The theme of this study is: 'Being in the right place at the right time.' The right place was the Department ...
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In this article, the author recalls his involvement in the early development of linear programming. The theme of this study is: 'Being in the right place at the right time.' The right place was the Department of Mathematics at Princeton University; the right time was the spring of 1948 and the period following. After finishing his military service in the United States Army in the Second World War in 1946, he had three years of financial support from the GI Bill of Rights, which allowed him to finish his undergraduate degree at Caltech in 1947 and gave him two years of graduate study at Princeton University. First, the model of nonlinearprogramming was flexible enough to encompass a large class of real-life problems that had not been adequately treated by the techniques then available. In societal terms, after the successes of operations research in the Second World War, a number of major industries were willing to try out this new model. By contrast, today the personal computer can solve practical problems of ever-increasing size; using large computers, there has been a radical explosion of size and speed.
The efficient point algorithm proposed by J. F. Bard for the computation of the solution of the Linear Two-Stage Optimization Problem does not always converge to the desired solution. A counterexample is provided and ...
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The efficient point algorithm proposed by J. F. Bard for the computation of the solution of the Linear Two-Stage Optimization Problem does not always converge to the desired solution. A counterexample is provided and the reasons for this lack of convergence are discussed.
The branch and bound principle has long been established as an effective computational tool for solving mixed integer linear programming problems. This paper investigates the computational feasibility of branch and bo...
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The branch and bound principle has long been established as an effective computational tool for solving mixed integer linear programming problems. This paper investigates the computational feasibility of branch and bound methods in solving convex nonlinear integer programming problems. The efficiency of a branch and bound method often depends on the rules used for selecting the branching variables and branching nodes. Among others, the concepts of pseudo-costs and estimations are implemented in selecting these parameters. Since the efficiency of the algorithm also depends on how fast an upper bound on the objective minimum is attained, heuristic rules are developed to locate an integer feasible solution to provide an upper bound. The different criteria for selecting branching variables, branching nodes, and heuristics form a total of 27 branch and bound strategies. These strategies are computationally tested and the empirical results are presented.
Successive Linear programming (SLP) has been used extensively in the refining and petrochemical industries for over 20 years. This paper concentrates on some recent work at Exxon to unify the treatment of nonlinear te...
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Successive Linear programming (SLP) has been used extensively in the refining and petrochemical industries for over 20 years. This paper concentrates on some recent work at Exxon to unify the treatment of nonlinear terms in “mostly linear” models. We first discuss the source of nonlinearities in refining and petrochemical problems and propose a multiplicative formulation for the linearized subproblems to be solved by SLP. We then describe a SLP algorithm which is shown to be related to the concept of trust regions. Finally, we present an example formulation and computational results for a series of large industrial applications.
A flexible manufacturing system (FMS) is an integrated, computer-controlled complex of automated material handling devices and numerically controlled machine tools that can simultaneously process medium-sized volumes ...
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A flexible manufacturing system (FMS) is an integrated, computer-controlled complex of automated material handling devices and numerically controlled machine tools that can simultaneously process medium-sized volumes of a variety of part types. FMSs are becoming an attractive substitute for the conventional means of batch manufacturing, especially in the metal-cutting industry. This new production technology has been designed to attain the efficiency of well-balanced, machine-paced transfer lines, while utilizing the flexibility that job shops have to simultaneously machine multiple part types. Some properties and constraints of these systems are similar to those of flow and job shops, while others are different. This technology creates the need to develop new and appropriate planning and control procedures that take advantage of the system's capabilities for higher production rates.
Successive Linear programming (SLP), which is also known as the Method of Approximation programming, solves nonlinear optimization problems via a sequence of linear programs. This paper reports on promising computatio...
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Successive Linear programming (SLP), which is also known as the Method of Approximation programming, solves nonlinear optimization problems via a sequence of linear programs. This paper reports on promising computational results with SLP that contrast with the poor performance indicated by previously published comparative tests. The paper provides a detailed description of an efficient, reliable SLP algorithm along with a convergence theorem for linearly constrained problems and extensive computational results. It also discusses several alternative strategies for implementing SLP. The computational results show that SLP compares favorably with the Generalized Reduced Gradient Code GRG2 and with MINOS/GRG. It appears that SLP will be most successful when applied to large problems with low degrees of freedom.
Planning the allocation of scarce resources to competing activities over multiple time periods is one of the most important problems facing decision makers in modern organizations. Much of the previous research in thi...
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Planning the allocation of scarce resources to competing activities over multiple time periods is one of the most important problems facing decision makers in modern organizations. Much of the previous research in this area has concentrated on the use of linear programming procedures and has assumed that the technology through which scarce resource inputs are transformed into competing activity outputs is fixed. A more realistic assumption in many situations is that certain technology coefficients are likely to vary over the planning horizon as a function of activity levels in previous periods.
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