The problems of optimal distribution of transfers within given budget limitations are formulated and analyzed. The mathematical model is presented as a bilevel linear optimization problem that contains linear problems...
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The problems of optimal distribution of transfers within given budget limitations are formulated and analyzed. The mathematical model is presented as a bilevel linear optimization problem that contains linear problems of integer optimization at the lower level. Both optimistic and pessimistic versions of the problem are considered. Far the approximate solution of optimistic version, the algorithm of finding local solutions for parametric lower-level integer programming problems on the basis of the method of directing neighborhoods is proposed. The auxiliary integer progrannning problem with Boolean variables of a higher level is solved bused on local algorithms.
For a special cutting problem we show that it is possible to derive full information about the regions of stability of an optimal solution by a slight modification of a dynamic programming procedure used for solving t...
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For a special cutting problem we show that it is possible to derive full information about the regions of stability of an optimal solution by a slight modification of a dynamic programming procedure used for solving the unperturbed problem. A simple algorithm for computing the optimal value function of this two-parametric discrete optimization problem will also be given. This algorithm is based on the dynamic programming idea too.
A parametric computer numerical control (CNC) program was developed to make a test complex surface on a vertical milling machine equipped with an external fourth rotational axis. parametric programming was used in ord...
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A parametric computer numerical control (CNC) program was developed to make a test complex surface on a vertical milling machine equipped with an external fourth rotational axis. parametric programming was used in order to get higher flexibility of the manufacturing process. The ball-end milling process was simulated and verified in a virtual model of the machine tool developed with the module integrated simulation and verification of the product lifecycle management software of Siemens NX7((R)). After that, the real process was carried out on the shop floor to machine the test surface. This demonstrates that the virtual machine tools are an effective resource to simulate and verify the performance of machining processes controlled by CNC parametric programs. The possibility of accurately simulating the parametric CNC program reduces the risk of its implementation and enables a more frequent use of this efficient feature of contemporary CNC machine tools.
The transportation problem with fuzzy supply values of the deliverers and with fuzzy demand values of the receivers is analysed. For the solution of the problem the technique of parametric programming is used. This ma...
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The transportation problem with fuzzy supply values of the deliverers and with fuzzy demand values of the receivers is analysed. For the solution of the problem the technique of parametric programming is used. This makes it possible to obtain not only the maximizing solution (according to the Bellman-Zadeh criterion) but also other alternatives close to the optimal solution.
In a paper by K. Richter the stability regions of the dynamic lot size model with constant cost parameters are analyzed. In particular, an algorithm is suggested to compute the stability region of a so-called generali...
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In a paper by K. Richter the stability regions of the dynamic lot size model with constant cost parameters are analyzed. In particular, an algorithm is suggested to compute the stability region of a so-called generalized solution. In general this region is only a subregion of the stability region of the optimal solution. In this note we show that in a computational effort that is of the same order as the running time of Richter's algorithm, it is possible to partition the parameter space in stability regions such that every region corresponds to another optimal solution.
This paper establishes theorems about the simultaneous variation of right-hand sides and cost coefficients in a linear program from a strictly complementary solution. Some results are extensions of those that have bee...
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This paper establishes theorems about the simultaneous variation of right-hand sides and cost coefficients in a linear program from a strictly complementary solution. Some results are extensions of those that have been proven for varying the right-hand side of the primal or the dual, but not both;other results are new. In addition, changes in the optimal partition and what that means in economic terms are related to the basis-driven approach, notably to the theory of compatibility. In addition to new theorems about this relation, the transition graph is extended to provide another visualization of the underlying economics.
This paper deals with the facility location problem for a public sector distribution system. The system is characterized by two conflicting goals: the authority's aspiration of expenditure minimization and the pre...
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This paper deals with the facility location problem for a public sector distribution system. The system is characterized by two conflicting goals: the authority's aspiration of expenditure minimization and the preference at each demand site for maximizing the amount supplied. In order to obtain a location/transportation plan at which both conflicting goals are satisfactorily traded off for all the parties involved, the fuzzy set-theoretic method is applied to render a parametric analysis of the conventional facility location problem. For the uncapacitated case, an efficient heuristic based on Erlenkotter's dual-based method is presented, along with computational results showing its efficiency. However for the capacitated case, only a brief sketch of the heuristic is provided mainly due to its associated complexity.
Weak disposability between outputs and pollutants, defined as a simultaneous proportional reduction of both outputs and pollutants, assumes that pollutants are byproducts of the output generation process and that a fi...
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Weak disposability between outputs and pollutants, defined as a simultaneous proportional reduction of both outputs and pollutants, assumes that pollutants are byproducts of the output generation process and that a firm can "freely dispose" of both by scaling down production levels, leaving some inputs idle. Based on the production axioms of monotonicity, convexity and weak disposability, we formulate a convex non-parametric least squares (CNLS) quadratic optimization problem to estimate a frontier production function assuming either a deterministic disturbance term consisting only of inefficiency, or a composite disturbance term composed of both inefficiency and noise. The suggested methodology extends the stochastic semi-nonparametric envelopment of data (StoNED) described in Kuosmanen and Kortelainen (2011). Applying the method to estimate the shadow prices of SO2 and NOx generated by U.S. coal power plants, we conclude that the weak disposability StoNED method provides more consistent estimates of market prices. (C) 2012 Elsevier B.V. All rights reserved.
We study the inverse optimization problem in the following formulation: given a family of parametrized optimization problems and a real number called demand, determine for which values of parameters the optimal value ...
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We study the inverse optimization problem in the following formulation: given a family of parametrized optimization problems and a real number called demand, determine for which values of parameters the optimal value of the objective function equals to the demand. We formulate general questions and problems about the optimal parameter set and the optimal value function. Then we turn our attention to the case of linear programming, when parameters can be selected from given intervals ("inverse interval LP"). We prove that the problem is NP-hard not only in general, but even in a very special case. We inspect three special cases-the case when parameters appear in the right-hand sides, the case when parameters appear in the objective function, and the case when parameters appear in both the right-hand sides and the objective function. We design a technique based on parametric programming, which allows us to inspect the optimal parameter set. We illustrate the theory by examples.
We consider linear semi-infinite optimization problems and prove characterizations for strong unicity. One of these is a weak alternation property. This result suggests the introduction of the property of regular stro...
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We consider linear semi-infinite optimization problems and prove characterizations for strong unicity. One of these is a weak alternation property. This result suggests the introduction of the property of regular strong unicity, which is equivalent to a stronger alternation property. The theorems are used in order to prove a Haar-type theorem for linear optimization problems. An application to best Chebyshev approximation is given.
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