For the problemP(λ): Maximizec T z subject toz∈Z(λ), whereZ(λ) is defined by an in general infinite set of linear inequalities, it is shown that the value-function has directional derivatives at every point \(\ba...
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For the problemP(λ): Maximizec T z subject toz∈Z(λ), whereZ(λ) is defined by an in general infinite set of linear inequalities, it is shown that the value-function has directional derivatives at every point \(\bar \lambda \)such thatP( \(\bar \lambda \) ) and its dual are both superconsistent. To compute these directional derivatives a min-max-formula, well-known in convex programming, is derived. In addition, it is shown that derivatives can be obtained more easily by a limit-process using only convergent selections of solutions ofP(λ n ), λ n → \(\bar \lambda \)and their duals.
A mathematical analysis of the dynamic lot size model with constant cost parameters is provided. First, stability regions for so called generalized and optimal solutions are found, which show how the cost input may va...
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A mathematical analysis of the dynamic lot size model with constant cost parameters is provided. First, stability regions for so called generalized and optimal solutions are found, which show how the cost input may vary, leaving the solution valid. Based on these results a BASIC dialog program has been designed to display the optimal solution and the stability regions to the decision maker. Secondly, an estimation of the initial optimal solution is given for the case, when the cost inputs leave the stability region. [ABSTRACT FROM AUTHOR]
Discrimination, whether of the reverse of the usual kind, distorts the allocation of resources in favour of, respectively against, the group or individual concerned. Affirmative action and institutional distinction ex...
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Discrimination, whether of the reverse of the usual kind, distorts the allocation of resources in favour of, respectively against, the group or individual concerned. Affirmative action and institutional distinction extraneous to work performance are examples where more weight is attached to the agent's subsequent output than is warranted by its intrinsic merit. We introduce this extra weight as a discrimination factor and propose a method of measuring the allocative effect on resources. Inasmuch as the discrimination factor measures a bias in the agent's behavior setting the article is relevant to eco-behavioral research.
The possibility of successful applications of stochastic programming decision models has been limited by the assumed complete knowledge of the distribution F of the random parameters as well as by the limited scope of...
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In this paper we discuss how to deal with decision problems that are described with LP models and formulated with elements of imprecision and uncertainty. More precisely, we will study LP models in which the parameter...
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In this paper we discuss how to deal with decision problems that are described with LP models and formulated with elements of imprecision and uncertainty. More precisely, we will study LP models in which the parameters are not fully known but only with some degree of precision. Even with incomplete information the model builder (or model user) is normally able to give a realistic interval for the parameters of an LP model. For the constraint vector this is combined with some wishes or some leeway on the constraints. Even with ambiquity in the objective function, there is normally some preference ordering to be found among alternative ways of action. We will demonstrate that these modelling complications can be handled with the help of some results developed in the theory of fuzzy sets. After an overview of some central contributions to fuzzy linear programming, we will develop an LP model in which the parameters are not fully known, only with some degree of precision, and show that the model can be parametrised in such a way that the optimal solution becomes a function of the degree of precision. The fuzzy LP model derived in this way appears to be fairly easy to handle computationally, which is demonstrated with a numerical example.
We treat semi-infinite optimization problems: Minimizep(x) subject tox ∈ ? m , anda(t,x) ≦b(t) for allt ∈T, whereT is a σ-compact topological space, andp,a,b are suitable (?∞, ∞]-valued functions on R m , respec...
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We treat semi-infinite optimization problems: Minimizep(x) subject tox ∈ ? m , anda(t,x) ≦b(t) for allt ∈T, whereT is a σ-compact topological space, andp,a,b are suitable (?∞, ∞]-valued functions on R m , respectively. Linear, convex, and quasi-convex semi-infinite programming are included in this concept. The main results of this paper are on the necessity of the compactness of the set of feasible points for (a,b), and the set of ?-optimal solutions for (p,a,b) for the (Hausdorff) upper semicontinuity of the feasible set-mapping in (a,b), and the ?-optimal solution-mapping in (p,a,b), respectively (where the parameter sets are provided with a suitable topology). Some more special results complete the paper.
Regression quantiles are a robust alternative to the popular least squares regression and provide good descriptive statistics for the data. The problem of determining all regression quantiles associated with a data se...
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Often, the coefficients of a linear programming problem represent estimates of true values of data or are subject to systematic variations. In such cases, it is useful to perturb the original data and to either comput...
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Often, the coefficients of a linear programming problem represent estimates of true values of data or are subject to systematic variations. In such cases, it is useful to perturb the original data and to either compute, estimate, or otherwise describe the values of the functionf which gives the optimal value of the linear program for each perturbation. If the right-hand derivative off at a chosen point exists and is calculated, then the values off in a neighborhood of that point can be estimated. However, if the optimal solution set of either the primal problem or the dual problem is unbounded, then this derivative may not exist. In this note, we show that, frequently, even if the primal problem or the dual problem has an unbounded optimal solution set, the nature of the values off at points near a given point can be investigated. To illustrate the potential utility of our results, their application to two types of problems is also explained.
In this paper we study second-order differential properties of an optimal-value functionϕ(x). It is shown that under certain conditionsϕ(x) possesses second-order directional derivatives, which can be calculated by so...
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In this paper we study second-order differential properties of an optimal-value functionϕ(x). It is shown that under certain conditionsϕ(x) possesses second-order directional derivatives, which can be calculated by solving corresponding quadratic programs. Also upper and lower bounds on these derivatives are introduced under weaker assumptions. In particular we show that the second-order directional derivative is infinite if the corresponding quadratic program is unbounded. Finally sensitivity results are applied to investigate asymptotics of estimators in parametrized nonlinear programs.
In this paper the possibility of the identification of a complete fuzzy decision (not only the maximizing alternative) in fuzzy linear programming by use of the parametric programming technique is presented. Also, it ...
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In this paper the possibility of the identification of a complete fuzzy decision (not only the maximizing alternative) in fuzzy linear programming by use of the parametric programming technique is presented. Also, it is shown that this fact can be useful in the Zimmermann approach to multiple objective linear programming. The presented remarks are illustrated by some numerical examples.
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