The geometric programming technique is widely recognized as an effective optimization tool for solving nonlinear optimization problems in modern times. While the conventional geometric programming problem assumes precise coefficients for each term in the objective and constraint functions, real-world scenarios often involve uncertain coefficients. To address this issue, we propose a chance-constrained geometric programming problem within an uncertain-based framework, accounting for the uncertainty in these coefficients. Specifically, we employ the Laplace uncertainty distribution to characterize this uncertainty. Our primary focus in this study is the development of a method that can establish an equivalent crisp geometric programming problem corresponding to the uncertain geometric programming problem. To validate our proposed method, we present a numerical example. Furthermore, we demonstrate the efficiency and efficacy of our approach through its application in an inventory model.

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Solving Geometric Programming Problems with Laplace Uncertainty Distribution

  • Tapas Mondal,
  • Akshay Kumar Ojha,
  • Sabyasachi Pani

摘要

The geometric programming technique is widely recognized as an effective optimization tool for solving nonlinear optimization problems in modern times. While the conventional geometric programming problem assumes precise coefficients for each term in the objective and constraint functions, real-world scenarios often involve uncertain coefficients. To address this issue, we propose a chance-constrained geometric programming problem within an uncertain-based framework, accounting for the uncertainty in these coefficients. Specifically, we employ the Laplace uncertainty distribution to characterize this uncertainty. Our primary focus in this study is the development of a method that can establish an equivalent crisp geometric programming problem corresponding to the uncertain geometric programming problem. To validate our proposed method, we present a numerical example. Furthermore, we demonstrate the efficiency and efficacy of our approach through its application in an inventory model.