A Probabilistic Inequality (F. W. Steutel)

SIAM Review ◽  
1975 ◽  
Vol 17 (4) ◽  
pp. 693-694
Author(s):  
Daniel Kleitman
Keyword(s):  
Probabilistic Inequality

scholarly journals Bonferroni-type inequalities

1987 ◽  
Vol 19 (02) ◽  
pp. 508-511 ◽  
Author(s):  
Elaine Recsei ◽  
E. Seneta
Keyword(s):  
Probabilistic Inequality

We derive the Sobel–Uppuluri and Galambos-type extensions of the Bonferroni bounds, and further extensions of the same nature, as consequences of a single non-probabilistic inequality. The methodology follows that of Galambos.

A Probabilistic Inequality

SIAM Review ◽  
1978 ◽  
Vol 20 (4) ◽  
pp. 855-855
Author(s):  
L. A. Shepp ◽  
A. M. Odlyzko
Keyword(s):  
Probabilistic Inequality

scholarly journals A Probabilistic Inequality Related to Negative Definite Functions

2013 ◽  
pp. 73-80 ◽  
Author(s):  
Mikhail Lifshits ◽  
René L. Schilling ◽  
Ilya Tyurin
Keyword(s):  
Probabilistic Inequality

A Probabilistic Inequality (L. A. Shepp and A. M. Odlyzko)

SIAM Review ◽  
1979 ◽  
Vol 21 (4) ◽  
pp. 564-565
Author(s):  
D. McLeish
Keyword(s):  
Probabilistic Inequality

scholarly journals Bonferroni-type inequalities

1987 ◽  
Vol 19 (2) ◽  
pp. 508-511 ◽  
Author(s):  
Elaine Recsei ◽  
E. Seneta
Keyword(s):  
Probabilistic Inequality

We derive the Sobel–Uppuluri and Galambos-type extensions of the Bonferroni bounds, and further extensions of the same nature, as consequences of a single non-probabilistic inequality. The methodology follows that of Galambos.

scholarly journals Embedding Ordinal Optimization into Tree–Seed Algorithm for Solving the Probabilistic Constrained Simulation Optimization Problems

2018 ◽  
Vol 8 (11) ◽  
pp. 2153 ◽  
Author(s):  
Shih-Cheng Horng ◽  
Shieh-Shing Lin
Keyword(s):  
Optimization Problems ◽  
Simulation Optimization ◽  
Inequality Constraint ◽  
Search Space ◽  
Ordinal Optimization ◽  
Np Hard ◽  
Heuristic Approaches ◽  
Probabilistic Inequality ◽  
Hard Problems ◽  
Np Hard Problems

Probabilistic constrained simulation optimization problems (PCSOP) are concerned with allocating limited resources to achieve a stochastic objective function subject to a probabilistic inequality constraint. The PCSOP are NP-hard problems whose goal is to find optimal solutions using simulation in a large search space. An efficient “Ordinal Optimization (OO)” theory has been utilized to solve NP-hard problems for determining an outstanding solution in a reasonable amount of time. OO theory to solve NP-hard problems is an effective method, but the probabilistic inequality constraint will greatly decrease the effectiveness and efficiency. In this work, a method that embeds ordinal optimization (OO) into tree–seed algorithm (TSA) (OOTSA) is firstly proposed for solving the PCSOP. The OOTSA method consists of three modules: surrogate model, exploration and exploitation. Then, the proposed OOTSA approach is applied to minimize the expected lead time of semi-finished products in a pull-type production system, which is formulated as a PCSOP that comprises a well-defined search space. Test results obtained by the OOTSA are compared with the results obtained by three heuristic approaches. Simulation results demonstrate that the OOTSA method yields an outstanding solution of much higher computing efficiency with much higher quality than three heuristic approaches.

scholarly journals A Multi-Objective Stochastic Solid Transportation Problem with the Supply, Demand, and Conveyance Capacity Following the Weibull Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1757
Author(s):  
Amrit Das ◽  
Gyu M. Lee
Keyword(s):  
Weibull Distribution ◽  
Transportation Problem ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Approach ◽  
Chance Constrained Programming ◽  
Solid Transportation Problem ◽  
Multi Objective ◽  
Probabilistic Inequality

This study addresses a multi-objective stochastic solid transportation problem (MOSSTP) with uncertainties in supply, demand, and conveyance capacity, following the Weibull distribution. This study aims to minimize multiple transportation costs in a solid transportation problem (STP) under probabilistic inequality constraints. The MOSSTP is expressed as a chance-constrained programming problem, and the probabilistic constraints are incorporated to ensure that the supply, demand, and conveyance capacity are satisfied with specified probabilities. The global criterion method and fuzzy goal programming approach have been used to solve multi-objective optimization problems. Computational results demonstrate the effectiveness of the proposed models and methodology for the MOSSTP under uncertainty. A sensitivity analysis is conducted to understand the sensitivity of parameters in the proposed model.

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