probabilistic inequality
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Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1757
Author(s):  
Amrit Das ◽  
Gyu M. Lee

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.



2018 ◽  
Vol 8 (11) ◽  
pp. 2153 ◽  
Author(s):  
Shih-Cheng Horng ◽  
Shieh-Shing Lin

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.



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


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

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.



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

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.



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


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