scholarly journals An Improvement for Fuzzy Stochastic Goal Programming Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Shu-Cheng Lin ◽  
Han-Wen Tuan ◽  
Peterson Julian
Keyword(s):  
Linear Programming ◽  
Goal Programming ◽  
Random Environment ◽  
Solution Process ◽  
Lower Side ◽  
Stochastic Goal Programming ◽  
Linear Programming Problems ◽  
Standard Linear ◽  
Standard Linear Programming

We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.

Shakedown as a Guide to the Design of Pressure Vessels

1969 ◽  
Vol 91 (3) ◽  
pp. 799-806 ◽  
Author(s):  
F. A. Leckie ◽  
R. K. Penny
Keyword(s):  
Linear Programming ◽  
Lower Bound ◽  
Pressure Vessel ◽  
Pressure Vessels ◽  
Design Decisions ◽  
Programming Techniques ◽  
Standard Linear ◽  
Standard Linear Programming

Using the theorems of plasticity lower bound estimates of shakedown loadings have been calculated for a number of shell-like structures commonly found in the pressure vessel industry. These have been determined by making use of elastic solutions, already available, in conjunction with standard linear programming techniques. Combinations of loadings and temperatures have been considered with a view to illustrating how calculations of these types can help in making design decisions.

A Geometric Algorithm for Hybrid Workpiece Localization/Envelopment Problem

1998 ◽  
Author(s):  
Y. X. Chu ◽  
J. B. Gou ◽  
Z. X. Li
Keyword(s):  
Linear Programming ◽  
Localization Problem ◽  
Euclidean Group ◽  
Geometric Algorithm ◽  
Hybrid Localization ◽  
Programming Techniques ◽  
Standard Linear ◽  
Workpiece Localization ◽  
Present Simulation ◽  
Standard Linear Programming

Abstract The problem of aligning the CAD model of a workpiece such that all points measured on the finished surfaces of the workpiece match closely to corresponding surfaces on the model while all unmachined surfaces lie outside the model to guarantee the presence of material to be machined at a later time is referred to as the hybrid localization/envelopment problem. The hybrid problem has important applications in setting up for machining of partially finished workpieces. This paper gives a formulation of the hybrid localization/envelopment problem and present a geometric algorithm for computing its solutions. First, we show that when the finished surfaces of a workpiece are inadequate to fully constrain the rigid motions of the workpiece, then the set of free motions remaining must form a subgroup G0 of the Euclidean group SE(3). This allows us to decompose the hybrid problem into a (symmetric) localization problem on the homogeneous space SE(3)/G0 and an envelopment problem on G0. While the symmetric localization problem is solved using the Fast Symmetric Localization (FSL) algorithm developed in one of our early papers, the envelopment problem is solved by computing the solutions of a sequence of linear programming (LP) problems. We derive explicitly the LP problems and apply standard linear programming techniques to solve the LP problems. We present simulation results to demonstrate efficiency of our method for the hybrid problem.

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