/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Mathematical programming

(1962). Management Models and Industrial Applications of Linear Programming. Journal of the Operational Research Society: Vol. 13, No. 3, pp. 274-275.

https://link.springer.com/content/pdf/10.1057%2Fjors.1962.42.pdf

Management Models and Industrial Applications of Linear Programming

https://cyberleninka.org/article/n/662470.pdf

Literature review of deteriorating inventory models by key topics from 2012 to 2015

The emergence of fuzzy sets makes job-shop scheduling problem (JSSP) become better aligned with the reality. This article addresses the JSSP with fuzzy execution time and fuzzy completion time (FJSSP). We choose the classic differential evolution (DE) algorithm as the basic optimization framework. The advantage of the DE algorithm is that it uses a special evolutionary strategy of difference vector sets to carry out mutation operation. However, DE is not very effective in solving some instances of FJSSP. Therefore, we propose a novel selection mechanism augmenting the generic DE algorithm (NSODE) to achieve better optimization results. The proposed selection operator adopted in this article aims at a temporary retention of all children generated by the parent generation, and then selecting N better solutions as the new individuals from N parents and N children. Various examples of fuzzy shop scheduling problems are experimented with to test the performance of the improved DE algorithm. The NSODE algorithm is compared with a variety of existing algorithms such as ant colony optimization, particle swarm optimization, and cuckoo search. Experimental results show that the NSODE can obtain superior feasible solutions compared with solutions produced by several algorithms reported in the literature.

Solving Fuzzy Job-Shop Scheduling Problem Using DE Algorithm Improved by a Selection Mechanism

A deteriorating inventory model with imperfect product and variable demand is formulated in this paper. A time-dependent deterioration factor is considered because the rate of deterioration is highly hinging on time. We introduce imperfect quality of production which leads to imperfect items in our proposed model. The retailer adopts inspection policy to pick over the perfect items from imperfect. Type Ⅰ and Type Ⅱ, both type of errors are included and the retailer invest some capital to improve the production process quality of the supplier. There is also a penalty cost for the retailer if they deliver some defective items by mistake. Sometime, there is a high amount of demand and, consequently, we assume shortages and partial backorder in our formulated model. The retailer adopts the trade-credit policy for his customers in order to promote market competition. The main objective of the paper is to show that the total cost is globally minimized and we have aimed at reducing the total cycle length, defectiveness of the system and the optimal order size by maximizing the total profit of the system. Then, we present three theorems and prove them to find an easy solution procedure to reduce the total cost of a system. The results are discussed with the help of numerical examples to approve the proposed model. A sensitivity analysis of the optimal solutions for the parameters is also provided. The paper ends with the conclusions and an outlook to possible future studies.

https://www.aimsciences.org/article/exportPdf?id=b93b1c12-9827-4197-aa93-d55750cbcd31

Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model

The conventional game theory is based on known payoffs. In the real situations, usually the payoffs are not known and have to be approximated. The aim of this paper is to develop a simple and an effective fuzzy multi-objective linear programming method for solving matrix game in which the payoffs are expressed with fuzzy intervals. Since, the payoffs of the matrix game are fuzzy intervals, the value of the matrix game is also fuzzy interval. Using upper and lower bounds of the payoffs, we obtain upper and lower bounds of the value of the matrix game by fuzzy multi-objective linear programming method. Lastly, a numerical example is given to illustrate the method.

An approach to solve fuzzy interval valued matrix game

Neutrosophic multi-objective green four-dimensional fixed-charge transportation problem

This paper is designed based on the mathematical models for bi-level programming in Stackelberg game under type-2 fuzzy environment. The parameters of the objective functions on both levels are considered as type-2 fuzzy numbers in the first case whereas the parameters of the objective functions and the constraints are chosen as type-2 fuzzy numbers in the second case. Critical value based reduction methods are applied to reduce type-2 fuzzy numbers to type-1 fuzzy numbers in the first case. After that, centroid method is used for completely defuzzifying type-2 fuzzy numbers. Besides this, the obtained results are compared with the help of LINGO iterative scheme and genetic algorithm. Coming to the second case, a chance constraint programming with the help of generalized credibility measure is utilized to convert the fuzzy problem to its equivalent crisp form. LINGO iterative scheme is used to solve the deterministic problem using fuzzy programming. The sensitivity analysis is shown to different credibility levels of right hand side of the constraints to find the value of objective function in each level. Finally, real-life based numerical problems are presented to show the performance of the proposed models and techniques. At last, conclusion about the findings and outlook are described.

Sankar Kumar Roy

Papers

Imperfection with inspection policy and variable demand under trade-credit: A deteriorating inventory model

An approach to solve fuzzy interval valued matrix game

Neutrosophic multi-objective green four-dimensional fixed-charge transportation problem

Reduction methods of type-2 fuzzy variables and their applications to Stackelberg game

Birough programming approach for solving bi-matrix games with birough payoff elements