A GOLDEN SECTION METHOD FOR THE MULTI-OBJECTIVE FRACTIONAL SOLID TRANSPORTATION PROBLEM USING THE EXPONENTIAL MEMBERSHIP FUNCTION

Year 2022, Volume: 18 Issue: 1, 121 - 141, 01.04.2022

Nurdan Kara , Hale Köçken

Abstract

The multi-objective Solid Transportation Problem (MSTP) is type of vector minimization (or maximization) problem with three parameters: source, destination, and mode of transport. It may have fractional objective functions in real-life applications to maximize the profitability ratio like profit/cost or profit/time. We refer to such transportation problems as the Multi-objective Fractional Solid Transportation Problem (MFSTP). In this article is presented a fuzzy approach that combines the usage of linear programming and the golden section algorithm with linear and exponential membership functions and a strongly efficient solution is obtained. Finally, a numerical example from the literature is solved to show the solution algorithm and a comparison is presented with the solution found by using a linear membership function.

Keywords

Solid Transportation Problem, Fractional Programming, Exponential Membership Function, Fuzzy Programming, Golden Section Method

Supporting Institution

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

ÇOK AMAÇLI ÜÇ BOYUTLU KESİRLİ TAŞIMA PROBLEMİ İÇİN ÜSTEL ÜYELİK FONKSİYONU KULLANARAK ALTIN ORAN METODU

Abstract

Çok amaçlı üç boyutlu taşıma problemi kaynak, varış yeri ve taşıma şekli parametrelerine sahip vektör minimizasyon (veya maksimizasyon) probleminin özel bir tipidir. Amaçları, kârlılık oranının- kâr/maliyet veya kâr/zaman- maksimizasyonu gibi iki lineer fonksiyonun oranı olabilir. Bu tür problemler, Çok Amaçlı Kesirli Üç Boyutlu Taşıma Problemi olarak adlandırılmaktadır. Bu çalışmada, lineer programlama ve altın oran yönteminin lineer ve üstel üyelik fonksiyonları ile kullanıldığı bulanık bir yaklaşım sunulmakta ve pareto-optimal bir çözüm elde edilmektedir. Son olarak, çözüm yöntemini göstermek için literatürden sayısal bir örnek çözülmüş ve doğrusal üyelik fonksiyonu kullanılarak elde edilen çözümle bir karşılaştırma yapılmıştır.

Keywords

Üç Boyutlu Taşıma Problemi, Kesirli Programlama, Üstel Üyelik Fonksiyonu, Bulanık Programlama, Altın Oran Metodu

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