scholarly journals Least-looping stepping-stone-based ASM approach for transportation and triangular intuitionistic fuzzy transportation problems

2021 ◽  
Author(s):  
Kedar Nath Das ◽  
Rajeev Das ◽  
Debi Prasanna Acharjya
Keyword(s):  
Optimal Solution ◽  
Transportation Engineering ◽  
Key Factors ◽  
Solution Quality ◽  
Transportation Problems ◽  
Stepping Stone ◽  
Intuitionistic Fuzzy ◽  
Real World Problem ◽  
Statistical Results ◽  
Made In

AbstractTransportation problem (TP) is a popular branch of Linear Programming Problem in the field of Transportation engineering. Over the years, attempts have been made in finding improved approaches to solve the TPs. Recently, in Quddoos et al. (Int J Comput Sci Eng (IJCSE) 4(7): 1271–1274, 2012), an efficient approach, namely ASM, is proposed for solving crisp TPs. However, it is found that ASM fails to provide better optimal solution in some cases. Therefore, a new and efficient ASM appoach is proposed in this paper to enhance the inherent mechanism of the existing ASM method to solve both crisp TPs and Triangular Intuitionistic Fuzzy Transportation Problems (TIFTPs). A least-looping stepping-stone method has been employed as one of the key factors to improve the solution quality, which is an improved version of the existing stepping-stone method (Roy and Hossain in, Operation research Titus Publication, 2015). Unlike stepping stone method, least-looping stepping-stone method only deals with few selected non-basic cells under some prescribed conditions and hence minimizes the computational burden. Therefore, the framework of the proposed method (namely LS-ASM) is a combination of ASM (Quddoos et al. 2012) and least-looping stepping-stone approach. To validate the performance of LS-ASM, a set of six case studies and a real-world problem (those include both crisp TPs and TIFTPs) have been solved. The statistical results obtained by LS-ASM have been well compared with the existing popular modified distribution (MODI) method and the original ASM method, as well. The statistical results confirm the superiority of the LS-ASM over other compared algorithms with a less computationl effort.

scholarly journals PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems

2018 ◽  
Vol 7 (4) ◽  
pp. 62-99 ◽  
Author(s):  
P.Senthil Kumar
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Optimal Solution ◽  
Fuzzy Representation ◽  
Objective Value

This article proposes a method for solving intuitionistic fuzzy solid transportation problems (IFSTPs) in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers (IFNs). The remaining parameters, namely: supply, demand and conveyance capacity, are all considered into crisp numbers. This type of STP is called a type-2 IFSTP. When solving the real life solid transportation problems (STPs) those tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the STPs under the uncertain environment. He formulates the intuitionistic fuzzy STPs and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P.Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the type-2 IFSTP and the optimal objective value of type-2 IFSTP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution of type-2 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. A case study is presented to illustrate the procedure of the proposed method.

A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

2018 ◽  
Vol 15 (01) ◽  
pp. 95-112 ◽  
Author(s):  
Abhishekh ◽  
A. K. Nishad
Keyword(s):  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Ranking Functions ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Fuzzy Transportation Problem

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

scholarly journals The optimization of distribution and transportation costs for common good products

2020 ◽  
Vol 1 (2) ◽  
pp. 111
Author(s):  
Fibi Eko Putra ◽  
Humiras Hardi Purba ◽  
Indah Astri Anggraeni
Keyword(s):  
Cost Reduction ◽  
Common Good ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Distribution Model ◽  
Transportation Problems ◽  
Stepping Stone ◽  
North West ◽  
Long Time ◽  
Single Method

Transportation problems, which concerned in finding the minimum cost of transporting a single commodity from a given number of sources to a given number of destinations, are an integral part of the industrial system that has been around for a long time. The number of potential losses caused by transportation problems has made many parties take initiatives and efforts to solve those problems, usually by designing an optimal distribution model. The current study employs two methods named North West Corner (NWC) and Stepping Stone (SS) method in order to find distribution model with the most optimal costs for common good products. Through this research, the NWC method is utilized to generate initial model or solution, while the SS method is used afterward to find the optimal solution. According to it scheme, the result shows that through the NWC method there was cost reduction of $ 8,301, while the distribution model obtained from the Stepping Stone method resulted in a significant cost increased of $ 307,369. Thus, it can be concluded that the use of single method, namely NWC method, in this study provides much better results than using the combined NWC and Stepping Stone method.

scholarly journals PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems

2019 ◽  
Vol 10 (2) ◽  
pp. 20-53 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Fuzzy Number ◽  
Transportation Problem ◽  
Graphical Representation ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Uncertain Environments ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number ◽  
Fuzzy Optimal Solution

In this article, the author categorises the solid transportation problem (STP) under uncertain environments. He formulates the mixed and fully intuitionistic fuzzy solid transportation problems (FIFSTPs) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P. Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the mixed and type-4 IFSTP and the optimal objective value of mixed and type-4 IFSTP is obtained in terms of triangular intuitionistic fuzzy number (TIFN). The main advantage of this method is that the optimal solution of mixed and type-4 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. Finally, the procedure for the proposed method is illustrated with the help of numerical examples which is followed by graphical representation of the finding.

scholarly journals A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems

2018 ◽  
Vol 9 (3) ◽  
pp. 90-122 ◽  
Author(s):  
P. Senthil Kumar
Keyword(s):  
Transportation Problem ◽  
Feasible Solution ◽  
Real Life ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Basic Feasible Solution ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number

This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertainty and hesitation in supply, demand, capacity of different modes of transport celled conveyance and when it has crisp cost it is known as IFSTP of type-1. From this concept, the generalized mathematical model for type-1 IFSTP is explained. To find out the optimal solution to type-1 IFSTPs, a single stage method called intuitionistic fuzzy min-zero min-cost method is presented. A real-life numerical example is presented to clarify the idea of the proposed method. Moreover, results and discussions, advantages of the proposed method, and future works are presented. The main advantage of the proposed method is that the optimal solution of type-1 IFSTP is obtained without using the basic feasible solution and the method of testing optimality.

scholarly journals IMPLEMENTASI KARAGUL-SAHIN APPROXIMATION METHOD UNTUK MEMINIMALISASI BIAYA PENDISTRIBUSIAN AIR PADA MASALAH TRANSPORTASI

2021 ◽  
Vol 5 (1) ◽  
pp. 46-53
Author(s):  
Sri Basriati ◽  
Elfira Safitri ◽  
Dinda Kurniyawan Nusantoro
Keyword(s):  
Approximation Method ◽  
Water Distribution ◽  
Optimal Solution ◽  
Cost Savings ◽  
Minimum Cost ◽  
Basic Feasible Solution ◽  
Stepping Stone ◽  
Level Of Satisfaction ◽  
The Cost ◽  
Made In

Transportation problems such as transportation activities and allocation to reach consumers is one of the factors that determine the level of satisfaction. To find the level of customer satisfaction, it requires an appropriate and efficient transportation model. One of which is in the Air Minum Mata Air Sikumbang business owned by Mr. Zulfikar, located in Rumbio, Kampar. Based on the results of the study the cost of distributing drinking water is still not efficient because it still uses estimation and there is no separate technique used to allocate water distribution. The solution made in this study using the Karagul-Sahin Approximation Method for the initial basic feasible solution and Stepping Stone for the optimal solution value so as to obtain the distribution of water at a minimum cost. Based on research using the method of  Karagul-Sahin Approximation and Stepping Stone, a weekly cost savings of Rp.469.515,00 is obtained.

scholarly journals Finding the Solution of Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems by Using Different Methods With Some Software Packages

2021 ◽  
pp. 278-320
Author(s):  
P. Senthil Kumar
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Computer Code ◽  
Programming Technique ◽  
Distribution Method ◽  
Transportation Problems ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
New Methodologies ◽  
Future Work

In this chapter, two different methodologies are proposed to find out the optimal solution to the balanced and unbalanced intuitionistic fuzzy transportation problems (UBIFTPs). In addition, the parameter of both the balanced and UBIFTPs are considered to be triangular intuitionistic fuzzy numbers (TIFNs). Two new methodologies, respectively method-1 and method-2, are presented in this chapter. Proposed method-1 is based on linear programming technique, and proposed method-2 is based on modified distribution method. Both the methodologies are used to solve the balanced and UBIFTPs. The ideas of the proposed methodologies are illustrated with the help of real-life numerical examples. The solutions obtained by the proposed methodologies are checked with some software (e.g., MATLAB, LINGO) and the computer code related to the proposed problems is also given. The unique results, comparative study, discussions, and the merits of the proposed methodologies are all given. At the end of the chapter, future work is mentioned.

scholarly journals Microbial-Driven Stabilisation of Archaeological Iron Artefacts

2021 ◽  
Vol 2 (2) ◽  
pp. 274-292
Author(s):  
Sarah James ◽  
Edith Joseph
Keyword(s):  
Health And Safety ◽  
Chloride Content ◽  
Key Factors ◽  
Passivation Layers ◽  
Archaeological Iron ◽  
Initial Results ◽  
Sulphur Species ◽  
Partial Success ◽  
Made In

The instability of iron artefacts is rooted in salt contamination during burial and damages associated with exposure to alternative oxygen levels and high relative humidity once excavated. While a combination of chemical and mechanical treatments is utilised to remove the harmful ions (chlorides, sulphur species) and excess bulky corrosion products, these methods can be hazardous for conservation staff’s health, have limited success, or require extensive treatment times. Bio-based treatments provide a potentially greener alternative for removing damaging corrosion and creating biogenic mineral passivation layers, thus remediating concerns over costs, duration, and health and safety. Pseudomonas putida mt-2 (KT2440) is capable of utilising iron under certain conditions and for phosphating mild steel; however, applications have not been made in the cultural heritage sector. To address the potential of using bacteria for conservation purposes, Pseudomonas was assessed for both the bioremediation of salt contaminates and the production of a passivation layer suitable for iron artefacts, with specific conservation concerns in mind. Key factors for optimisation include the role of agitation, chloride content, and oxygen content on bacterial growth and biomineralisation. The initial results indicate a growth preference, not reliance, for NaCl and agitation with partial success of bioconversion of a mineral source.

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