The PSK Method: A New and Efficient Approach to Solving Fuzzy Transportation Problems

The PSK Method: A New and Efficient Approach to Solving Fuzzy Transportation Problems

P. Senthil Kumar
Copyright: © 2023 |Pages: 49
DOI: 10.4018/978-1-6684-8474-6.ch007
OnDemand:
(Individual Chapters)
Available
$37.50
Current Special Offers
No Current Special Offers
TOTAL SAVINGS: $37.50

Abstract

We have several logics to obtain the fuzzy optimal solution for fuzzy transportation problems (FTPs). But there is no logic to solve transportation problem (TP) under four different uncertain environments using a particular method in the literature. So, the author divided the TP under four different environments and formulates the problems and utilizes the fuzzy numbers to solve them. A method, namely PSK (P. Senthil Kumar) method, to find the fuzzy optimal solutions to the FTPs is proposed. Applications of the PSK method compared to other existing methods are demonstrated with four different numerical examples. To illustrate the PSK method, different types of FTPs are solved by using the PSK method with the help of software, for example, Lingo, Matlab, Tora, RGui, and RStudio, and the obtained results are compared, analyzed, and discussed. Conclusions on the study and recommendations for future research are also given.
Chapter Preview
Top

Nomenclature

  • FTP: Any one of the parameters in TP is in fuzzy number

  • CTP: Crisp/conventional transportation problem

  • CTT: The parameters in the transportation table are all crisp numbers

  • Type 1 FTP: The transportation problem deals with fuzzy supply and fuzzy demand, but with crisp costs

  • Type 2 FTP: The transportation problem deals with crisp supply and crisp demand, but with fuzzy costs

  • Type 3 FTP: The transportation problem deals with a mixture of crisp and fuzzy numbers in all the parameters (supply, demand, and costs)

  • Type 4 FTP: The transportation problem deals with fuzzy supply, fuzzy demand, and fuzzy costs, i.e., the parameters are all neither crisp nor a mixture of crisp and fuzzy numbers

Indices:

  • Ai: Origins/factories (i=1,2,…,m)

  • Gj: Destinations/warehouses (j=1,2,…,n)

  • ai: Suppl

  • 978-1-6684-8474-6.ch007.m01: Fuzzy supply

  • bj: Demand

  • 978-1-6684-8474-6.ch007.m02: Fuzzy demand

  • cij: Cost

  • 978-1-6684-8474-6.ch007.m03: Fuzzy cost

  • 978-1-6684-8474-6.ch007.m04: Fuzzy profit

  • yij: Decision variable

  • 978-1-6684-8474-6.ch007.m05: Fuzzy decision variable

  • 978-1-6684-8474-6.ch007.m06: or Z Crisp objective function

  • 978-1-6684-8474-6.ch007.m07: Fuzzy objective function

The above nomenclature tables are added at the beginning of the chapter to help the reader understand the different parameters, variables, sets, and indices used in the chapter, as well as the meaning of type 1, 2, 3, and 4 FTPs.

Top

Introduction And Literature Review About Transportation Problem

Resource allocation is used to assign the existing resources in an economic way. When the resources/goods to be allocated are inadequate, an ingenious action is necessary for a decision-maker (DM) to attain the optimum utility. If the supplying sources (e.g., factories) and the receiving agents (e.g., stores) are limited then the best pattern of allocation to get the maximum return/the best plan with the least cost, whichever may be applicable to the problem is to be found out. This type of problems is known as ‘Allocation Problems’ and is splitted into 2 categories. They are:

  • 1.

    Transportation problems (TPs) and

  • 2.

    Assignment problems (APs).

Generally, we call both the TPs and APs are optimization problems (OPs).

Complete Chapter List

Search this Book:
Reset