Solving Solid Transportation Problems With Multi-Choice Cost and Stochastic Supply and Demand

Abstract

In this chapter, the authors propose a new approach to analyze the Solid Transportation Problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming, which is incorporated in three constraints, namely sources, destinations, and capacities constraints, followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into a solid transportation problem, and this new problem is called Multi-Choice Stochastic Solid Transportation Problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique that will select an appropriate choice from a set of multi-choice, which optimize the objective function. The stochastic constraints of STP converts into deterministic constraints by stochastic programming approach. Finally, the authors construct a non-linear programming problem for MCSSTP, and by solving it, they derive an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.

Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set

“…The transportation algorithm for solving TPs with equality constraints was given by Dantzig (1963). Taha (2008), Ghazali et al (2012), Ahmed et al (2016), Ficker et al (2017, Xie et al (2017), Gupta and Arora (2018), Sadeghi (2018), Roy and Mahapatra (2018), Das and Jana (2018) and many authors have solved classical/STPs under crisp environment. Hungarian algorithm for solving APs was given by Kuhn (1955).…”

Multi-choice Linear Programming in Fuzzy Random Hybrid Uncertainty Environment and Their Application in Multi-commodity Transportation Problem

“…where each alternative values of the multi-choice parameters are fuzzy random variables which are given as follows: ), 2.7, 3.7)c 2 2 = (N∼(28, 3 2 ), 2.5, 0.5)c 3 2 = (N∼(29, 2 2 ), 1.8, 0.8) Letz = (r, β, γ ) be a fuzzy random variable where r is a normal random variable withE(r) = μ, Var(r) = σ 2 . According to definition 2.4, the mean value ofz is calculated as follows which is random variable [18]:…”

“…Mahapatra [16,17] considered a multi-choice random transportation problem in which supply and demand parameters are constrained Weibull random variables. A new method for solving a multichoice stochastic solid TP was proposed by Roy and Mahapatra [18]. Roy [19] also studied a TP with multi-choice cost and demand and random supply.…”