Multi-choice stochastic transportation problem involving weibull distribution

Abstract

This paper explains the important role in application of stochastic distribution and multichoice framework on the field of transportation environment. The purpose of this paper is to provide a solution procedure to multi-choice stochastic transportation problem involving the parameters as supply and demand of Weibull distribution and cost coefficients of a single criterion of minimization of objective function which are multi-choice in nature. At first, all stochastic constraints are transformed into deterministic constraints by using the stochastic approach. Recently, Mahapatra et al. [14] have proposed a methodology to transfer the multi-choice stochastic transportation problem to an equivalent mathematical programming model which can accumulate a maximum of eight choices on the cost coefficients of the objective function. In this paper, a generalized transformation technique is also present to discuss the two types of transformation technique. Using any one of the transformation technique, the decision maker can handle a parameter of the cost coefficients of objective function with finite number of choice associated with additional restriction for obtaining the equivalent deterministic form. Finally, a numerical example is provided to validate the theoretical development and solution procedure.

A Goal Programming Approach to Multichoice Multiobjective Stochastic Transportation Problems with Extreme Value Distribution

“…Biswal and Samal [12] obtained an equivalent deterministic model of MCSTP in which they considered that both $a i $ and $b j $ follow Cauchy distribution. Mahapatra [2] considered an MCSTP with extreme value distribution, serving as a basis of inspiration for this research. e novel contribution of this paper is to include the multiobjective problem within the model and to represent the multichoice problem in terms of aspiration levels instead of a cost coefficient parameter.…”

“…e novel contribution of this paper is to include the multiobjective problem within the model and to represent the multichoice problem in terms of aspiration levels instead of a cost coefficient parameter. Mahapatra [2] also studied an MCSTP model involving Weibull distribution, whereas Quddoos et al [13] presented an MCSTP involving a general form of distribution. Roy [14] introduced Lagrange's interpolating polynomial to deal with the multichoice transportation problem.…”

“…where f i (x) is the linear function of the i th goal, g i is the aspiration levels of the i th goal, x ij is the amount shipped, a i is the amount of supply at source i, b j is the amount of demand at destination j, n i is the negative deviational variable, and p i is the positive deviational variable. is led to three different models (for more details, see Mahapatra [2]. e final transformed constraint is then considered here as the probabilistic constraint (4) transformed into a deterministic linear constraint:…”

“…In this section, a case study from Mahapatra [2] is considered with modifications and the assumption of extreme value distribution instead of Weibull distribution. In this case study, a cold drink supply company transports cold drinks from three product centres at Dankuni, Howrah, and Asansol to four destination centres at Jhargram, Kharagpur, Tarkeshwar, and Contai.…”

“…Mahapatra [2] considers a model of a multichoice stochastic transportation problem (MCSTP), where the supply and demand parameters of the constraints follow extreme value distribution. Some of the cost coefficients of the objective function are a multichoice type.…”