Abstract
This paper investigates a multi-objective capacitated solid transportation problem (MOCSTP) in an uncertain environment, where all the parameters are taken as zigzag uncertain variables. To deal with the uncertain MOCSTP model, the expected value model (EVM) and optimistic value model (OVM) are developed with the help of two different ranking criteria of uncertainty theory. Using the key fundamentals of uncertainty, these two models are transformed into their relevant deterministic forms which are further converted into a single-objective model using two solution approaches: minimizing distance method and fuzzy programming technique with linear membership function. Thereafter, the Lingo 18.0 optimization tool is used to solve the single-objective problem of both models to achieve the Pareto-optimal solution. Finally, numerical results are presented to demonstrate the application and algorithm of the models. To investigate the variation in the objective function, the sensitivity of the objective functions in the OVM model is also examined with respect to the confidence levels.
Highlights
In the physical world, we frequently encounter numerous situations where, in addition to the source-destination constraints, other constraints associated with product type or modes of transportation are present. Such TP is known as the solid transportation problem (STP), and it was first presented by Schell (1955)
The results for the uncertain multi-objective capacitated STP (CSTP) (MOCSTP) determined using the expected value model (EVM) and optimistic value model (OVM) are shown
The uncertain MOCSTP model is first transformed into its deterministic EVM and OVM models using the expected and optimistic value criterion of uncertainty theory
Summary
Transportation is an integral component of the growing local and global economy of the world these days. This study is instigated to deal with the real-life MOCSTPs, where one wants to optimize multiple objectives simultaneously while transporting products from available sources to destinations using different conveyances with capacitated constraints under the uncertain environment (rather than fuzzy or random environment). The results of EVM and OVM models are acquired by utilizing the two classical approaches: minimizing distance method and fuzzy programming technique These two solution approaches find a wide number of applications in the uncertain transportation problems with multiple objectives because of their simple and efficient use. Definition 2.2 Liu (2010): A measurable function from uncertainty space , , M to such that B is an event for any Borel set B of real numbers, is known as an uncertain variable. CC states that iff M r M r for some predefined level r
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