Solving Multi-objective Bi-item Capacitated Transportation Problem with Fermatean Fuzzy Multi-Choice Stochastic Mixed Constraints Involving Normal Distribution

Abstract

The transportation problem (TP) is an important type of linear programming problem. The aim of TP is to optimize the objective function by allocating product shipments from various sources to multiple destinations. When limitations exist during transportation in the number of products transported from a source to destination due to a variety of factors, such as storage limitations, budgetary constraints, and so on, then TP becomes the capacitated transportation problem (CTP). The business entrepreneurs are keen on transporting multiple items with multiple objectives to generate maximum revenue for an organization, which leads to the development of a multi-objective bi-item capacitated transportation problem (MOBICTP). If a supplier's resources significantly increase or decrease, and the demand needs also significantly increase or decrease, the MOBICTP transforms into a MOBICTP with mixed constraints. Most real-world problems have uncertain parameters due to insufficient data, fluctuating market costs for an item, variation in weather conditions, and so on. Such uncertain parameters are addressed using fuzzy, multi-choice, or stochastic programming. In this article, we examined a novel integrated model for a multi-objective bi-item capacitated transportation problem, which includes a fermatean fuzzy multi-choice stochastic mixed constraint that follows normal distribution. First, the Fermatean fuzzy multi-choice stochastic parameter in the constraints is transformed into a multi-choice stochastic parameter in the constraints by using the (α, β )-cut technique and accuracy function. Then the improved chance-constrained method is developed using Newton divided difference interpolation polynomial. The improved chance-constrained method is used to transform the multi-choice stochastic parameter in the constraints into its equivalent deterministic constraints. Secondly, we propose a novel approach, the improved global weighted sum method, which transforms a multi-objective problem into a single objective problem and utilizes Lingo 18.0 software to find the optimal compromise solution to the equivalent deterministic problem. The main aim of this paper is to help business entrepreneurs improve their profit margins by optimizing the quantity of multiple items while minimizing damage costs, labor costs, transportation time, and transportation costs, and maximizing discounts. To show the model’s validity and significance, a numerical example is solved using the Lingo 18.0 software. In order to emphasize the proposed method, a comparative analysis is conducted with other existing methods. The final component includes a sensitivity analysis and conclusions with future research directions.