Multi-item two-stage fixed-charge 4DTP with hybrid random type-2 fuzzy variable

• Published in: Soft computing (Berlin, Germany) Vol. 25; no. 24; pp. 15083 - 15114
• Main Authors: Devnath, Sudeshna, Giri, Pravash Kumar, Mondal, Seema Sarkar, Maiti, Manoranjan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2021
• Subjects: Artificial Intelligence; Computational Intelligence; Control; Engineering; Mathematical Logic and Foundations; Mechatronics; Optimization; Robotics; Two-stage multi-item 4D transportation problems; CV-based reduction method; Generalized credibility measure technique; Random type-2 trapezoidal and gamma fuzzy variables; CV-centroid method
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-021-06371-3

Parameters of some real-life decision-making problems are simultaneously uncertain, imprecise, and vague. In this paper, for the first time, we introduce two such new hybrid uncertain variables—random type-2 trapezoidal (RT2TF) and gamma fuzzy (RT2GF) variables, their derandomization and defuzzification methods, and applications. Mimicking two-stage public distribution system of the developing countries, breakable multi-item two-stage fixed-charge four-dimensional transportation problems (MITSFC-4DTPs) are formulated and solved. Here, some breakable items are transported from sources to destinations via warehouses using some conveyances, traveling through connecting routes and incurring transportation costs and fixed charges at each stage. The objective is to find suitable conveyances, appropriate travel routes, and corresponding transported amounts at each stage so that total transportation cost is minimum. The model’s parameters—transportation costs, fixed costs, availabilities, demands, and conveyances’ capacities are considered as RT2TF and RT2GF. The models’ random type-2 fuzzy objectives and constraints are first derandomized using expectation and probability chance constraint techniques, respectively. The reduced type-2 fuzzy models are transformed into type-1 fuzzy problems by the CV-based reduction technique (CV-bRT), which are then converted to deterministic ones using two methods—generalized credibility measures (GCM) theory and centroid techniques (trapezoidal fuzzy problem only) separately. All these deterministic models are solved by the generalized reduced gradient (GRG) method using LINGO 12.0 and numerically illustrated. A real-life problem and several particular models under different uncertain environments are solved using some input data. Results from two CV-based methods—CV-bRT-GCM and CV-bRT-centroid for type-2 fuzzy, are compared, and superiority of proposed CV-bRT-GCM is established. In 4DTPs, the importance of multi-routes is numerically illustrated. Some managerial insights are also presented.