Optimization of a Multi-Item Supply Chain Model with Shortages under Parametric Type-2 Interval Environments

Authors

• Sourav Kumar Kumar Giri, Department of Mathematics, University of Kalyani, Kalyani, Nadia-741235, West Bengal, IndiaFollow
• Totan Garai, Department of Mathematics, Syamsundar college, Syamsundar, Purba Bardhaman-713424, West Bengal, IndiaFollow
• Sahidul Islam, Department of Mathematics, University of Kalyani, Kalyani, Nadia-741235, West Bengal, IndiaFollow
• Haridas Mondal, Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, IndiaFollow
• Shariful Alam, Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, IndiaFollow

Authors' ORCIDs

Sourav Kumar Giri: https://orcid.org/0009-0006-4928-435X

Totan Garai: https://orcid.org/0000-0002-0476-6447

Sahidul Islam: https://orcid.org/0000-0002-4142-0947

Haridas Mondal: https://orcid.org/0009-0003-1980-210X

Shariful Alam: https://orcid.org/0000-0001-8263-117X

Article Type

Research Article

Abstract

Modern supply chain systems frequently operate in environments where demand, costs and inventory-related parameters are uncertain and difficult to estimate accurately. These uncertainties become more critical in multi-objective decision-making situations, where decision makers must simultaneously balance several conflicting goals. Conventional optimization techniques often fail to represent the ambiguity and vagueness present in practical decision environments. To overcome these limitations, this study develops a multi-item supply chain model for a single supplier and a single buyer by incorporating Type-2 interval representations into the modelling framework. The proposed approach introduces a structured set of arithmetic operations for Type-2 intervals to manage uncertain information more effectively. In addition, a new ranking procedure based on the expected-value concept of parametric Type-2 intervals is designed to support the comparison and prioritization of uncertain alternatives. The developed methodology is then applied to a multi-objective supply chain problem involving shortages, enabling simultaneous evaluation of multiple operational objectives under imprecise conditions. To examine the applicability of the model, numerical examples and sensitivity analyses are carried out under different system conditions. The results indicate that the proposed framework generates stable and adaptable solutions even when uncertainty levels vary significantly. Comparative observations show that the Type-2 interval approach provides improved consistency in decision outcomes and better handling of ambiguous information than traditional interval-based techniques. Sensitivity analysis further demonstrates the responsiveness of the model to changes in demand and shortage-related parameters, confirming its practical suitability for uncertain supply chain environments. Overall, the study presents an effective uncertainty-handling framework that enhances the reliability of multi-objective supply chain decision-making and offers valuable insights for solving complex real-world optimization problems characterized by incomplete and imprecise information.

Keywords

Type-2 interval uncertainty, Expected value ranking method, Multi-item inventory optimization, Integrated single-buyer, Single-supplier strategy

How to Cite

Giri, Sourav Kumar Kumar; Garai, Totan; Islam, Sahidul; Mondal, Haridas; and Alam, Shariful (2026) "Optimization of a Multi-Item Supply Chain Model with Shortages under Parametric Type-2 Interval Environments," Neutrosophic Systems with Applications: Vol. 26: Iss. 5, Article 4. DOI: https://doi.org/10.63689/2993-7159.1334