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.
Giri et al. (Tue,) studied this question.