Designing a single-vendor and multiple-buyers’ integrated production inventory model for interval type-2 fuzzy demand and fuzzy rule based deterioration

¹ Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
² Government Polytechnic, Saharsa, DST Bihar, Bihar 852201, India

^* Corresponding author: goswami@maths.iitkgp.ac.in

Received: 26 March 2021
Accepted: 21 November 2021

Abstract

In this paper, a single-vendor and multiple-buyers’ integrated production inventory model is investigated where demand of the item at the buyers’ location is considered as interval type-2 fuzzy number (IT2FN). Deterioration rate of the item is assumed to change in accordance with the weather conditions of a particular region. It relies upon the values of certain attributes that have a direct influence on the extent of deterioration. These parameter values are easily forecasted and thereby can be utilized to determine the item depletion rate, which is executed here using Mamdani fuzzy inference scheme. Besides, a nearest interval approximation formula for the defuzzification of IT2FN is developed and applied in the proposed integrated production inventory model. The model optimizes the total number of shipments to be made to the buyers within a complete cycle so as to minimize the overall integrated cost incurred. A detailed illustration of the theoretical results is further demonstrated with the help of numerical example, followed by sensitivity analysis which provides insights into better decision making.