Multi-warehouse partial backlogging inventory system with inflation for non-instantaneous deteriorating multi-item under imprecise environment

Abstract

In this study, we explored a multi-item inventory model for non-instantaneous deteriorating items under inflation in fuzzy rough environment with multiple warehouse facilities, where one is an owned warehouse and others are rented warehouses with limited storage capacity. Due to a number of uncertainties in the environment, the various expenditures and coefficients are considered as a fuzzy rough type. The objective and constraints in fuzzy rough are made deterministic using Tr–Pos chance constrained technique. The demand of items is considered as stock dependent, and deterioration of items is assumed to be constant over time. The model allows shortages in owned warehouse subject to partial backlogging. The purpose of this study is to find the retailer’s optimal replenishment policies to maximize the total profit. To illustrate the proposed model and also test the validity of the same, a numerical example is solved using the Mathematica-8.0 software. Sensitivity analysis is also performed to study the impact of important parameters on system decision variables, and its implications are discussed.