# Two-Warehouse Inventory Model: Interval Valued Costs, Advanced Payment, Stock-Dependent Demand, and Partial Backlogging

## Authors

• Ashfar Ahmed Department of Mathematics, School of Science, GITAM-Hyderabad Campus, Hyderabad-502329, India, and Department of Mathematics, Malla Reddy Engineering College (AUTONOMOUS)
• Krishna Kummari Department of Mathematics, School of Science, GITAM-Hyderabad Campus, Hyderabad-502329, India
• Ravikumar Bandaru Department of Mathematics, School of Advanced Sciences,}VIT-AP University, Andhra Pradesh-522237, India
• Rahul Shukla Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha 5117, South Africa

## Keywords:

Inventory, Two-warehouse, Partial backlogging, Interval-valued inventory cost, Interval-valued Deterioration

## Abstract

A great deal of inventory costs are typically unpredictable because of the unpredictability of a competitive market. The fluctating demand from customer's and the unpredictability of the market economy make it difficult for researchers and operation research practitioners to appropriately replicate an inventory problem. In order to prevail this type of unpredictability circumstances, in this paper, we have represented the inventory parameters as interval. Using this concept, we progressed a two-warehouse inventory model for deteriorating items with a fixed Shelf life, partially backlogging shortages and interval-valued deterioration rate. In addition to this the parameters like ordering cost, purchase cost, shortage cost, deterioration cost for both the rented and owned warehouse except the backlogging parameter have been considered as interval-valued. The uncertainty in the inventory parameters motivated us to view them as interval-valued in the present research. Based on the assumptions, the cost function of this problem is a highly nonlinear constraint optimization problem. Mathematica is used to tackle this nonlinear optimization problem.  A numerical example has been presented to demonstrate the computational result. Then, a sensitivity analysis has been performed to study the effect of changes of different parameters of the model on the optimal policy.