Inventory Model for Instantaneously Deteriorating Items with Multiple Trade Facilities, Stock- and Price-Dependent Demand, and Full Backlogging

This paper formulates six inventory models for products with instantaneous deterioration, focusing on the impacts of full and partial advance payment structures. The demand function depends on both price and stock levels and accounts for shortages through full backlogging. The primary objective is to determine the optimal payment policy under varying trade facilities, analyzing six distinct payment scenarios commonly employed in business practice. Each model is presented with closed-form solutions and supported by mathematical formulations. For each case, algorithms and mathematical proofs are developed to determine the optimal cycle duration and corresponding unit cost. Numerical examples and 2D graphical representations generated using MATLAB are included to validate the proposed models. Additionally, a sensitivity analysis is conducted to examine the effects of each payment policy and parameter variation, providing key managerial insights into payment planning in inventory management.