Optimal analysis of time-price discount-advertisement dependent demand with credit policy for inventory models

The effective management of permissible payment delays and credit interest is a crucial aspect of financial inventory control. This research delves into payment policies such as acceptable credit terms, permissible payment delays, and interest rates on overdue payments in the context of managing perishable and non-perishable inventory items. The primary aim of our study is to formulate a total cost minimization problem with respect to optimal cycle time and ordering quantities, considering time-, price discount-, and advertisement-dependent demand patterns to simulate real-world scenarios. In today’s highly competitive market, determining optimal ordering policies and pricing strategies is paramount. Suppliers employ various tactics, including incentives for retailers and advertising, to boost sales. We specifically examine the impact of permissible payment delays within the framework of trade-credit policies, which can significantly benefit businesses. Additionally, our model incorporates practical elements such as partial backlogged shortages, lost sales, instantaneous replenishment, an infinite time horizon, and constant lead times. The objective of the current paper is to develop advanced inventory models that account for demand patterns influenced by time, price discounts, and advertisements, while incorporating trade-credit policies for both perishable and non-perishable items. By analyzing the objective functions, we derive optimal solutions for various scenarios within the inventory problem. An SGO (Swarm-based Global Optimization) algorithm is proposed to demonstrate the applicability of the developed models and to minimize the retailer’s total costs. Additionally, a comparative analysis of trade-credit policies for perishable and non-perishable items is conducted to highlight their respective impacts. We provide numerous numerical examples to validate our statistically independent processes and offer graphical analyses of the convexity of each nonlinear objective function. Our findings emphasize the substantial influence of each parameter on the optimal total cost within the proposed model. The findings indicate that as demand becomes increasingly sensitive to price, time, and advertisement, the benefits of coordination in inventory management are significantly enhanced, particularly in conjunction with trade-credit policies.