Inventory Model and Pricing with linear functions price-dependent demand, time-dependent holding cost and Discount amount (purchase cost)

In inventory models based on the Economic Order Quantity, Demand rate and holding cost are assumed have constant value and the purchase cost is assumed constant regardless of the order size. In actual applications, the demand rate can be affected by many variables such as seasonality, selling price, and availability. Moreover, the holding cost tends to be higher for extended storage periods. Additionally, the unit purchase cost is generally lower for larger order sizes due to quantity discounts. The purpose of this paper is to develop an inventory and pricing model of a product in a supply chain consisting of multiple suppliers, multiple producers and multiple customers that have linear functions price-dependent demand, time-dependent holding cost, and cost of purchase depends on the size, so that three cases are considered simultaneously in the model. Based on these assumptions, a formulated mathematical model and an optimal solution solution algorithm are developed to maximize total profits, a case study of the problem in a manufacturing plant was carried out using real data Modified, a numerical example is given, and sensitivity analysis is performed on the effect of different parameters on the optimal solution. Our findings indicate that, first, demand function parameters and then cost and purchase parameters are the most influential factors on the profit function.