Improvement of multi-item order systems and inventory management models using optimal control theory

In the competitive market, applying effective and efficient inventory control and order management methods to reduce costs and improve service efficiency and quality, leading to profit maximization, becomes an absolute necessity at the organizational and supply chain level. Therefore, this study used the optimal control theory to propose an order system and inventory management model. The model is presented from the company’s resourcing stage with a desirable accountability level from the supplier side in a continuous review period with dynamic multi-item demand and budget constraints. In the present model, the order was regarded as a time-dependent function and a control variable. In addition, the need for each item is time-dependent and specified. The present model indicates the order and inventory system as an optimal control problem. In addition, Pontryagin’s maximum principle for optimal control problems, Generalized Reduced Gradient Method (GRG), and Kuhn–Tucker conditions were used to seek the optimal order. The model aimed to maximize the total order profit and inventory management systems. Finally, the results were presented numerically and graphically, and some management decisions were derived.