Determination of the optimal strategy of a circular manufacturing-inventory logistics model with continuous time

Abstract

The study examines a single-product circular logistics system. The logistics system has two warehouses for new and returning used products. Products in the system can be divided into three categories: new products, reworked products and waste products. In the logistics system, the demand is known, and it is assumed that not all of the reflowing used products are returned, but the rate of reflow is constant and follows the demand with a known time delay.Manufacturing, rework and disposal costs are convex, as well as production costs known in microeconomics. The inventory costs of the two warehouses are linear. The planning time horizon is also given, e.g. one year. Total costs must be minimized in the optimization problem. After specifying the optimality conditions, some properties of the optimal trajectory are presented, and then the optimal solution is illustrated with a numerical example.  The research investigates the behaviour of decision variables in optimal solutions, such as the need for production, recycling or waste disposal, and the conditions for the existence of an optimal solution. The model not only explores the possibilities of cost minimisation, but also predicts that public interventions, such as taxing environmentally damaging processes (production, landfilling) or encouraging environmentally friendly processes (recycling), can shift the economic optimum towards a more sustainable direction. The aim of the research is to explore the properties of a model of the waste cycle for these cases. The paper illustrates the functioning of the model through numerical examples and highlights its practical relevance, for example in the REpont recycling scheme.