A new inventory model for cold items that considers costs and emissions

A new inventory model that considers both cost and emission functions is proposed for environments where temperature-controlled items need to be stored at a certain, non-ambient temperature and to do so modular temperature-control units are used. Transportation unit capacity and storage unit capacity are considered, which results in non-linear, non-continuous cost and emissions functions. A set of exact algorithms are developed to find the optimal order quantity based on cost and emission function minimization, and the mathematical proof of the optimality of the solutions are presented. Using a variety of parameter ratios, a set of experiments are run to show the effectiveness of the proposed model compared to the current models in the literature and to provide managerial insights into the cold item inventory problem. Optimum order quantity for cost function optimization and emission function optimization are compared against each other and the tradeoff between the functions is analyzed to provide insights.