A Production Inventory Model to Study the Supply Chain of Agri-Product for a Time Reliant Population

In the field of inventory management, the production inventory plays a vital role in optimizing the production rate and minimizing the cost involved in production and inventory control. In most of the cases it is observed that, demand is taken as function of price, time, stock, etc., however, the quantity of consumption by a particular population group is often neglected while developing a production inventory model. Further, to cope up with average consumption of a time dependent population in a certain region, it is necessary to determine the optimal production rate to maintain the supply chain. In this paper, an attempt has been made to develop a production inventory model to determine the optimum production rate of an agricultural product under the assumption of average consumption by a population. The objective function consists of setup cost, deterioration cost, transportation cost, carbon emission cost and the production cost. The model is solved under three different cases such as- considering holding cost, green investment, and preservation cost. Moreover, a comparison has been made among the different cases taken under study for least average total cost. Further, the model is validated with numerical examples followed by sensitivity analysis of the systems parameters.