Sustainable inventory models for a three-echelon food supply chain with growing items and price- and carbon emissions-dependent demand under different emissions regulations

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Industrial-scale food production systems often comprise of different parties such as farmers, processors and retailers involved in various activities along the supply chain. These activities are aimed at converting growing items such as crops and livestock into processed and packaged food products that are safe for human consumption. This paper develops inventory models for a three-echelon food supply chain comprising of growing items. The items are grown at the farming echelon, then processed at the processing echelon and finally sold at the retail echelon provided that the various activities that take place at each of those echelons result in the release of carbon emissions. Furthermore, the customers at the retail echelon are both price-conscious and environmentally-conscious and therefore, demand is assumed to be a function of the retail selling price and the amount of carbon emissions released. The inventory system is studied under three different carbon emissions regulations, namely, carbon cap, carbon cap-and-trade and carbon tax regulations. The results from a numerical analysis indicate that the carbon cap-and-trade regulation yields the highest supply chain profit. Moreover, while both carbon cap-and-trade and carbon tax regulations are effective at minimising carbon emissions generated across the supply chain, the cap-and-trade regulation is better at incentivising the supply chain members to reduce their carbon footprint.