Pricing and inventory decisions in the food supply chain with production disruption and controllable deterioration

Food deterioration is becoming a crucial problem for most countries in the world, which may cause both economical losses and environmental damages. In this paper, a Stackelberg gaming model for a three-level food supply chain (consists of one retailer, one vendor and one supplier) with production disruption is established, which aims to study the optimal pricing, inventory and preservation decisions that maximize the individual profit. In the decentralized supply chain, upstream firms act as leaders and downstream firms as followers. Due to the mathematical complexity, an illustrative algorithm is developed to solve the problem. Numerical tests show that retailer's preservation investment not only benefits itself, but also benefits the vendor and the supplier. Comparing the optimal decisions to that in the 'forward integration' and 'backward integration' model, supply chain members' vertical cooperation helps to enhance the total profit. Meanwhile, the carbon footprint of the food supply chain is also studied. It is found that, vertical cooperation contributes to the reduction of carbon emission. In most situations, 'forward integration' outperforms 'backward integration' strategy because it incents the retailer to invest more in preservation and reduce food deterioration. Other managerial implications are also shown in the paper.