Cold supply chain inventory models for agricultural products with multi-stage stochastic deterioration rates

In India, majority of the families depend upon agricultural business. Also, 40% of agricultural food and vegetables are rotted due to improper planning. It is predicted in 2023 that US$ 293.27 billions will be wastage of food. That's why, the cost of these items are high in the retail market and farmers get least price for their produce. It is essential to avoid the loss by adopting cold supply chain and its impact will help to increase the GDP of country. Here, we proposed the supply chain model which includes one warehouse and multi-retailers. Cold storage facility is available at warehouse, transport facility and retailers. To support the proposed model, we have collected the numerical data of coriander (highly perishable) product from the market yard, Pune, India. The proposed model solved by using real world numerical case study. The life of this product is very less hence it needs to develop a cold supply chain for this item. Also, we solved multiple inventory differential equations by using boundary value problem. To solve the proposed models for single retailer and multiple retailers, we have developed a solution methodology based on evolutionary algorithm. We have observed that, optimum profit is highly sensitive to the warehouse demand and purchase cost. Hence it is essential to reduce the deteriorated items at storage point. The warehouse, retailer and customer demand significantly affect on the deteriorated items. In single and multiple retailer, for low warehouse and retailer demand, we get maximum profit. Thus, less number of deteriorated items of the supply chain will helps to the society, as well as country to increase the profit of the supply chain.