The value of perishable products is most affected by the time delays in a supply chain. A major issue is how to integrate the existing practices in production, inventory holding and distribution, besides considering the perishable nature of the products, so as to deliver an optimized policy for the perishable commodities. Standard inventory control models are often not adequate for perishable products and there is a need for a new integrated model to focus on consolidation of production, inventory and distribution processes. We develop such a mathematical model to search for an optimal integrated inventory policy for perishable items in a multi-stage supply chain. We specifically assume the exponential deterioration rate so as to be consistent with the growth rate of the microorganisms responsible for deterioration. We propose and analyze some general properties of the model and apply it to a three-stage supply chain. We show that this integrated model which includes inventory control and fleet selection can be optimized with an evolutionary technique like genetic algorithm. A novel genetic algorithm that avoids revisits and employs a parameter-less self-adaptive mutation operator is developed. The results are compared with those obtained with CPLEX for small sized problems. We show that our model and optimization approach gives near optimal results for varied demand scenarios.