An MINLP model to support the movement and storage decisions of the Indian food grain supply chain

Abstract This paper addresses the novel three stage food grain distribution problem of Public Distribution System (PDS) in India which comprises of farmers, procurement centers, base silos and field silos. The Indian food grain supply chain consists of various activities such as procurement, storage, transportation and distribution of food grain. In order to curb transportation and storage losses of food grain, the Food Corporation of India (FCI) is moving towards the modernized bulk food grain supply chain system. This paper develops a Mixed Integer Non-Linear Programming (MINLP) model for planning the movement and storage of food grain from surplus states to deficit states considering the seasonal procurement, silo capacity, demand satisfaction and vehicle capacity constraints. The objective function of the model seeks to minimize the bulk food grain transportation, inventory holding, and operational cost. Therein, shipment cost contains the fixed and variable cost, inventory holding and operational cost considered at the procurement centers and base silos. The developed mathematical model is computationally complex in nature due to nonlinearity, the presence of numerous binary and integer variables along with a huge number of constraints, thus, it is very difficult to solve it using exact methods. Therefore, recently developed, Hybrid Particle-Chemical Reaction Optimization (HP-CRO) algorithm has been employed to solve the MINLP model. Different problem instances with growing complexities are solved using HP-CRO and the results are compared with basic Chemical Reaction Optimization (CRO) and Particle Swarm Optimization (PSO) algorithms. The results of computational experiments illustrate that the HP-CRO algorithm is competent enough to obtain the better quality solutions within reasonable computational time.