A multi-period inventory transportation model for tactical planning of food grain supply chain

•Presents an inventory-transportation model for cost minimization of food grain supply chain.•Incorporates the intermodal shipment, multi-period and novel vehicle preference constraints into the formulated MINLP model.•Propose the variant of Max-Min Ant System algorithm called Improved Max-Min Ant System (IMMAS) to solve the model.•Computational results and statistical analysis demonstrate the efficacy of proposed algorithm.•Sensitivity analysis of the model based on three parameters is performed.

The food grain supply chain problem of the Public Distribution System (PDS) of India is addressed in this paper to satisfy the demand of the deficit Indian states. The problem involves the transportation of bulk food grain by capacitated vehicles from surplus states to deficit states through silo storage. A mixed integer non-linear programming (MINLP) model is formulated which seeks to minimize the overall cost including bulk food grain shipment, storage, and operational cost. The model incorporates the novel vehicle preference constraints along with the seasonal procurement, silo storage, vehicle capacity and demand satisfaction restrictions. The management of Indian food grain supply chain network is more intricate and difficult issue due to many uncertain interventions and its chaotic nature. To tackle the aforementioned problem an effective meta-heuristic which based on the strategy of sorting elite ants and pheromone trail updating called Improved Max-Min Ant System (IMMAS) is proposed. The solutions obtained through IMMAS is validated by implementing the Max-Min Ant System (MMAS). A sensitivity analysis has been performed to visualize the effect of model parameters on the solution quality. Finally, the statistical analysis is carried out for confirming the superiority of the proposed algorithm over the other.