A mathematical model and solution methods for rail freight transportation planning in an Indian food grain supply chain

This paper addresses the rail transportation of food grains undertaken by Food Corporation of India (FCI) to meet the requirements of the food security programme called Public Distribution System (PDS). The research focuses on improving the allocation of railway rakes transporting food grains to a set of storage warehouses. A penalty factor based approach is adopted to represent the considerations in transportation planning and three penalty factors such as rake penalty factor, weekly penalty factor and capacity utilization penalty factor are introduced for the purpose. The single source - multiple destination problem is formulated and solved using exact method to minimize the sum of these three penalty factor values, termed total penalty. Further, a heuristic named optimum rake allocation algorithm is developed and tested using a set of 35 problem instances. The proposed heuristic is found to be highly efficient in terms of solution quality and computation time. A case study of FCI Kerala Region is also carried out to validate the formulated model and the proposed heuristic. The work provides valuable insights into the practical issues encountered in rail freight transportation planning and proposes an effective solution methodology to address them.