An effective heuristic for multi-period multi-foodgrain inventory transportation problem in India

ABSTRACT This study investigates a storage and inter-state transportation problem of foodgrains faced by Food Corporation of India (FCI) for the Indian public distribution system. FCI carries out the activities of procurement, storage and transportation of foodgrains in different states of India to meet the monthly demand of each state for different foodgrains without shortages. Due to mismatch in procurement, demand and available storage capacity among the states, the problem is to find the optimal quantity of each foodgrain to be stored in different type of warehouses of all states and transportation plan for movement of each foodgrain between the warehouses. The problem is formulated as a mixed integer linear programming problem for minimizing the total relevant costs with an implicit consideration of reduction of the wastage of foodgrains due to storage in open space. We propose a heuristic-based algorithmic solution approach exploiting the unique structure of the problem and devising activity-based decision rules. Extensive computational experimentation is carried out by randomly generating the problem instances using real data. A lower bounding scheme based on linear relaxation is devised to compare the performance of the proposed solution approach. With the average solution gap of 6.61% with respect to the lower bound, the proposed solution approach is found effective and efficient compared to Cplex for practical size problem instances.