Solving multi-region multi-facility inventory allocation and transportation problem: A case of Indian public distribution system

- We present foodgrain distribution problem for public distribution system in India.
- MILP model is formulated to minimize total annual relevant costs.
- A decomposition based heuristic solution approach is proposed for the problem.
- The factual secondary data is used to generate problem instances.
- Computational experiments reveal efficiency of the proposed solution approach.

In this paper, we study an inventory allocation and transportation problem in a supply chain consisting of multiple storage facilities (warehouses) located in different regions of a large geographic area, which is motivated by the case of the Indian public distribution system. The procurement in each region is known and the item procured within a region needs to be allocated for storage in the warehouses of the same region. The demand of each region is satisfied by the warehouses located in the respective regions. Consideration of region-wise aggregated demand/procurement over multiple facilities located in each region makes the proposed study different from the existing literature. There is a mismatch in procurement, demand, and available storage capacity of warehouses across all the regions. Therefore, the problem is to determine an optimal plan for holding inventory at different storage facilities and to satisfy the demand of all regions without shortages by transporting items between different storage facilities. A mixed integer linear programming model is formulated to minimize the total relevant costs over a finite planning horizon. A heuristic devising activity based decision rules is proposed to solve the problem by decomposing the problem into sub-problems. The performance of the proposed approach is compared with the exact solutions obtained using Cplex for several problem instances. The results of the computational analysis reveal that the proposed solution approach is computationally efficient and gives good quality solutions with an average cost deviation from the optimal solution of less than 6%.