Abstract

Food-grain supply chains involve several activities such as procurement, processing, transportation, storage, and distribution. In the Public Distribution System (PDS) of India, these activities are closely connected because procured paddy has to be processed in rice mills before the milled rice can be stored and distributed to different demand locations. This study develops a dynamic Mixed-Integer Linear Programming (MILP) model for a four-stage food-grain supply chain consisting of procurement centres, rice mills, warehouses, and PDS distribution points. The model considers milling recovery, period-wise milling capacity, procurement availability, route activation, warehouse capacity, inventory balance, demand fulfilment, opportunity cost, and shortage penalty. Transportation costs are calculated from inter-node distances using the applicable Jharkhand Government transportation-rate structure.

The model is tested through computational experiments using the East Singhbhum network and is further examined using observed procurement-stage data and a calibrated downstream representation of the Seraikela-Kharsawan district network. For the East Singhbhum simulation, the total system cost decreases from INR 76,102,850.08 under the baseline allocation to INR 75,105,464.62 with the proposed MILP, giving a reduction of 1.31%. Sensitivity analysis further shows that PDS demand and transportation cost have relatively strong effects on total system cost, while paddy availability, milling capacity, and milling recovery affect both cost and systemic shortage over the tested ranges. For the Seraikela-Kharsawan network, the calibrated validation gives a reduction in total system cost from INR 7,813,080.15 to INR 7,114,689.99, corresponding to 8.94%, while maintaining the prescribed paddy throughput and zero shortage. The Stage-1 transportation calculation was also checked using the Modified Vogel’s Approximation Method (VAM), with a difference of 0.84% between the manual and MATLAB-based calculations. The results indicate that the proposed model can be used to evaluate food-grain flows, processing capacity, inventory, transportation expenditure, and PDS demand fulfilment in a multi-stage network.

Keywords

Rice milling, Public Distribution System, Transportation cost, Inventory management, Supply chain network, Jharkhand.

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