Benders decomposition approach with heuristic improvements for the robust foodgrain supply network design problem

We investigate the problem of designing a supply chain for foodgrains distribution under uncertainty, which is motivated from the Indian public distribution system (PDS). Initially, a deterministic mixed-integer programming (MIP) model is formulated to determine the strategic decisions of storage and transportation capacity hiring and the tactical decisions of procurement, inventory, and transportation planning to minimise the total cost over a finite planning horizon. The storage capacity hiring decision is characterised by the options of hiring under long-term contract for the entire planning horizon and from spot market for individual period. Next, we extend the model to consider the uncertainties associated with supply, demand and procurement parameters, and propose a scenario-based robust optimisation model to minimum the total relative regret. An MIP-based fix-and-optimise heuristic is proposed to efficiently solve the deterministic equivalent problem of each scenario. To solve the robust model, we implement Benders decomposition algorithm (BDA) with several heuristic techniques including warm-start strategy to build an initial feasible solution, trust region for master problem, and logical inequalities to accelerate the performance of the BDA. Finally, the effectiveness of the solution approach is demonstrated through extensive computational experiments using the test instances simulating the Indian PDS.