Optimal and heuristic base-stock levels and rationing policy for a divergent supply chain

Abstract

A critical problem often faced by distribution centres that hold finished-good inventory is inventory rationing. A rationing problem arises when the available resources cannot satisfy all demand, indicating a shortage at the distribution centre. We consider a divergent two-stage supply chain with one distributor and four retailers. Retailers face external demand, and they in turn place the replenishment demand to the distributor. The unsatisfied demand is assumed to be backlogged at both distributor's and retailer's ends. Our study focuses on determining a rationing policy and base-stock levels (assuming order-up-to level policy), where the available stock at the distributor is rationed among the successors (i.e. retailers) in case of shortage, with the objective of minimising total holding and backlog costs in the supply chain. We present a mathematical programming model, which can give optimal solutions in the class of base-stock policy, and a genetic algorithm-based heuristic methodology for determining the base-stock levels and rationing fractions.