LAUSR

We consider a production inventory problem of a deteriorating product that begins to deteriorate immediately on production. Two models of three echelon supply chain are developed whose rate of demand, production and deterioration are assumed to be constant. The second model allows backlogging of the demand, while the first model does not allow backlogging. In both models, the producer's cycle starts with zero stock and the production continues till the stock level reaches an optimal value. There will be demand and deterioration and consequently stock level falls to zero during the non-production phase. The demand subsequently received is backordered in the second model and a fraction of it is met by restarting the production process. Optimal lot sizes of distributor and retailer is identified within each of the producer's cycle. A numerical example is illustrated. Comparison between the models shows that backordering reduces the total supply chain cost.