This paper deals with the co-ordination of a single producer, multi distributors and multi retailers for a supply chain management to get the maximum profit at minimum investment when shortages is permitted at the retailer‘s end and they are the partially backlogged. Most previous studies on supply chain have dealt with a moderately simpler chain with a single producer and a single buyer. The requirement of the producer is directly proportional to demand of the distributor, while the demand of the distributor is dependent on retailers’ requirement. This passes on rationally to the whole supply chain. The proposed model of this paper considers deteriorating items where the deterioration rate is considered as constant.

This paper derives a deterministic inventory model for deteriorating items with inventory dependent demand rate. This study develops an order level inventory model with single warehouse where shortages are allowed and it is completely backlogged. The planning horizon is finite. This paper shows that there exists a unique optimal cycle time to minimize the total inventory cost per cycle. Truncated Taylor’s series expansion is used for finding closed form optimal cycle time, optimal time to finish positive inventory and optimal total inventory cost per cycle. The numerical example is given to validate the proposed model. The sensitivity analysis of the solution with the changes of the values of parameters associated with the model has also been discussed.