Integrated three layer supply chain inventory model for price sensitive and time dependent demand with suggested retail price by manufacturer

Document Type : Research Paper


1 Department of Mathematics, Dr Harisingh Gour Vishwavidyalaya, Sagar MP India

2 Ujjain Engineering Collage Ujjain (M. P.) India

3 Department of Management Studies (DOM), Indian Institute of Technology (IIT), Madras, India

4 Department of Mathematics, Ujjain Engineering Collage, Ujjain M.P. India


This paper presents an integrated three layer supply chain policy for multi-channel and multi-echelon consisting manufacturer, distributors and retailers as  supply chain members. The demand of retailers end is considered as linear function of  time and retail price. The average net profit function per unit  time is derived for each  supply chain member which are based on demand of retailer's  end. Since  holding cost of goods/inventory is expensive in developed areas, we have introduced a new concept  to share holding cost among distributors and retailers. We have  optimized lot size, retailing price and replenishment time interval for retailers. We have also optimized initial inventory level and wholesale price for distributors and manufacturer respectively. This  study is performed in two different  categories one is decentralized and other  is centralized scenario. The profit function of each supply  chain members has been derived and shown as a concave function with respect to decision variables. More over propositions and results are made to illustrate the proposed model and we have sensitive  analyzed it with numerical example.