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# A three echelon supply chain model with stochastic demand dependent on price, quality and energy reduction

• * Corresponding author: Santanu Kumar Ghosh
• While developing supply chain models, many researchers have shown great interest on how to reduce the consumption of non-renewable sources of energy, as non-renewable sources of energy is limited. The purpose of this paper is to formulate a three echelon supply chain model when the demand of items is assumed to be stochastically dependent on price, quality and reduction of energy. In the centralized model, suppler, manufacturer and retailer are the three members of the supply chain. The model is solved analytically to obtain optimal values of order quantity, unit price, promotional effort and amount of energy consumption which maximizes the profit function of the supply chain. Two decentralized models namely MR-Nash and MS-Nash have also been considered in a separate section. These two models have also been solved analytically to obtain the optimal solution of the decision variables. Three proposed models have been illustrated with a numerical example by considering exponential distribution of customer's demand. The sensitivity of the optimal solution revealed the appropriate channel strategy in case of decentralized scenario. It is speculated that when the manufacturer and the supplier collaborates, the profit difference is reduced by $39 \%$ than that of the MR-Nash.

Mathematics Subject Classification: 90B15.

 Citation: • • Table 1.  Optimal solutions for different scenarios with energy reduction

 Parameters Centralized Decentralized MR- Nash MS- Nash $p^*$ 1767.57 965.4 920.63 $u^*$ 516.89 480.87 450.23 $T^*$ 339.19 330.5 310.46 $Q^*$ 640.10 540.25 500.3 $\Pi_c$ 429211.0 - - $\Pi_{mr}$ - 256874.56 - $\Pi_{ms}$ - - 210456.7 $\Pi_s$ - 5214.5 - $\Pi_r$ - - 8795.34 $\Pi_T$ - 262089.06 219251.34
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