The effect of promotional cost sharing on the decisions of two-level supply chain with uncertain demand

Abstract

In much of today’s competitive marketplace, consumers have the opportunity to choose where they spend their money based on their examination of a company’s corporate social responsibility. A company’s social reputation and its promotional efforts may influence consumer choice. Sustainable development is highly regarded by governments, experts, decision-makers and managers in organizations and two-level supply chains. This supply chain includes a manufacturer (acting as leader) and a retailer (acting as follower), both of whom face demand uncertainty. In this article, the cost of advertising is considered in two ways for the manufacturer and the retailer. In the first model, the retailer determines the optimal retail price and order quantity, and the manufacturer determines the optimal wholesale price and the promotional efforts value so that their profits are maximized. In the second model, the retailer determines the optimal retail price, order quantity, and promotional efforts value, and the manufacturer determines the optimal wholesale price. We will also study the impact of promotional cost sharing on the coordination of the supply chain and the issue will be further explained with numerical examples. Therefore, in this research, the simultaneous effect of increased advertising and value consumer surplus is studied We examine cases when the retailer is a provider of promotional cost and profit, when consumer surplus is directed toward the retailer, and when both retailer and manufacturer achieve higher profits than when the manufacturer is responsible for promotional cost and profit.

Appendix A

Calculate the consumer surplus:

$$ \begin{aligned} M & = \int_{0}^{{q_{\alpha } }} {\frac{x}{{2\rho_{\alpha } (A - bP_{\alpha } )}}dx} \\ M & = \frac{{q_{\alpha }^{2} }}{{4\rho_{\alpha } (A - bP_{\alpha } )}} \to P({\rm I})_{mkt} = \frac{A}{b} - \frac{{q_{\alpha }^{2} }}{{4\rho_{\alpha } bM}} \to P({\rm I})_{\hbox{max} } = \frac{A}{b} \\ CS_{\rm I} & = \left( {\frac{{(A - bP_{\alpha } )}}{b}} \right)\left[ {q_{\alpha }^{2} - 2\rho_{\alpha } (A - bP_{\alpha } )} \right] \\ {\text{N}} & = \int_{{q_{\alpha } }}^{{2\rho_{\alpha } (A - bP_{\alpha } )}} {\frac{{q_{\alpha } }}{{2\rho_{\alpha } (A - bP_{\alpha } )}}dx} \\ N & = q_{\alpha } - \frac{{q_{\alpha }^{2} }}{{2\rho_{\alpha } (A - bP_{\alpha } )}} \to P({\rm I}{\rm I})_{mkt} = \frac{A}{b} - \frac{{q_{\alpha }^{2} }}{{2\rho_{\alpha } b(q_{\alpha } - N)}} \to P({\rm I}{\rm I})_{\hbox{max} } = \frac{A}{b} \\ CS_{{{\rm I}{\rm I}}} & = \left( {\frac{{(A - bP_{\alpha } )}}{b}} \right)\left[ {q_{\alpha } - q_{\alpha }^{2} - \rho_{\alpha } (A - bP_{\alpha } )} \right] \\ {\text{CS}}_{Total} & = CS_{\rm I} + CS_{{{\rm I}{\rm I}}} \\ {\text{CS}}_{Total} & = \left( {\frac{{(A - bP_{\alpha } )}}{b}} \right)[q_{\alpha } - \rho_{\alpha } (A - bP_{\alpha } )] \\ \end{aligned} $$