Optimal Sales Promotion in a Supply Chain Using Consignment Contract under Stochastic Demand

Sales promotion is getting more and more prosperous in Chinese cross-border e-commerce platforms where the demand is uncertain. However, most existing literature on promotion strategies is focusing on deterministic demand. In this paper, we propose a game-theoretical model under multiplicative stochastic demand to investigate the pricing, inventory quantity and sales promotion strategies for a supply chain which is consisted of one cross-border distributor and one capital-constrained retailer under a consignment contract. We obtain the equilibrium outcomes under stochastic demand, and find that the optimal price and promotion investment depend on demand uncertainty under endogenous inventory decisions. With exogenous unlimited inventory, the retailer prefers owing promotion right when the elasticity of price and promotion is small enough and its capital is sufficient, while the distributor always prefers to control sales promotion. With endogenous inventory quantity, the sensitivity of demand to price is influence by the demand uncertainty. The retailer prefers to decide the promotion when the price-elasticity is small, while the distributor prefers to decide the promotion under large promotion-elasticity. And the intensity of optimal sales promotion made by retailers may be stronger than that when the distributor owns the promotion right, which depends on the elasticity of price and promotion. More importantly, it is always better for consumers when the distributor reserves the promotion right as a lower optimal retailing price is offered.