Impact of risk levels on optimal selling to heterogeneous retailers under dual uncertainties

Consider the optimal selling problem of a supplier who sells the same product to two competing retailers under two types of uncertainty—the selling costs of retailers and external demand. The confidence level is used to characterize the risk caused by the two uncertainties and the profits of the participants in the supply chain channel. Our results demonstrate that higher risk levels correlate with lower belief-degree costs of the two retailers and higher belief-degree sizes of the market. For the vertically integrated channel, the supplier always supplies a larger quantity to the retailer with the low belief-degree cost than to the other retailer. Whereas, for the decentralized channel, the optimal selling decision of the supplier sometimes violates the volume ranking suggested by the quantities of the vertically integrated channel, i.e., when the belief-degree cost differences between the two retailers are not significant and the competitive intensity is high, the supplier supplies more units of the product to the retailer with the high belief-degree cost than to the other retailer. Furthermore, a decrease in the risk borne by the channel or an increase in the competitive intensity often reduces the quantities supplied to the retailers. However, in some cases, increased risk or intense competition increases the quantity supplied to the retailer with the low belief-degree cost or to the other retailer. Finally, we design a contract menu of two-part tariffs with quantity controls such that the optimal quantities supplied and retailer profits are the same for the relaxed and original models in the decentralized channel