Optimizing a robust capital-constrained dual-channel supply chain under demand distribution uncertainty

Dual-channel supply chain (DCSC) is one type of patterns that combines offline channel and online channel in a common market. It is known that demand plays an important role in DCSC. In the literature, however, the demand is assumed to be deterministic or stochastic with completely known probability distribution. In contrast, this paper addresses the uncertain demand from a new perspective by considering the distribution uncertainty, and the uncertainty source comes from subjectivity. When only partial demand distribution information is available, this paper introduces a new uncertainty distribution set to characterize the ambiguous demand distribution. Based on the proposed uncertainty distribution set, a novel distributionally robust bilevel optimization modeling framework is developed for our capital-constrained DCSC. In order to address the upstream manufacturer’s capital constraint, three financing strategies, i.e., bank financing, trade credit and hybrid financing (a combination of bank and equity financing) are considered. An analytically tractable method is developed to obtain the corresponding robust equilibrium solutions under the three financing strategies. Numerical analysis are conducted to demonstrate how the demand ambiguity and the equity ratio affect the manufacturer’s equilibrium financing strategy. The numerical results show that the change of the uncertainty perturbation parameters can change the manufacturer’s financing strategy. When the values of uncertainty perturbation parameters are relatively small, the equilibrium financing strategy is either trade credit or hybrid financing. When the values of uncertainty perturbation parameters are medium or large, bank financing is the equilibrium financing strategy. Also, the manufacturer’s equilibrium financing strategy is affected by the equity financing ratio. When the equity financing ratio is small, the equilibrium financing strategy is either trade credit or hybrid financing. When the equity financing ratio is medium or large, the equilibrium financing strategy is always hybrid financing. The demand uncertainty can affect the manufacturer’s financing strategy. As a result, the capital-constrained manufacturer should take into account the demand uncertainty to make her informed financing decisions. • The possibility distribution information of uncertain demand is partially available. • A uncertainty distribution set is presented to characterize ambiguous distribution. • A robust bilevel optimization model is developed for a capital constrained DCSC. • Numerical analysis is conducted to validate the proposed optimization method.