Price differentiation and inventory decisions in a socially responsible dual‐channel supply chain with partial information stochastic demand and cannibalization

Corporate social responsibility (CSR) has received much of the attention in supply chain management, in particular the pricing decisions. Most existing models that enable CSR integration into pricing decisions in a supply chain context assume deterministic demand and focus on a single distribution channel. Despite the fact that dual‐channel supply chain (DCSC) has received popularity, most pricing decisions models in DCSC assume fixed and deterministic market share distribution between channels, and no demand leakages (cannibalization). This paper addresses these gaps by proposing a CSR enabled DCSC model pricing in which the demand is considered to be stochastic and market share distribution between channels in DCSC is optimally determined using a differentiation price, and the impact of demand leakages is also taken into consideration. Unlike existing studies, which only enable pricing decisions due to deterministic demand consideration, comprehensive DCSC models are proposed that provide joint decisions framework on CSR investment, pricing, and inventories. We have also considered the extension of the demand scenario when the distribution of demand is unknown. The two most common coordination schemes, the centralized (integrated) and the decentralized coordination is explored for the three demand situations: (i) deterministic demand; (ii) stochastic with full information; and (iii) stochastic with partial information. We are able to find analytical (closed‐form) solutions for most demand situations. The centralized coordination performed better compared to the decentralized for all demand scenarios. The models are benchmarked when the demand is stochastic with known and unknown distributions, as well as, the case of the deterministic demand. A detailed numerical analysis is also presented in order to study the impact of using the price differentiation for market segmentation, the demand leakage, and partial knowledge on the stochastic demand on the players’ decisions and revenues in the supply chain.