Optimization on dual-channel supply chain model with pricing decision and trapezoidal fuzzy demand under a controllable lead time

This paper considers a dual-channel supply chain with one vendor and multiple buyers in which (1) one channel is an offline channel where standard products are produced and shipped to the buyers and (2) the second channel is an online channel with the flow of customized products between the vendor and the online buyers/consumers. The first channel follows a vendor managed inventory with consignment stock (VMI-CS) agreement between the vendor and buyers. The supply lead time between the vendor and the buyer is considered controllable, at a cost. Two models are analyzed: (1) in the first model, the standard and customized product’s demand rate is assumed to be price and lead time-sensitive, and (2) in the second model, the demands are uncertain or ambiguous and are treated as a trapezoidal fuzzy number. It is reasonably complex to obtain analytical solutions. Hence, two algorithms are proposed to obtain the numerical solution with the objective of maximizing total profit. Numerical examples, sensitivity analysis, and managerial insights are given to test the model. Finally, conclusions and directions for future research are provided.