Deciding on the number and configuration of distribution centers (DC) is one of the most impactful decisions that create a pathway for competitiveness and responsiveness. In this research, the allocation of distribution center problem is studied under demand uncertainty. The purposes of this study were to specify the optimal number and allocation of distribution centers out of candidate ones. This paper proposes a three-step model with probabilistically distributed demand where the coefficient of variation is the measure of risk along with the enforced level of service metrics that are focused on responsiveness which aligns with real-world problems and the considered company, working as a backward linkage of the fast fashion industry. To consider uncertainty, a set of scenarios for customer demands is created based on the Monte Carlo simulation. The best network structure is identified by optimizing each scenario and detecting which configuration has been observed the highest amount of times. Furthermore, the uncertainty of demands creates variations of the optimized total cost which is imposed on the logistical system. Notably, this research has been done in one of the oldest textile yarn distribution firms in Bangladesh.