ABSTRACT
Most of the consumers relied heavily on e-commerce for products and services for the past few years due to the recent COVID-19 pandemic. This kind of an unexpected behaviour among the consumer society has taken every industry by surprise so that many industries have begun operating online and offline businesses to ensure future competitiveness. Firms introducing online sales are deplorably facing many challenges in terms of logistics and delivery processes, such as short lead times, flexible delivery, capacity of warehouse, and the production process for controlling carbon emissions. Keeping these challenges in mind, a sustainable dual-channel vendor-buyer supply chain model has considered for a controllable emission under fuzzy demand and energy consumption. The model deals with limitation on warehouse floor-space area, and the warehouse divides into two stages such as one for satisfying online orders and the other for satisfying offline orders. The demand rate and energy consumptions are treated as the trapezoidal fuzzy number, and we use the signed distance method to defuzzify the fuzzy joint expected total cost. The objective focuses on obtaining a trade-off between cost and emissions, thereby determining the optimal production-distribution strategy and a proper sustainable plan for handling both online and offline orders. The aforesaid scenario is mathematically formulated in the form of constrained non-linear programme (NLP) and derive a Lagrangean multiplier method to solve it. An iterative solution algorithm is designed, and for better illustration of the developed theory, numerical analysis is carried out followed by a wide discussion on the sensitivity analysis for various parameters. Our results indicate that the optimal solutions of the sustainable fuzzy model slightly fluctuate from the solutions of the sustainable crisp model. According to results, considering the uncertainty in the system is a crucial factor to achieve the economic and environmental sustainability of the production sector. The research reveals that the practitioners should be careful in accounting flexibility in the input factors demand and energy to tackle the uncertainties that always fit the real situation.