Order placing and delivery always play a significant role in any business industry. Nowadays, most customers want useful products at their doorstep without visiting any retail store. In this current study, an advanced dual-channel supply chain model is constructed for a single product with two players. Customers can order online or offline from the retail store. In contrast, retailers use only offline mode to take the product from the manufacturer, and retailers charge a different amount for delivery. To optimize profit and satisfy the consumers, retailers only provide a free transportation service when customers order a certain quantity. If customers order less than the desired amount, a transportation charge will be applied to the customers. Contrary to the existing research, demand for the products varies with the selling price online and offline and is also affected by the free home delivery service. Manufacturers use a single-setup multi-delivery (SSMD) transportation strategy to enrich the system's profit. To make the study more applicable, all unit costs are considered fuzzy. Signed-distance defuzzification technique is adopted to defuzzify the fuzzy values. Finally, the total profit of the supply chain is optimized along with the optimized value of the decision-making variable through an uncertain optimization technique. Numerical experiments are carried out along with sensitivity analysis to show the applicability and optimality of this study. Though the crisp data set provided a 0.72% better result compared to the fuzzy data set, but fuzzy data set provided a more realistic result. Numerical results prove that the home delivery service provided 14.59% better profit. Finally, it can be stated that the home delivery policy with some charged amount based on ordered quantity is the best retailing strategy for the dual-channel supply chain.
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