Is the online-offline buy-online-pickup-in-store retail strategy best among other product delivery strategies under variable lead time?

Every industry improves customer satisfaction by either preventing stockout situations or fulfilling the customer's demand by reducing lead time and variance of the lead time with several services offered. This study considers online selling, offline selling, and buy-online-pickup-in-store policies for selling products from retail stores. This study builds a characteristic relation between buy-online-pickup-in-store, backorder, and on-hand inventory by giving an exact total profit function instead of the expected profit function. The marginal values on lead time and variance of the lead time earn more exact outcomes for any retail strategy. The specific transportation cost for different retail strategies is considered and tested. This paper shows the analytical results which prove that the total profit of the sustainable supply chain is a convex function of both lead time and variance of the lead time. As different channel selling is crucial to any industry for increasing customer demand, the retailer sells their products by hybrid channel and advertises their products online to make them more famous. The model is solved through a classical optimization technique to get a semi-closed-form solution. In this method, it is possible to find out the optimum results for the decision variables separately by equating the first order partial derivative of the total profit with respect to the decision variables to zero and the global optimality by the Hessian matrix. A numerical experiment is conducted here, and the result shows that the supply chain system gives 14.48% more profit if advertisement policy is applied. The supply chain system gives 57.31% less profit and 72.72% less profit when only an online or offline channel is adopted, respectively. A sensitivity analysis is done for the managerial effects of cost parameters on the total profit.