Managing product variety with advance selling and capacity restrictions

In this research we analyze the impact of advance selling with price discount on a firms׳ ability to maximize the expected profit. The production environment of the firm is characterized by short selling cycle, multiple products, demand variability, and capacity restrictions. The advance orders are randomly distributed with the parameters dependent on the discount levels under advance selling. The advance orders are used to update the demand forecast of selling season, and are delivered at the start of the selling season. The problem is modeled as a three-stage, stochastic non-linear programming problem. We derive the concavity of the problem under customers willingness to buy in advance. Our solution methodology comprises the variance reduction technique of 'Antithetic Variates' that gives credible value of price discount levels for different sets of demand values. We also provide sensitivity analysis of the problem parameters to derive insights into the behavior of the expected profit, and the benefits due to advance selling under capacity restrictions.