Optimal Advertising Budget Allocation in Luxury Fashion Markets with Social Influences: A Mean-Variance Analysis

Optimizing advertising budget allocation in the luxury fashion industry is an important problem. In this study, motivated by real-world practices, we consider a luxury fashion firm serving a conspicuous market consisting of two groups of consumers who influence one another. We investigate the optimal customer portfolios and budget allocation problem using the mean-variance (MV) framework. Under the basic model in which all budget must be spent, we identify different scenarios and propose an algorithm to construct the MV efficient frontier for each scenario. Interestingly, different from the classic investment portfolio problem, we reveal that: (i) not all budget allocations between the two groups of consumers are MV efficient, which means that the efficient frontier is not continuous; (ii) in the presence of social influence, diversification of customer portfolio does not always lead to a smaller variance, which counterintuitively means that focusing on a single consumer group can reduce risk. We also prove that to maximize expected profit, the optimal strategy is to allocate all advertising budget to one group of consumers only (i.e., a polarized strategy). We illustrate analytically, the importance of identifying the right scenario for budget planning. Finally, we examine the budget saving strategy in the extended model and uncover that the respective range of efficient solutions is smaller than the one under the all budget spending strategy. This shows that the budget saving strategy offers less flexibility for MV efficient budget allocation than the all budget spending strategy.