Spillover Effect Matters: A Multiproduct Newsvendor-Like Model With Pay-Per-Click Advertising

Pay-per-click (PPC) advertising has become a dominant tool for e-tailers to increase product exposure and boost sales. This study investigates a multiproduct newsvendor-like problem that jointly optimizes advertising budget allocation and order quantity decisions. A key feature of the problem is the consideration of the spillover effect of PPC advertising, where the demand for a product depends not only on its own ad clicks, but also on those of related products. We introduce a linear demand function to capture this dependence and validate its predictive power using real-world data. The theoretical analyses reveal that the spillover effect leads to nontrivial interactions between advertising and ordering decisions, while also amplifying demand uncertainty and complicating the computation of the optimal solutions. To address these challenges, we consider two heuristic methods. The first follows the common practice of neglecting the spillover effect, while the second simplifies it by approximating random ad clicks with their mean value. Numerical experiments demonstrate that the first heuristic can lead to substantial performance loss (up to 28.72%), whereas the second yields near-optimal solutions with performance loss within 1%. We further conduct robustness tests with respect to ad-click distributions, market conditions, and ad-click uncertainty to evaluate the performances of both heuristic methods under different scenarios. A sensitivity analysis to assess the impact of changing key parameters (e.g., the coefficients of spillover effects and advertising budget) is also developed to provide more managerial insights.