Multiproduct newsvendor with cross-selling and narrow-bracketing behavior using data mining methods

Behavioral studies have pointed out that in the face of two or more decision tasks, people tend to consider decision tasks separately and show narrow-bracketing characteristics, deviating from the rational decision maker’s overall consideration of multiple task combinations. We construct multiproduct newsvendor models with cross-selling under two dimensions: rational or narrow-bracketing newsvendors, with budget constraints or not. We first provide conditions for optimal order quantities, and obtain analytical results for model comparisons under a special case. We then examine the impacts of the cross-selling effect between products on decisions and profits across different models through numerical analysis. We further develop decision rule heuristics for the decision sequence of narrow-bracketing newsvendor with a budget constraint by employing classic data mining methods (i.e., Apriori and C4.5 algorithms) for the two-product settings. We find that: (1) The narrow-bracketing newsvendor orders no more product types than the rational newsvendor in the presence of cross-selling effects among products when there is a budget constraint. (2) In a complementary two-product setting for the rational or narrow-bracketing newsvendors, as the cross-selling effect caused by the shortage of one product increases, the optimal order quantity of this product increases, and the optimal order quantity of the other product decreases, leading to lower expected profits for both products, regardless of the budget constraint condition. (3) For the narrow-bracketing newsvendor with two complementary products and budget constraints, the product with lower cost or higher active cross-selling effect should be ordered first, and the product cost has higher priority in most cases. Robustness checks and managerial implications are also discussed.