Linear carrot-and-stick: Compensation design with ordering delegation and demand updating

Delegating ordering to the salesforce leverages local market knowledge but complicates incentive alignment. Motivated by data from a major Amazon apparel seller, we study a Linear Carrot-and-Stick (LCS) scheme that couples a sales commission (“carrot”) with a leftover inventory penalty (“stick”). Using weekly SKU-level transaction data from June 2017 to May 2019, we observe that the adoption of LCS decreased the firm’s total shipments and sales relative to the prior Linear Pure-Commission Scheme (LPS). To interpret these patterns and offer design guidance, we develop a two-period principal-agent model in which the salesperson updates demand forecasts based on realized outcomes and also chooses the effort and places orders. We show that the optimal commission reflects the salesperson’s ability to convert effort into sales, while the penalty ratio balances overstocking liabilities with understocking opportunity costs, akin to the critical ratio in the newsvendor problem. To ensure that the salesforce utility remains competitive despite inventory penalties, we examine a utility protection mechanism, finding that higher values for both the components, carrot and stick, are essential for retaining a valuable person who faces attractive employment alternatives. A numerical study of the partner’s top-selling SKUs indicates that LCS can deliver a win-win outcome, improving both firm profitability and salesperson motivation compared to LPS. We further extend the analysis to information asymmetry, target-based demand updating, Bayesian demand updating, and a two-product setting, all of which widely confirm the robustness of our findings.