Optimal Capacity and Price Designs Under Ex Ante and Ex Post Theft

Problem definition: Internal theft poses a significant challenge in retail firms’ operations. Owing to a lack of effective monitoring tools, a firm cannot observe every action in daily operations of its employees, providing opportunity for wrongdoing, such as capacity and cash stealing. As a result, a common practice is to increase the price of goods to offset the loss in revenue due to the increasing threat of theft. However, we show that such practices are not optimal. Methodology/results: We model the internal theft problem in retailing as a principal-agent model, where the principal (firm) contracts an agent (retail manager) for capacity planning and daily sales. The agent is subject to moral hazard and may steal the capacity (procurement budget or company asset) before demand realization (ex ante stealing) or steal the sales revenue after demand realization (ex post stealing). We solve for the optimal capacity, price, and agent’s commission decisions to maximize the principal’s utility. We find that capacity and price decisions are not monotone in terms of the severity of moral hazards. In particular, the principal should first decrease and then increase (increase and then decrease) the price (the capacity) when ex post stealing becomes more prevalent. We also provide an optimal commission scheme to the agent, which is simple and can be easily implemented. Finally, we investigate the sensitivities of price and capacity decisions to demand uncertainties in the presence of moral hazard. Managerial implications: Simply increasing retail prices and shifting the margin to consumers to combat loss in revenue caused by internal theft can amplify the agency problem in some scenarios because it leads to a significant loss in demand and insufficient commission to the agent. Retail firms should instead focus on jointly optimizing capacity and price and providing their employees with appropriate commissions. Funding: F. Tian acknowledges funding support from Hong Kong Research Grants Council General Research Fund [Grant 17503424] and the HKU Seed Fund for PI Research—Basic Research [Grant 2202100678]. Ruiting R. Zuo acknowledges funding support from Guangzhou Municipal Science and Technology Project [Grant 2024A04J4546], Guangzhou Municipal Education Bureau University Research Project [Grant 2024312314] and the Guangzhou-HKUST(GZ) joint funding program [Grant 2024A03J0630]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2025.0024 .