Predictive Production-and-Service Planning: Ambiguity Aversion with Performance Guarantees

We consider a two-stage joint production and service planning problem under demand ambiguity. The product-service provider receives a fixed amount of revenue from the recipient in advance (first-stage), and is committed to fulfill all the demands realized over a specific period (second-stage). The provider aims to determine the portfolio of products with the associated service levels and the capacity to maximize the expected total profit. We study the problem in a data-driven setting assuming the historical information on demand and the associated covariates are available, where the service decision is itself a key covariate for demand. In order to capture the effect of demand correlation and variance-heterogeneity across products and the effect of service dependency under demand ambiguity, we construct a predictive ambiguity set leveraging seemingly unrelated regression (SUR) estimated with feasible generalized least squares (FGLS), which treats the service level as a regressor and addresses the heteroskedasticity. We then develop a decision-dependent two-stage distributionally robust optimization (DRO) model. Operationally, we identify that the developed predictive DRO model can be reformulated as an empirical counterpart under the predicted demand distribution regularized by a perceived shortage cost as the shadow price for ambiguity aversion. Exploiting this structure, we analyze the ambiguity-averse operational properties and risk exposure in terms of worst-case performance sensitivity. Statistically, our approach enjoys finite-sample performance guarantee and asymptotic consistency under several regularity conditions. Computationally, the proposed model can be reformulated as a mixed-integer conic program that enjoys an appealing structure for optimization. Finally, sufficient numerical experiments demonstrate the effectiveness of the proposed approach. This paper was accepted by J. George Shanthikumar, data science. Funding: S. M. Wang is supported by the National Natural Science Foundation of China [Grants 72471224, 72171221, 71922020, and 71988101], the Fundamental Research Funds for the Central Universities [Grant UCAS-E2ET0808X2], and a grant from the MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS. F. Saldanha-da-Gama and S. M. Wang are also jointly supported by the President’s International Fellowship Initiative [Grant 2025PVA0080] of the Chinese Academy of Sciences (CAS). S. Y. Wang is supported by the National Natural Science Foundation of China [Grant 71988101]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.00608 .