Robust Pricing and Production with Information Partitioning and Adaptation

Abstract

We introduce a new distributionally robust optimization model to address a two-period, multiitem joint pricing and production problem, which can be implemented in a data-driven setting using historical demand and side information pertinent to the prediction of demands. Starting from an additive demand model, we introduce a new partitioned-moment-based ambiguity set to characterize its residuals, which also determines how the second-period demand would evolve from the first-period information in a data-driven setting. We investigate the joint pricing and production problem by proposing a cluster-adapted markdown policy and an affine recourse adaptation, which allow us to reformulate the problem as a mixed-integer linear optimization problem that we can solve to optimality using commercial solvers. We also extend our framework to ensemble methods using a set of ambiguity sets constructed from different clustering approaches. Both the numerical experiments and case study demonstrate the benefits of the cluster-adapted markdown policy and the partitioned moment-based ambiguity set in improving the mean profit over the empirical model—when applied to most out-of-sample tests. This paper was accepted by J. George Shanthikumar, data science.

Joint pricing and inventory management under minimax regret

“…We focus on the joint pricing and inventory management for a single product type. One may extend our model to the multiple‐product setting, and study the joint pricing and ordering decisions for multiple substitutable products (e.g., Chen & Chen, 2018; Gao & Zhang, 2022; Lim et al., 2008; Perakis et al., 2022). In addition, while our model setting assumes that the parametric form of the demand model is known, a more interesting problem is to model the price–demand relationship with a more general functional form.…”

Redundancy allocation under state‐dependent distributional uncertainty of component lifetimes

“…(2020) for vehicle pre‐allocation, Perakis et al. (2022) for joint pricing and production, and ours for redundancy allocation. In particular, our redundancy allocation model has a structure of chance‐constrained optimization, which is distinct from the model structures of the above three papers.…”

“…We also emphasize that the cross‐deviation measure 4 used here enjoys advantages in characterizing the lifetime distributional information as compared with the mean absolute deviation employed in Wang and Li (2020), which is justified by our numerical experiments (Section 6). Remark There are several approaches that can be employed to form the above state‐dependent ambiguity set of component lifetimes using the SI $$\bm {\tilde{s}}\in \mathcal {S}_k, k\in [K]$$, such as K‐means clustering (Cheng et al., 2020), CART (Hao et al., 2020; Perakis et al., 2022), spectral clustering (Ng et al., 2001), hierarchical clustering (Sibson, 1973), and regression trees (Quinlan, 1986), per convenience. Also, the state probabilities $$p_k, k\in [K]$$ can be estimated via different approaches, for example, using the logistic regression that maps the SI to the probabilities for each state.…”

“…As for the DRO approaches, some existing studies use the event-wise ambiguity set proposed in Chen et al (2020) to leverage the side information, but these studies and ours focus on different application areas perspectively: Cheng et al (2020) for drone delivery scheduling, Hao et al (2020) for vehicle pre-allocation, Perakis et al (2022) for joint pricing and production, and ours for redundancy allocation. In particular, our redundancy allocation model has a structure of chance-constrained optimization, which is distinct from the model structures of the above three papers.…”

Inference on the Optimal Assortment in the Multinomial Logit Model

“…Apart from the intractable optimization solutions, the aforementioned works treated assortment planning as a deterministic process without accounting for the uncertainty induced by random input. Rusmevichientong and Topaloglu (2012) brought the robustness against perturbation into the scope of assortment optimization under the MNL model by considering the robust optimization approach (Bertsimas and Sim, 2004;Ahipaşaoglu et al, 2019;Chen and Sim, 2021;Chen et al, 2022a;Perakis et al, 2022;Zhu et al, 2022), where they aimed to find the optimal offer set that maximizes the worst-case expected revenue over an uncertain set of possible preference scores. However, the robust optimization is tailored to the worst-case scenario and will fail to quantify the uncertainty for general cases.…”