Stochastic choice-based discrete planning is a broad class of decision-making problems characterized by a sequential decision-making process involving a planner and a group of customers. The firm or planner first decides a subset of options to offer to the customers who, in turn, make selections based on their utilities of those options. This problem has extensive applications in many areas, including assortment planning, product line design, and facility location. A key feature of these problems is that the firm cannot fully observe the customers’ utilities or preferences, which results from intrinsic and idiosyncratic uncertainties. Most works in the literature have studied a specific type of uncertainty, resulting in customized decision models that are subsequently tackled using ad hoc algorithms designed to exploit the specific model structure. In this paper, we propose a modeling framework capable of solving this family of sequential problems that works for a large variety of uncertainties. We then leverage an approximation scheme and develop an adaptable mixed-integer linear programming method. To speed up the solution process, we further develop an efficient decomposition approach. We show that our solution framework can yield solutions proven to be (near-)optimal for a broad class of problems. We illustrate this by applying our approach to three classical application problems: constrained assortment optimization and two facility location problems. Through extensive computational experiments, we demonstrate the performance of our approach in terms of both solution quality and computational speed, and we provide computational insights. In particular, when we use our method to solve the constrained assortment optimization problem under the exponomial choice model, it improves the state of the art. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: Y. H. Lin was supported by the National Natural Science Foundation of China [Grant 72288101]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0694 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0694 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The choice-based facility location (CBFL) problem arises in various industrial and business contexts. The problem stands on a decentralized perspective: Companies set up chains of facilities, and customers determine from which chain or facility to seek service according to their own preferences. Essentially, customer preferences or choices play a key role in characterizing various CBFL problems, which differ mainly in the models or rules used to characterize the choice. Consequently, a large number of formulations appear and are often solved by dedicatedly designed approaches in the literature. Such a situation significantly complicates practitioners’ decision-making process when they are facing practical problems but are unsure which ad hoc model is suitable for their cases. In this article, we address this dilemma by providing a unified modeling framework based on the concept of preference dominance. Specifically, we conceptualize the choice behavior as a sequential two-step procedure: Given a set of open facilities, each customer first forms a nondominated consideration set and then splits the buying power within the set. Such an interpretation renders practitioners high modeling flexibility as they can tailor how preference dominance is constructed according to their specific contexts. In particular, we show that our model can represent several streams of CBFL problems. To support our model’s applicability, we design an efficient exact decomposition algorithm. Extensive computational studies reveal that although the algorithm is designed for a general purpose, it outperforms most approaches that are tailored for ad hoc problems by a large margin, which justifies both the effectiveness and the efficiency of the unified framework. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0366 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0366 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .