Smarter Choices Under Uncertainty: A Unified Framework for Planning with Imperfect Information
Gerardo Berbeglia and his co-authors latest research introduces a powerful framework for solving what’s known as stochastic choice-based discrete planning problems.
The Challenge of Customer Choice and Business Planning
When businesses design product lines, plan retail assortments, or decide where to open new facilities, they must consider how customers will respond to the options offered. But customer choices are inherently uncertain—shaped by individual preferences and external factors that are rarely fully known in advance. This creates a problem for planners: how to make smart decisions today when customer behavior tomorrow is unpredictable?
Gerardo Berbeglia and his co-authors tackle this challenge head-on. Their latest research introduces a powerful framework for solving what’s known as stochastic choice-based discrete planning problems. These problems are widespread in business contexts where firms must select from a finite set of options—products, store locations, price points—without knowing precisely how customers will react.
A Unified Model for Diverse Decision Problems
What sets this work apart is its scope and flexibility. Most past studies developed highly specialized models tailored to a specific type of uncertainty or choice behavior. Berbeglia’s team instead builds a unified model that can accommodate a broad range of uncertainties—both intrinsic (like distance or price) and idiosyncratic (such as individual taste). This makes their framework applicable to a wide variety of settings, from assortment planning to facility location and pricing.
The key innovation is a robust approximation scheme that uses scenario sampling to convert uncertain, probabilistic customer behavior into a solvable mathematical program. Specifically, the researchers translate the original stochastic problem into a mixed-integer linear program (MILP)—a format that can be handled by commercial solvers like Gurobi, albeit with high computational demands.
To keep the problem tractable, especially at large scale, the authors develop a customized algorithm called sampling-based Benders decomposition (SBBD). This advanced technique decomposes the planning problem into two parts: a “master problem” for the business planner and a “subproblem” for simulating customer choices. It allows the model to generate near-optimal solutions efficiently, even when dealing with thousands of possible customer scenarios.
Solving Assortment and Location Problems at Scale
To showcase the framework’s versatility, the authors apply it to three classical business problems:
- Assortment Optimization: A retailer must choose a limited number of products to display, aiming to maximize expected revenue given uncertain customer preferences. Their method outperforms existing heuristics, especially under complex choice models like the “exponomial” model where customer utility follows non-standard distributions.
- Facility Location and Pricing: A service provider must decide where to open facilities and what prices to charge, given that customers are spread out geographically and prefer nearby or cheaper options. The model accounts for both location decisions and discrete pricing choices, leading to better demand capture and revenue.
- Market Share Maximization: A company wants to place new outlets to maximize its share against a competitor, taking into account how service quality and customer proximity influence choices. The researchers show how even when rewards are uncertain and depend on customer preferences, their framework still delivers strong results.
Across these applications, the SBBD method consistently achieves high-quality solutions and dramatically improves computation times compared to state-of-the-art benchmarks. It also provides statistical estimates of solution quality, giving decision-makers confidence in the outputs.
Analytics Innovation with Real-World Impact
This work demonstrates how advanced analytics—specifically, optimization under uncertainty—can bring clarity to complex decision environments. The research provides a rare blend of mathematical rigor and practical utility, offering a blueprint for more resilient and data-informed planning in retail, logistics, and service operations.
For business leaders, the key takeaway is that better decision-making under uncertainty doesn’t require sacrificing accuracy or scale. With the right modeling and computational tools, it is possible to plan more confidently—even when customer behavior is only partially understood.
