A distinguishing factor between textbook optimization problems and their real-world counterparts is the necessity of exploring multiple alternative formulations. In this study, I demonstrate the effectiveness of a multi-modeling approach by examining three real-world problems: the Cutting Stock Problem (CSP), the Unit Commitment Problem (UCP), and the Warehouse Storage Space Problem (WSSP).
For the CSP, I investigate both Bin-Packing and Column Generation models. For the UCP, I analyze Mixed Integer Programming (MIP) and Pseudo-Analytical models. Finally, for the WSSP, I evaluate both Continuous and Discrete models.
Practical applications reveal that embracing a multi-modeling approach significantly expands the arsenal of solving techniques, effectively addressing multiple functional requirements and criteria. Furthermore, it facilitates the delivery of multiple optimal or near-optimal solutions, which is crucial for the end-user's decision-making process.

We consider the service network design problem (SND). SND-like problems are essential to the operation and the design of supply chain network of online retailers such as Amazon. SND is a well studied problem and is known to be difficult to solve exactly at scale. In this work, we start with a simple decomposition approach that separates the problem into two stages of topology design and timing optimization. Using this decomposition approach we obtain lower bounds and upper bounds on the solutions of the SND problem, however gap between the two bounds could be large. To address this issue, we introduce a family of cuts, called the time-window cuts, to provide the topology design problem with partial timing awareness. We experiment on a family of publicly available service network design instances (Boland et al. 2017), and a class of large instances arising in operations at Amazon. Our experiments show that adding time window cuts increases the quality of the decomposition significantly for both.

Any real-world service network faces uncertainty from many sources. These uncertainties must be accounted for in day-to-day execution planning, but also in longer-term network planning. Tactical day-to-day planning typically has fewer degrees of freedom, sometimes reducing the complexity of uncertainty modeling. In contrast, long-term network plans must be adaptable to potentially large changes in network structure, in order to provide better plans for tactical execution. This adaptability raises substantial computational challenges. In this talk, we describe practical methods for incorporating stochasticity into long-term service network plans.

Amazon offers millions of unique items for sale on its website. The popularity of these items is not evenly distributed, and the mean weekly demand for different products on Amazon spans multiple orders of magnitude. Because of this enormous scale and selection, deciding how to optimally place this inventory throughout our fulfillment network is very challenging. Directly modeling all products is not feasible without advanced decomposition techniques and massive compute power. On the other hand, down-sampling products typically does not adequately capture the behavior of the “long tail”. We propose a scalable method for modeling both head and tail demand, and placing the inventory to best utilize our network assets. Our model matches the ship and storage capacity of nodes in our network with the velocity profile of demand in order to minimize fulfillment cost. We use this framework to derive insights on the relationship between placement strategy and customer experience.