FalCom: A Sampling Framework for Districting and Hierarchical Facility Location, with Applications to Emergency Response and Healthcare Zoning

Alaittin Kırtışoğlu

Spatial partitioning of a geographical region into contiguous and balanced districts is a core combinatorial problem in operations research, arising in political redistricting, sales-territory design, and service districting such as waste collection, emergency response, and healthcare zoning. Balance describes the desire for districts of equitable size, measured by workload, sales potential, or number of eligible voters. The classical approach is to solve the problem for a single solution under capacity and equity constraints. In this talk, we introduce FalCom (Facility Combination Method), the first Markov chain Monte Carlo sampling framework for hierarchical capacitated facility location and districting (to the best of our knowledge). FalCom extends the spanning-tree proposal of the Recombination method from single-level political redistricting to multi-level service systems with capacity–demand balance and facility-location decisions. We demonstrate that it scales to spatial partitions of 50,000 basic units, an order of magnitude beyond published hierarchical methods.

FalCom samples ensembles of feasible plans, enabling boundary-robustness maps, essentialvs-substitutable facility analysis, and capacity-utilization distributions that no single-solution method can produce. The framework is validated on synthetic grids and a London Ambulance Service case study and released as an open-source Python library with an interactive visualizer.

This is joint work Hemanshu Kaul.

Short Bio

Alaittin Kirtisoglu is a fifth-year PhD candidate in Applied Mathematics at the Illinois Institute of Technology, Chicago, graduating in summer 2026. His doctoral research, advised by Hemanshu Kaul, develops sampling algorithms for hierarchical districting and facility location with applications to equitable network design problems. His research interests also include vehicle routing problems and graph theory. He received his M.Sc. in mathematics from Hacettepe University in 2021, with a dissertation in extremal graph theory advised by Lale Özkahya, and his B.Sc. in mathematics from Mustafa Kemal University in 2018. He has served as a graduate teaching assistant at TED University (2019–2021) and the Illinois Institute of Technology (2021–2026).

Venue

Friday, May 15, 2026, 4.00 pm

IE Building, Halim Doğrusöz Auditorium (IE 03)