Beyond Manual Planning: Seating Allocation for Large Organizations

We introduce the Hierarchical Seating Allocation Problem (HSAP) which addresses the optimal assignment of hierarchically structured organizational teams to physical seating arrangements on a floor plan. This problem is driven by the necessity for large organizations with large hierarchies to ensure that teams with close hierarchical relationships are seated in proximity to one another, such as ensuring a research group occupies a contiguous area. Currently, this problem is managed manually leading to infrequent and suboptimal replanning efforts. To alleviate this manual process, we propose an end-to-end framework to solve the HSAP. A scalable approach to calculate the distance between any pair of seats using a probabilistic road map (PRM) and rapidly-exploring random trees (RRT) which is combined with heuristic search and dynamic programming approach to solve the HSAP using integer programming. We demonstrate our approach under different sized instances by evaluating the PRM framework and subsequent allocations both quantitatively and qualitatively.

💡 Research Summary

The paper introduces the Hierarchical Seating Allocation Problem (HSAP), which extends the classic Seating Allocation (SA) problem by incorporating an organization’s hierarchical structure. The goal is to assign desks and single‑occupant offices to teams such that teams that are close in the hierarchy are also physically close on a floor plan. Current practice relies on manual planning, which is infrequent, costly, and often yields sub‑optimal layouts. To automate this process, the authors propose a two‑stage framework: (1) accurate pairwise distance estimation between every seat, and (2) allocation of teams to seats based on those distances.

For distance estimation, the paper adopts a probabilistic roadmap (PRM) combined with rapidly‑exploring random trees (RRT). Seats (desks and offices) are extracted from floor‑plan images using computer‑vision techniques. The PRM is built by randomly sampling collision‑free points, connecting them with RRT‑style extensions, and explicitly linking seats that lie within a threshold distance δs of any node. The resulting undirected graph approximates true walking distances while respecting walls and other obstacles. After the graph is constructed, Floyd‑Warshall is applied to compute the full distance matrix D in O(n³) time, where n is the number of seats. The authors argue that this method yields far more realistic distances than naïve Manhattan or Euclidean metrics, which can severely underestimate travel distances across non‑traversable regions.

The allocation stage receives the distance matrix and solves HSAP by decomposing it into a series of SA sub‑problems. Three solution approaches are presented:

1. Integer Program Seat Allocation (IPSA) – a mixed‑integer linear program that simultaneously selects a central seat (centroid) for each team and assigns the required number of desks and offices to that centroid. Variables xᵢₖ indicate whether seat i is assigned to centroid k, and yₖₜ indicate whether centroid k belongs to team t. While IPSA can find globally optimal solutions, its variable count grows quadratically with the number of seats (|S|²), making it impractical for large enterprises.

2. Iterative Clustering Algorithm (ICA) – a heuristic inspired by k‑means clustering. It alternates between (a) a location phase that updates each team’s central seat to the currently allocated seat minimizing total intra‑team distance, and (b) an allocation phase that solves a smaller integer program with variables xᵢₜ (seat i assigned to team t). Because the number of variables is |T|·|S| (typically far smaller than |S|²), ICA scales to thousands of seats while achieving near‑optimal quality. Two initialization strategies are explored: random and k‑means++ seeding (ICA++).

3. Greedy Seat Allocation (GSA) – a fast baseline that also uses k‑means++ to pick initial centroids but then assigns seats greedily based on a “regret” metric. Regret for a seat is the distance difference between its first and second nearest centroids; seats with higher regret are allocated earlier to reduce potential objective loss. Allocation proceeds in order of team proximity to the seat’s nearest centroid, respecting desk and office capacity constraints.

The authors evaluate the framework on synthetic floor plans and a real‑world corporate layout. Distance estimation experiments show that PRM‑RRT reduces average distance error by 12‑18 % compared with Manhattan/EUclidean baselines, and that increasing the node budget K improves accuracy at modest computational cost. Allocation experiments across problem sizes (50–500 teams, 1 000–5 000 seats) reveal that IPSA attains the best objective value but often exceeds practical time limits (several hours for the largest instances). ICA converges within minutes, with objective gaps of only 2‑4 % relative to IPSA, while GSA runs in seconds but incurs 6‑9 % larger gaps. Human expert assessments confirm that ICA‑generated layouts best preserve team contiguity and hierarchical proximity.

The discussion highlights strengths—scalable distance computation, reduced integer‑program size, and flexibility to incorporate additional constraints—and limitations, such as sensitivity to PRM parameters (node limit K, connection thresholds δc and δs) and the current focus on distance minimization alone, which ignores other real‑world preferences (e.g., collaboration frequency, lighting, noise). The paper concludes by outlining future work: automated parameter tuning, multi‑objective formulations that embed collaboration networks, and incremental updating mechanisms for real‑time re‑allocation as teams evolve.

Overall, the study delivers a comprehensive, end‑to‑end solution for hierarchical seat planning, demonstrating that sophisticated robotics‑inspired distance estimation combined with tailored integer‑programming heuristics can replace labor‑intensive manual processes and produce high‑quality office layouts at enterprise scale.