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Public Services

Service sector · decision type · thirteen models

Operations research carries special moral weight when applied to public services — every misallocated fire truck, misassigned school seat, or unclaimed kidney affects lives directly. From RAND's fire-department deployment analysis for New York City (Walker, Chaiken & Ignall, 1974) to the market-design tradition of Roth, Sönmez & Ünver recognised by the 2012 Nobel Prize in Economic Sciences, this is the OR subfield where efficiency must be weighed against equity, accessibility, and institutional legitimacy. Thirteen applications below, organised along a service sector × decision type matrix anchored on Larson & Odoni's Urban Operations Research.

Educational resource. Pages on this site describe mathematical models used in public-sector decision-making. They are teaching tools, not policy advice, legal guidance, or operational plans. Real-world deployment requires stakeholder consultation, ethical review, and — where applicable — legal and regulatory expertise. Several applications discussed here have substantial critical scholarship documenting the limits and harms of the underlying models; that literature is cited on the individual application pages.

Why public-services OR matters

Three landmark moments · each verifiable, each consequential

1974
RAND's Fire Department Deployment Analysis (R-1566-NYC) demonstrated that relocating a small number of fire companies materially reduced response-time disparities across New York City boroughs — the founding case study of public-services OR.
Walker, Chaiken & Ignall, RAND Corporation · rand.org/pubs/reports/R1566
2003
New York City's Department of Education replaced its legacy student-choice system with a deferred-acceptance mechanism following the Abdulkadiroğlu – Pathak – Roth redesign; Boston Public Schools followed in 2005.
Abdulkadiroğlu, Pathak, Roth (2005) · doi:10.1257/0002828054201242
2012
Nobel Prize in Economic Sciences awarded to Lloyd Shapley and Alvin Roth “for the theory of stable allocations and the practice of market design” — citing kidney exchange and school choice as signature applications.
The Royal Swedish Academy of Sciences · nobelprize.org/economic-sciences/2012

Decision framework

Four lenses on the same thirteen applications

The primary taxonomy draws on Larson & Odoni's Urban Operations Research (1981, 2007 reprint) and the broader public-sector OR literature (Pollock, Rothkopf & Barnett, 1994). Applications are organised along two axes: the service sector (rows) and the decision type (columns). Dashed cells are honest gaps — decision problems that exist in practice but are not yet modelled here.

Sector ↓  ·  Decision →
Location & Coveragep-median, MCLP, hypercube
Districtingpartitioning territory
Matching & MechanismDA, TTC, kidney exchange
Scheduling & RoutingCPP, JSP, VRP
Allocation under ScarcityIP, multi-objective
Network Design & FlowMST, max-flow
Public SafetyEMS, fire, police
Gap · police-beat districting
Gap · EMS dispatch network
Educationschools, seats
Gap · school-zone districting
Gap · bus routing
Gap · grant allocation
·
Transportationtransit, paratransit
Gap · stop placement
Gap · transit-zone design
·
Gap · driver scheduling
·
Environmentwaste, water
Gap · recycling-plant siting
Gap · collection districts
·
·
Gap · water network
Justicecourts, parole
Gap · court siting
Gap · judicial districts
Gap · jury assignment
Gap · public-defender load
·
Social Serviceswelfare, housing
Gap · service-centre siting
·
Gap · housing assignment
·
·
Humanitariandisaster, refugees
Gap · shelter siting
·
Gap · relief routing
Gap · food-bank allocation
Civic & Electoraldistricts, voting
·
·
Gap · poll-station routing
Gap · public-good provision
·

Icon flags an application with substantial critical-scholarship literature (see the Critical Lens tab). NEW marks applications added in the current restructure.

Public-services OR is defined by the tension between efficiency (minimise cost, travel time, makespan) and equity (ensure fair access, bounded worst-case outcomes, respect for affected communities). The plane below positions each application by its dominant objective. Hover a dot to read the full name; click to open the page. See Marsh & Schilling (1994) for equity measures in facility location and Karsu & Morton (2015) for an OR-wide survey of inequity-averse optimisation.

Existing application
New in this restructure
Substantial critical-scholarship literature

Public-services OR does not serve a single decision-maker. Models are commissioned by governments, implemented by nonprofits, and bear on the lives of citizens and communities — often with competing interests. The columns below group the thirteen applications by whose question the model most directly answers. An application can legitimately appear in more than one column; only the primary decision-maker is shown here.

Citizens & Users
Where the model's output is an individual assignment, match, or service entitlement.
NGOs & Operators
Nonprofit and quasi-public organisations running programmes on behalf of citizens or refugees.
Affected Communities
Where documented critical scholarship shows disproportionate effects on particular groups — these pages cite that literature explicitly.

This lens highlights applications whose mathematical formulations are in tension with documented real-world harms, reform histories, or impossibility results from the fairness literature. The individual pages cite peer-reviewed critiques. Silence on these critiques would be a doctoral-level failure of intellectual honesty; naming them is the minimum.

Reading this lens. Applications below carry references to specific peer-reviewed critiques of their formulations. If you are deploying any of these models in practice, read the critical references before — not after — implementation. Other applications on this site (fire-station siting, school location, transit network design, kidney exchange, evacuation routing, etc.) have their own Limitations & Critique sections on their individual pages.
Police Patrol — fairness in predictive policing
Efficiency-maximising patrol routes can entrench feedback loops: more patrols in historically over-policed neighbourhoods produce more recorded incidents, which justify still more patrols. Predictive-policing tools have been documented to amplify racial disparities; the routing optimisation inherits whatever biases are present in the input incident data.
Lum & Isaac (2016). To predict and serve? Significance 13(5).
Chouldechova (2017). Fair prediction with disparate impact. Big Data.
Barocas, Hardt & Narayanan (ongoing). Fairness and Machine Learning.
See police-patrol.html.
Political Districting — gerrymandering and compactness tradeoffs
Districting MILPs can satisfy compactness, contiguity, and equal-population constraints while still producing maps that distort partisan representation. There is no single “neutral” objective; the choice between Polsby-Popper compactness, minority-majority preservation, and proportional-outcome targets is inherently political.
Altman (1997). Is automation the answer? NP-hardness of automated redistricting.
Mehrotra, Johnson & Nemhauser (1998). Political districting MILP. Operations Research.
Ricca, Scozzari & Simeone (2013). Political districting review. Annals of OR.
See political-districting.html.
School Choice — Boston-mechanism manipulability reform
The original Boston priority-matching mechanism rewarded strategic families who misrepresented their true preferences. The city's switch to deferred acceptance in 2005 was not a technical upgrade but a response to documented inequities borne by families without the information or time to game the old system. The reform history is the lesson, not just the mechanism.
Abdulkadiroğlu, Pathak, Roth, Sönmez (2005). The Boston Public School match. AER.
Abdulkadiroğlu, Pathak, Roth (2009). Strategy-proofness vs. efficiency in matching with indifferences: Redesigning the NYC high-school match. AER.
See school-choice-mechanism.html.

Application catalog

All thirteen pages · click a card to open the application

MCLP Public Safety
Fire Station Siting
Site p fire stations so the maximum population falls within a 4–6 minute response radius — the Maximal Covering Location Problem (Church & ReVelle, 1974; Walker, Chaiken & Ignall, 1974 RAND).
p-Median Education
School Location Planning
Open p schools from candidate sites to minimise the weighted distance travelled by students to their nearest open school (Hakimi, 1964; Teitz & Bart, 1968).
Network Design Transportation
Transit Network Design
Select routes and frequencies on a transit network to minimise total passenger travel time (in-vehicle + waiting + transfer) subject to fleet constraints (Mandl, 1979; Ceder & Wilson, 1986).
Chinese Postman Environment
Garbage Collection Routing
Traverse every street segment with a fleet of capacitated trucks at minimum cost — the Capacitated Arc Routing Problem (Edmonds & Johnson, 1973; Golden & Wong, 1981).
Arc Routing Public Safety
Police Patrol Routing
Design patrol routes that cover high-incident arcs while respecting shift constraints. Page includes an expanded Limitations & Critique section on predictive-policing bias (Lum & Isaac, 2016).
Job-Shop Justice
Court Hearing Scheduling
Assign hearings to judges and courtrooms across a weekly calendar to minimise backlog, respecting lawyer availability and case-priority rules — a job-shop scheduling problem.
Max-Flow Humanitarian
Evacuation Routing
Route the maximum flow of evacuees from threat zones to shelters over a time-expanded network, using shortest-path and max-flow/min-cut algorithms (Ford & Fulkerson, 1962).
IP Knapsack Social Services
Municipal Budget Allocation
Select a subset of capital projects to fund within an annual budget that maximises weighted public value — a 0-1 knapsack with equity-aware weights (Marsh & Schilling, 1994).
Deferred Acceptance Education
School Choice Mechanism
Assign students to public schools using deferred acceptance (Gale & Shapley, 1962) or top trading cycles — stable, strategy-proof mechanisms (Abdulkadiroğlu & Sönmez, 2003). Used by NYC DOE (2003) and Boston (2005).
Matching Public Safety
Kidney Exchange
Pair incompatible donor-recipient dyads into cycles and chains that maximise transplants, the foundational market-design win (Roth, Sönmez & Ünver, 2004, 2005). Operationally deployed via UNOS, NKR, APD.
MILP Districting Civic
Political Districting
Partition census units into equal-population, contiguous, compact districts — and confront the gerrymandering tradeoffs that no single compactness objective resolves (Hess et al., 1965; Altman, 1997).
Multi-Objective Public Safety
Vaccine Allocation under Scarcity
Allocate a fixed vaccine supply across regions and priority groups to balance expected lives saved, equity of access, and logistical feasibility — a problem crystallised by COVID-era scholarship (Bertsimas et al., 2022).
Matching Humanitarian
Refugee Resettlement Matching
Match refugee families to resettlement locations to maximise expected employment outcomes, using two-sided matching with capacity constraints (Jones & Teytelboym, 2017; Bansak et al., Science 2018).

Current research frontiers

Where public-services OR is actively evolving

Algorithmic fairness in public decisions

Impossibility results (Chouldechova, 2017; Kleinberg, Mullainathan & Raghavan, 2017) show that calibration, predictive parity, and equalised odds cannot in general be satisfied simultaneously — forcing public-sector model designers to choose explicitly which fairness axiom to prioritise.

Market design for scarce public goods

Expanding the deferred-acceptance and kidney-exchange toolkit to refugee resettlement (Jones & Teytelboym, 2017; Bansak et al., 2018), organ allocation across other organs, daycare, and housing assignment. Each domain raises new incentive-compatibility and stakeholder-consent questions.

Humanitarian and climate-driven operations

Pre-positioning of relief supplies, shelter siting under sea-level-rise scenarios, and multi-stage stochastic planning for climate-driven displacement. The OR Society and INFORMS Humanitarian Operations communities treat this as the field's fastest-growing branch.

Equity-aware optimisation

Moving beyond min-max regret (Karsu & Morton, 2015) toward formal fair-division guarantees (Nash social welfare, envy-freeness, max-min share) for indivisible public goods — increasingly relevant for participatory budgeting and platform-mediated services.

Key references

Cited above · DOIs & permanent URLs

Larson, R. C., & Odoni, A. R. (1981, reprint 2007).
Urban Operations Research.
Prentice-Hall; Dynamic Ideas reprint, Belmont MA. The canonical public-services OR textbook.
Pollock, S. M., Rothkopf, M. H., & Barnett, A. (Eds.). (1994).
Operations Research and the Public Sector.
Handbooks in Operations Research and Management Science, Vol. 6. North-Holland.
Walker, W., Chaiken, J., & Ignall, E. (1974).
Fire Department Deployment Analysis: A Public Policy Analysis Case Study.
RAND Corporation, R-1566-NYC. rand.org/pubs/reports/R1566
Toregas, C., Swain, R., ReVelle, C., & Bergman, L. (1971).
“The location of emergency service facilities.”
Operations Research 19(6), 1363–1373. doi:10.1287/opre.19.6.1363
Church, R., & ReVelle, C. (1974).
“The maximal covering location problem.”
Papers of the Regional Science Association 32, 101–118. doi:10.1111/j.1435-5597.1974.tb00902.x
Larson, R. C. (1974).
“A hypercube queuing model for facility location and redistricting in urban emergency services.”
Computers & Operations Research 1(1), 67–95. doi:10.1016/0305-0548(74)90076-8
Gale, D., & Shapley, L. S. (1962).
“College admissions and the stability of marriage.”
American Mathematical Monthly 69(1), 9–15. doi:10.2307/2312726
Abdulkadiroğlu, A., & Sönmez, T. (2003).
“School choice: A mechanism design approach.”
American Economic Review 93(3), 729–747. doi:10.1257/000282803322157061
Abdulkadiroğlu, A., Pathak, P. A., Roth, A. E., & Sönmez, T. (2005).
“The Boston Public School match.”
American Economic Review 95(2), 368–371. doi:10.1257/000282805774669637
Roth, A. E., Sönmez, T., & Ünver, M. U. (2004).
“Kidney exchange.”
Quarterly Journal of Economics 119(2), 457–488. doi:10.1162/0033553041382157
Jones, W., & Teytelboym, A. (2017).
“The local refugee match: Aligning refugees' preferences with the capacities and priorities of localities.”
Journal of Refugee Studies 31(2), 152–178. doi:10.1093/jrs/fex022
Bansak, K., Ferwerda, J., Hainmueller, J., Dillon, A., Hangartner, D., Lawrence, D., & Weinstein, J. (2018).
“Improving refugee integration through data-driven algorithmic assignment.”
Science 359(6373), 325–329. doi:10.1126/science.aao4408
Hess, S. W., Weaver, J. B., Siegfeldt, H. J., Whelan, J. N., & Zitlau, P. A. (1965).
“Nonpartisan political redistricting by computer.”
Operations Research 13(6), 998–1006. doi:10.1287/opre.13.6.998
Altman, M. (1997).
“Is automation the answer? The computational complexity of automated redistricting.”
Rutgers Computer & Technology Law Journal 23, 81–142.
Marsh, M. T., & Schilling, D. A. (1994).
“Equity measurement in facility location analysis: A review and framework.”
European Journal of Operational Research 74(1), 1–17. doi:10.1016/0377-2217(94)90200-3
Karsu, Ö., & Morton, A. (2015).
“Inequity averse optimization in operational research.”
European Journal of Operational Research 245(2), 343–359. doi:10.1016/j.ejor.2015.02.035
Chouldechova, A. (2017).
“Fair prediction with disparate impact: A study of bias in recidivism prediction instruments.”
Big Data 5(2), 153–163. doi:10.1089/big.2016.0047
Lum, K., & Isaac, W. (2016).
“To predict and serve?”
Significance 13(5), 14–19. doi:10.1111/j.1740-9713.2016.00960.x
Barocas, S., Hardt, M., & Narayanan, A. (ongoing).
Fairness and Machine Learning: Limitations and Opportunities.
MIT Press / fairmlbook.org. fairmlbook.org
The Royal Swedish Academy of Sciences. (2012).
“The Prize in Economic Sciences 2012: Stable Matching — Theory, Evidence, and Practical Design.”

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Data and numerical examples are illustrative. Pages on this site are educational tools, not investment, policy, legal, or operational advice.