STOR-i Masterclass: Professor Laura Albert

Public Sector OR

At the end of February, Professor Laura Albert visited us at STOR-i to give a two day masterclass on Pubic Sector Operational Research. Laura is an Industrial and Systems Engineering Professor at the University of Wisconsin-Madison. At the time of the masterclass, Laura was on sabbatical in Germany at RWTH Aachen University. Her research focusses on applied optimisation in the public sector in the US; applications include homeland security, disasters, emergency response, public services and healthcare. Some current projects are:

Emergency medical service deployment and dispatch,
Cyber-security and trustworthy computing,
Next-generation policing models to divert opioid users from the criminal justice system.

Laura also authors the blogs Punk Rock OR and Badger Bracketology.

History of Public Sector OR

The masterclass initiated with an introduction to Public Sector OR, detailing some of the historical applications. Following a period of civil unrest during the 1960s in the US, cities faced many challenges: crime, fire alarms. solid waste and drug use. Dr. Al Blumstein chaired the Commission’s Science and Technology Task Force (CMU) to address fundamental societal problems. With no extra money in the budget for public sector organisations, an increase in problem size meant there was only one solution: Operational Research. This is when the golden age of public safety research began.

Following this, some early contributions to public sector OR were made. Much of this research was put into practice and influenced policy. These papers appeared in the best operations research journals and received major awards.

What is Public Sector OR?

Public Sector Operational research is a problem whose outputs are subject to public scrutiny

Public sector OR is concerned with complex systems that encompass people, processes, vehicles and critical infrastructure. It can include problems in the following areas:

Public health and safety
Police, fire, emergency services and public health
Community development
Planning, transportation
Human services
Public assistance, welfare, drugs and alcohol treatment, homeless services
Nonprofit management
Management of community-oriented service providers

Developing models to deal with these issues often involves multiple stakeholders or decision-makers and requires many objectives, often with conflicting aims. These models should aim to balance equity with efficiency, whilst remaining below some predetermined budget. Here are some examples of such models:

Food bank distribution networks,
Airport location or expansion using multi-criteria decision analysis,
Military procurement decisions,
Delivering relief aid,
Post-disaster reconstruction,
School bus schedules,
Public library location and management,
Undesirable facility location and management,
Public transport routes.

In the following sections, I will outline examples of public sector OR models that Laura presented during the masterclass

Small Scale: Facility Location Models

Suppose we want to site p ambulances at stations in a region to “cover” the most calls in 9 minutes. Here, there are two decisions to make: where to locate the stations and which calls are assigned to which station? This is modelled as an optimisation problem to achieve some balance between cost and service. Here, we maximise or minimise an objective subject to capacity constraints. Specifically, we consider a discrete problem where the locations are at predefined points using an integer program. In this problem, there are multiple distance criteria:

The total distance between calls and their assigned stations (this is usually demand weighted),
The maximum distance between a call and its assigned station,
The coverage – this is the number of calls covered if the distance is within some specified radius.

The model must also restrict the number of stations being built by considering the fixed cost associated with opening an ambulance station (including construction, leasing and labour costs). Remember: we want no more than p stations. Laura presented 5 models:

(Uncapacitated) Fixed-charge location problem:
minimise fixed cost + demand weighted distance
P-median problem:
minimise demand weights distance
such that locate less than p stations
P-center problem:
minimise maximum distance
such that locate less than p stations
Set covering location problem:
minimise number of stations
such that cover all calls
Maximum covering location problem:
maximise covered demands
such that locate less than p stations

These models must also ensure that all calls are satisfied and calls are not assigned to a closed station. In order to cover the most calls in 9 minutes, the maximum coverage problem poses most appropriate. However, there are additional features that could be included to improve the model:

Different call volumes at different locations,
Non-deterministic travel times,
Each ambulance responds to the same number of calls,
Ambulances are not always available to backup coverage.

Even when these additional features are accounted for in the model, there still remains two sources of uncertainty: ambulance unavailability and probabilistic travel times. Models that incorporate both sources of uncertainty generate a configuration that covers up to 26% more demand at no extra cost.

Such facility location problems are not restricted to just ambulance station location but many other areas within the public sector:

Fire stations,
Airline hubs,
Blood banks,
Hazardous waste disposal sights,
Schools,
Bus stops.

Large Scale: Emergency Response for Homeland Security and Disaster Management

Laura also discussed applications within OR but on a much greater scale in terms of disaster management. Disasters can include those that are natural (e.g. earthquakes, droughts, tsunamis, etc.), terrorist induced (e.g. cyber attacks or nuclear blasts), technological and accidental (e.g. nuclear power plants or power outages). Disasters tend to follow a common lifecycle:

Each stage in the cycle (except vulnerability) lends itself to OR; we detail each stage and some applications:

Vulnerability is the potential for physical harm and social disruption.
– Vulnerability does not typically lend itself to OR applications
Mitigation includes actions taken prior to the disaster to prevent or reduce the impact.
– Checkpoint screening for security
– Network design
– Pre-locating medical facilities and response stations
Preparedness also includes actions taken prior to a disaster but this time, to aid in response and recovery.
– Pre-positioning crews and supplies in advance of a disaster
– Evacuation planning
– Emergency crew scheduling
Emergency response includes actions during and after a disaster to protect and maintain systems, rescue and respond to casualties and survivors, and restore essential public services.
– Urban search and rescue
– Routing and distribution of supplies and commodities
– Hospital evacuation
Recovery includes efforts to reestablish pre-disaster systems and services.
– Debris clean up and removal
– Roads, bridge and facility repair and restoration
– Replanting and restoration of forests and wetlands affected by a natural disaster

The model criteria of disaster models differ slightly from that of a standard model. Rather than quality, cost, profit, and distance, we are now concerned with loss of life, morbidity, coverage, and delivery of critical commodities.

I would like to thank Prof. Laura Albert for delivering this masterclass. I really enjoyed learning about different OR models applied to the public sector.

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