Operational Research – Eleanor D'Arcy

STOR-i Masterclass: Professor Laura Albert

Eleanor D'Arcy — Mon, 20 Apr 2020 08:50:18 +0000

Public Sector OR

At the end of February, Professor 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 and

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:

��

Disaster 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.

Slot Scheduling in Air Transportation

Eleanor D'Arcy — Mon, 23 Mar 2020 09:42:00 +0000

Following Alexandre Jacquillat’s talk at the STOR-i Annual Conference 2020 on Analytics for Operations, Scheduling and Pricing in Air Transportation, I was inspired to investigate this topic some more. I was particularly interested in the concept of slot scheduling to better use scarce airport capacity in order to improve the efficiency of the air transportation system. After reading some of the relevant literature and attending a talk by Konstantinos G. Zografos, I decided to write my first STOR-i research report on models proposed to deal with slot allocation inefficiencies. I have detailed the one-page summary of my report below:

Summary of Research Report

The slot scheduling problem has recently received a great deal of consideration in the literature due its size and complexity. As demand for air transportation rises but opportunities for the expansion of infrastructure remain limited, demand management measures are fundamental to help balance supply and demand. Supply side solutions, through airport capacity expansion or enhancement, are capital intensive and require a long term horizon for implementation. Such operations are also often subject to physical or political constraints. Instead, demand management is recognised as the principal instrument to deal with delays in air transport since such solutions are immediate and easily implementable. Slot scheduling is a method of managing demand through best allocating scarce airport resources.

Prior to the summer or winter scheduling season, airlines request slots at an airport; a slot allows them to use all of the infrastructure necessary for landing and take-off. For airports who are designated as `coordinated’, due to supply-demand imbalances, a coordinator is responsible for allocating slots. Currently slot schedules exhibit large deviations from requested slot times. Airport capacity is usually expressed in terms of the number of available slots and the demand for these slots often exceeds capacity, but this capacity is rarely used optimally. Slot scheduling models aim to best use capacity so that all airlines are allocated slots as close to their requests as possible, subsequently slots are used more efficiently and delays are minimised. There is large room for improvement in the current slot allocation process.

The first mathematical model to be compliant with scheduling regulations was proposed in 2012. This model aims to minimise the distance between requested and allocated slot times subject to an artificial measure of capacity and turnaround time constraints, at a single airport. This ensures capacity is not exceeded, so delays are minimised, and allows the aircraft sufficient time on the ground to prepare for the next flight. Using this simple formulation, the resulting schedule demonstrates large improvements on current procedures. Following from this, other models have been developed to also incorporate fairness and accessibility restrictions. These encourage flights to remotely located airports and aim to ensure no airline suffers greater displacement from their requested slots. This means all airlines are treated equally and all airports, regardless of size, are accessible. Other models aim to minimise similar objectives, but consider a network of airports. This means that dependencies between airports are accounted for in order to avoid the multiplier effect of delays once one flight is interrupted. Considering a network of airports creates a larger and more complex problem, but this helps to formulate a more realistic representation of the situation at hand.

This report reviews the current slot allocation procedure, detailing each stage necessary to formulate a slot schedule. Additionally, we discuss different allocation models in the surrounding literature, at the single and network level, and use computational results to compare them to the existing methods, as well as one another. Finally, we aim to identify any gaps in the research that present interesting ideas for future investigation.

STOR-i Annual Conference 2020: Christine Currie

Eleanor D'Arcy — Mon, 24 Feb 2020 13:06:54 +0000

Making Random Things Better: Optimisation of Stochastic Systems

At the STOR-i Annual Conference earlier this year, Professor Christine Currie presented two interesting applications of optimisation, where the elements of the system are subject to uncertainty. Optimisation involves finding a value that maximises or minimises a function, this is often a complicated and random function. In many real-life situations, it is optimistic to assume all data elements in the system are known quantities and that none are subject to uncertainty. Christine outlined examples in the passenger transportation industry and in healthcare where the inputs and outputs of the system are uncertain.

Christine at the STOR-i Conference

Christine is Associate Professor of Operational Research in Mathematical Sciences and Director CORMSIS (the Centre for Operational Research, Management Science and Information Systems) at the University of Southampton. Additionally, she is Editor-in-Chief for the Journal of Simulation. Christine’s research is concerned with simulation optimisation, mathematical modelling of epidemics, optimal pricing and applications of simulation in healthcare.

Airline Revenue Management Example

Firstly, Christine delivered an optimisation example for network revenue management of tickets for an airline. This is modelled as an optimisation problem because the aim is to maximise revenue subject to capacity, demand and sales. It is difficult to set prices for these tickets since it is uncertain how many will be sold, we say there is stochastic demand. If it was certain that there would be a high demand for a certain flight, then it is likely that the airline will set higher prices to maximise revenue. To complicate this further, airlines often sell different classes and packages of tickets, so it must be decided at what prices different seats will be sold. Since the seats have no value once the plane departs, we have a perishable inventory and it is fundamental to sell all tickets in order to maximise revenue.

Whilst the demand is uncertain, bounds can be assumed and a probability distributed assigned to it. Therefore, Christine suggests maximising the minimum revenue or minimising the maximum regret instead of just maximising revenue. This approach uses the bounds and distribution of demand, so it is not required to know demand exactly.

Healthcare Example

Christine provided us with a different example within healthcare to illustrate the idea of subset selection. Here, patients are waiting for transport to an acute hospital ward before rehabilitation. The ward is set up with an arbitrary number of bays and within each bay, there is an arbitrary number of beds but each bay must be single sex. These make up the constraints for the optimisation problem where the primary objective is to minimise waiting time. Additionally, the secondary aim is to maximise bed utilisation and minimise patient transfers around the ward.

Clearly, this quickly turns into a complicated optimisation problem. This requires a complex decision to be made with multiple objectives and a large number of options (including patients and beds). Christine’s work suggests providing the system expert with a subset of solutions rather than a single optimal solution, this avoids a situation where the expert is presented with a solution they cannot implement. Therefore, rather than a single solution, it is proposed that a subset of the system is chosen such that we are within some proportion of the optimum solution with some probability.

I thoroughly enjoyed listening to applications of optimisation in real-life situations; it was interesting to see how Christine approached the challenges of uncertainty and complexity. To read more about Christine’s research you can visit her . Additionally, please read my blog post about the STOR-i conference and all of the talks to find out more.

STOR-i Annual Conference 2020: Alexandre Jacquillat

Eleanor D'Arcy — Mon, 10 Feb 2020 15:49:34 +0000

Analytics for Operations, Scheduling and Pricing in Air Transportation.

Alexandre Jacquillat opened the STOR-i Annual Conference 2020 in early January. I thoroughly enjoyed his talk on Analytics for Operations, Scheduling and Pricing in Air Transportation so I decided to write an overview of the work he delivered. Alexandre demonstrated applications of both Statistics and Operational Research methods to the transportation industry. I had not witnessed such an application prior to this and I really appreciated this practical use of two topics I am currently studying. To find out more about the STOR-i conference, please read my post that details the event and all of the talks.

Alexandre at the STOR-i Conference

Alexandre is an Assistant Professor of Operations Research and Statistics at the MIT Sloan School of Management. His research applies to areas in transportation with the aim to promote efficient scheduling, operations and pricing practices. Alexandre is the recipient of several research awards, including the George B. Dantzig Dissertation Award and the Best Paper Prize in Transportation Science and Logistics from INFORMS.

This talk focussed on work that lies at the interface between analytics and transport, both of which are dynamic and growing industries. Specifically, the air transportation industry currently faces many challenges because they operate at or above capacity in order to avoid wasting any resource or time. This approach leads to flight delays and incurs costs for the airline provider. As the volume of flights increases, there is likely to be more delays set against more sales and profit. However, with fewer flights and hence fewer sales, it is likely that the number of delays will decrease. Using various results from analytical projects, Alexandre explained how they aim to support operations, scheduling and pricing practices in air transportation. In turn, this will improve the efficiency, reliability and profitability of the industry as a whole.

Operations

Alexandre started by discussing how his work has supported operations within the air transportation industry. This involves ensuring making the best use of available capacity. I mentioned above that airports operate at maximum capacity in order to avoid wasting any resource, but this often leads to delays and becomes costly. Alexandre proposes modeling this as an optimisation problem, this aims to minimise flight and passenger delays subject to flight, passenger and capacity constraints. Previously, passenger delays were not accounted for in this problem. When considering a network of flights, there is not a one-to-one correspondence between passenger and flight delays because passengers often travel through connecting flights. Therefore, a minor flight delay may cause a passenger to miss their connection and results in a major overall passenger delay once they reach their final destination. Including a new layer of passenger delays to the model proves to make flight operations more consistent.

Scheduling

Secondly, Alexandre presented ideas to optimally schedule flights. Airlines request a time slot for each of their flights and often they are allocated to a different slot because the demand for a specific slot tends to exceed the capacity. In order to minimise the overall displacement from an airline’s request, Alexandre presented a large-scale optimisation approach to slot allocation. By breaking the large-scale problem into smaller chunks, this delivered high quality, fast solutions compared to the current process. This method delivered optimal, or near-optimal, solutions at some of the largest schedule-coordinated airports. Additionally, Alexandre proposed an integrated model of both scheduling and operations that optimises scheduling in a network of airports but also captures the interdependencies between flight schedules and air traffic flow management.

Pricing

Lastly, Alexandre focussed on tackling the pricing practices in the industry. Often, flights between two destinations are priced the same even though one flight is direct and another has some number of stops for a significant length of time. This means that prices are not competitive. Alexandre outlined an experiment conducted with a global airline to assess a new, competitive pricing strategy. This demonstrated that making some minor changes to the baseline pricing practices results in a significant increase in revenue.

Global Flight Routes in 2009

Alexandre concluded with some ideas for future research prospects, to read more about Alexandre’s research feel free to visit his . I really enjoyed this talk and it encouraged me to read some more into the area, consequently, I have decided to write my first STOR-i research project on ‘Mathematical Models and Algorithms for Allocating Scarce Airport Resources’. The main focus of this project is to review relevant literature, therefore I intend to further investigate aspects of Alexandre’s research.

Future Reading

I have included a couple of papers by Alexandre that I have found interesting relating to the slot scheduling problem in air transportation

Jacquillat, A. and Odoni, A.R., 2015. An integrated scheduling and operations approach to airport congestion mitigation. Operations Research, 63(6), pp.1390-1410.
Available at:
Jacquillat, A. and Vaze, V., 2018. Interairline equity in airport scheduling interventions. Transportation Science, 52(4), pp.941-964.
Available at: