With speakers from academics and working professionals in the UK and worldwide, there were a variety of talks in Statistics and Operational Research, both in academia as well as industry. Bringing together researchers, students and industry professionals interested in similar fields, I had the opportunity to meet like-minded academics and learn more about the different areas of research that they focus on.

There was also a poster presentation delivered mainly by PhD students of the STOR-i programme which showcased the work being carried out in several areas of OR and statistics at STOR-i. It was inspiring and exciting to see the variety of research that is being conducted in collaboration with strategic partners such as the Naval Postgraduate School, Northwestern University, etc. and also industrial partners such as Tesco, BT, etc.

Two talks that stood out to me personally were those delivered by Dries Goosens of Ghent University and Maria Paola Scaparra from the University of Kent. Dries Goosens presented his research on Sports scheduling with a team to categorise sports scheduling problems, generate a set of diverse and realistic benchmark instances along with an instance space analysis for solution methods for sports scheduling problems. Organising the messy variety of sports scheduling problems in the literature is an important step towards improving the quality and potential of research in the scheduling community. I also found that the methods of classification and categorisation of problems and instances could be extended not only to other timetabling problems such as University course timetabling and Nurse scheduling, but also to other related fields in Operational Research and Combinatorial Optimization such as Vehicle Routing Problems, Job scheduling problems, Assigment and Matching problems, etc.

Maria’s talk showcased the use of OR in real-world case studies with the theme of attaining Sustainable Development Goals (SDGs). The first case study demonstrated the use of data-driven models and interdisciplinary methods in finding optimal flood mitigation strategies for Vietnamese cities. The second case study involved healthcare projects in Africa using OR to improve health services in refugee camps of Ethiopia as well as ambulance services in South Sudan. It was inspiring to see the power of OR in transforming the lives of people as well as realistic challenges faced during the progress of building a sustainable future. Indeed, it is work like this that inspired me to undertake further study in OR and statistics.

It was a brilliant first conference with the series of motivating and captivating talks and discussions over the two days. Furthermore, I was deeply inspired by the room of like-minded individuals who were keen to develop scientific ideas, share them and discuss potential future ideas that could be explored. This air of inspiration has left me keen for the next STOR-i conference and other conferences in the future!

About Nurse Rostering and other Scheduling Problems

In my dissertation, I reviewed the literature surrounding several scheduling problems such as sports scheduling and University course timetabling. These problems aim to find the “best” schedule that allocates work/jobs to machines/people while meeting certain requirements.

In particular, I worked on the nurse rostering problem which involves the allocation of nurses to hospital shifts over a planning horizon while meeting certain requirements such as contract hours, minimum rest periods and days-off requests. The nurse rostering problem has several variants based on different compulsory requirements (constraints) and objectives which define a “good” nurse schedule. In order to consider several constraints that have been used in the Nurse Rostering literature, I created a table of constraints along with a comparison of which papers in the literature use these constraints as hard (compulsory) and soft (preferred) constraints.

Solving the Nurse Rostering Problem

I also attempted to solve a formulation of the Nurse Rostering Problem introduced by by implementing a hybrid algorithm that combines a Greedy Heuristic with Variable Neighbourhood Search (VNS), a local search method, to find a “good” nurse schedule. The greedy heuristic is used to construct an initial feasible schedule, i.e., a schedule which satisfies all the hard (compulsory) constraints. 

Variable Neighbourhood Search

Variable Neighbourhood Search (VNS) is a local search heuristic which uses an initial feasible solution, defines feasible neighbours and improves the current solution by choosing a “better” feasible neighbour.  The VNS algorithm is used to improve the initial feasible solution provided by the Greedy Heuristic. An example of neighbourhood structures that can be formed from an initial schedule of nurses A, B and C over a four-day planning period is given in Figure A below. 

The algorithm updates the current best solution to be the best neighbourhood structure so far and iteratively finds improvements to the current best solution until some stopping criterion is reached. Figure B below contains the pseudo-code for the VNS algorithm, which is widely used for solving several problems in Operational Research beyond the Nurse Rostering Problem.

The VNS algorithm was tested on 24 benchmark instances of the Nurse Rostering Problem from the . It was found that VNS improved the quality of nurse schedules in most instances. However, there was an indication of the possibility that the final solutions obtained in some cases were local minima and not global optima. This motivated the search for alternative/improved solution methods to solve the problem.

Overall Experience

As my first experience solving an Operational Research problem in depth, this dissertation provided an invaluable journey of personal and academic growth. The periods of literature review were inspirational with the exposure to extensive work being carried out on the problem over several decades and across several continents. Working under the supervision of Dr. Sergio García Quiles helped me explore several ideas in an informed manner. I also thoroughly enjoyed implementing a solution method to solve a problem that interests me. While working on the dissertation, I came to be sure that further study in Operational Research, through a PhD, would be my next best step forward.