Stochastic Modelling and Simulation are core methodology areas not only in modern management science and business analytics but also in machine learning and artificial intelligence. They can be employed to support decision making in a wide range of contexts in which taking account of stochastic variation is important. These models, methods and algorithms are of key importance to help with gaining insight into complex situations, designing well-functioning systems, developing well-performing procedures, and making decisions under uncertainty or risk. The group members have substantial collective expertise developing methodology in this area, partnering with industrial and other partners to employ it to real-world problems and teaching these topics to the highest standard at all levels.

Methodology Research and Collaboration

The methodology expertise in both stochastic modelling (applied probability) and simulation at Lancaster University is recognised as being of the world leading level and the group members regularly publish in leading academic journals. The group members are regularly invited to co-organise and present at the specialised world-leading conferences such as INFORMS Applied Probability Society Conference, EURO WG Stochastic Modelling Meeting, INFORMS Winter Simulation Conference, ORS Simulation Workshop, European Conference on Queueing Theory, etc.

The group members specialise in topics that can be found on their personal webpages and are supported by several visiting researchers and professors emerita. The collective expertise currently covers the following research subareas:

Simulation Modelling (Amjad Fayoumi, Luke Rhodes-Leader): analysis methodology, modelling methodology, discrete-event simulation, dynamic simulation, agent-based modelling and simulation, validation and calibration of simulation models on empirical data, multi-fidelity modelling, simulation optimisation, etc.

Optimisation under Uncertainty (Alp Arslan, Yu Jiang, Peter Jacko, Chris Kirkbride, Dong Li, Rob Shone): Sequential decision making, stochastic dynamic programming, approximate dynamic programming, simulation-based dynamic programming, reinforcement learning, data-driven optimisation, Markov decision processes, stochastic optimisation, decision theory, decision analysis, decision trees, distributionally-robust optimisation, stochastic game theory, stochastic optimal control, resource allocation under uncertainty, resource-constrained project scheduling, stochastic scheduling, optimal search, Markovian and restless multi-armed bandits, index policies, etc.

Learning from Experimentation (Peter Jacko, Dong Li): Reinforcement learning, machine learning, design and analysis of sequential experiments, A/B testing, data-driven learning, Bayesian learning, Bayesian decision theory, bandit algorithms, computer simulation experiments, adaptive randomised controlled trials, demand learning, dynamic pricing, etc.

Queueing and Random Systems (Alp Arslan, Amjad Fayoumi, Rob Shone): steady-state queueing theory, time-dependent queueing systems, queueing networks, queueing disciplines, performance evaluation, social networks, systems analysis and design, business process modelling, process mining, requirements modelling, modelling with random variables and stochastic processes (Markov chains, Markov processes), data-driven modelling, routing/dispatching policies, staffing of service systems, etc.

Partner with Us

Impact on organisations and society is a priority of the group. Our research and knowledge transfer has achieved major improvements in decision making leading to boosted efficiency of allocation of resources, improved automation, enhanced service level and customer satisfaction, decreased risks, increased revenue and/or reduced costs. Our group members have engaged with companies across different industries, government and non-profit organisations, including automobile makers, healthcare and pharmaceutical organisations, aviation companies, telecom providers, retailers, and many SMEs. As an academic group, we can give independent suggestions and are not tied to any software product. Our solutions always consider the most practical approach and the best match for your organisation. 

Teaching & Problem-solving

PhD: The group members have led the organisation of the NATCOR PhD-level course on Stochastic Modelling biennially since NATCOR’s inception in 2007. They also co-organise the EURO PhD school on Reinforcement Learning Applied to Operations Research held in July 2022. They are involved in supervision of PhD students in the programmes PhD Management Science and PhD Statistics and Operational Research (and in supervision of postdoctoral research associates), many of which are in collaboration with industrial and/or academic partners worldwide. Recent PhD theses include:

Simulation Modelling:

• Multi-fidelity modelling for networks of simulation models (ongoing)   
• Optimising Stochastic Systems using Streaming Simulation Data (with Naval Postgraduate School, ongoing)    
• To What Extent Can Chance Constrained Selection of the Best be Used in Wildlife Reserve Design? (ongoing)
• Simulation Optimisation for the Housing of Homeless Populations (ongoing)
• Input Uncertainty and Data Collection Problems in Stochastic Simulation (with Naval Postgraduate School; 2023)
• Replicating Agent-Based Simulation Models of Herding in Financial Markets (2021)
• Multi-fidelity Modelling Approach for Airline Disruption Management Using Simulation (with Northwestern University & Rolls-Royce plc; 2020)
• An Agent-based Classroom Lessons Model and Simulation (2020)
• Quantifying and Reducing Input Modelling Error in Simulation (with Northwestern University; 2019)
• Improving and Comparing Data Collection Methodologies for Decision Rule Calibration in Agent-Based Simulation: A Case Study of Dairy Supply Chain in Indonesia (2019)

Optimisation under Uncertainty:

• Inventory management for preventive and corrective maintenance under supply chain risks (with Shell, ongoing)    
• Approximate Dynamic Programming and Heuristic Methods for Maintenance of Transportation Infrastructure Networks (with Naval Postgraduate School; ongoing)
• Dynamic Allocation of Mobile Servers (ongoing)
• Searching and Patrolling Dispersed Locations (2025)
• The border patrol game (2024)
• Parametric Distributionally Robust Optimisation Models for  Resource and Inventory Planning Problems (with British Telecom; 2023)
• Simulation and Optimization of Scheduling Policies in Dynamic Stochastic Resource-Constrained Multi-Project Environments (2022) 
• Dynamic Cash Management Models (2021)
• On the Dynamic Allocation of Assets Subject to Failure and Replenishment (with Naval Postgraduate School; 2021)
• Optimal Search in Discrete Locations: Extensions and New Findings (with Naval Postgraduate School; 2020)
• Robust and Stochastic Approaches to Network Capacity Design under Demand Uncertainty (2020)  

Learning from Experimentation:

• Simulation Analytics for Deeper Comparisons (2023)
• Evaluation of the Intelligence Collection and Analysis Process (2022) 
• Stochastic Models for Dynamic Resource Allocation (2022)
• Bayesian Bandit Models for the Design of Clinical Trials (2020) 

Queueing and Random Systems:

• Online Simulation for the Operational Management of Inpatient Beds (2019) 

Master: For the programmes MSc Business Analytics, MSc Logistics & Supply Chain Management, and MRes Management Science, the group members lead modules on Operational Research & Prescriptive Analytics, Statistics & Descriptive Analytics, Simulation & Stochastic Modelling, Pricing Analytics & Revenue Management, Spreadsheet Modelling, and analytics computing (e.g., R, Python, VBA). For the MRes Statistics and Operational Research at the STOR-i Centre for Doctoral Training, the group members lead modules on Stochastic Processes and Stochastic Simulation, and teach scientific computing (e.g., R, Python, Matlab, Julia, C++). Recent MSc dissertations include:

Simulation Modelling:

• Use of Markovian Queues to Improve Simulation Optimisation of Queueing Networks (2024)
• Modelling to Support the Design of Same Day Emergency Care (2024)
• Process Flow for patients undergoing physiotherapy through the RLI (2022)
• Investigate methods for adaptively controlling Passive Optical Network capacity (2022)
• Agent-Based Modelling of Conflict within Social Networks of Information System Projects (2021)
• Modelling the Impacts of Operation Characteristics in Theatre Scheduling: An Application of Simulation Experiments (2020)
• Modelling Treatment Pathways for MDR-Tuberculosis (with Liverpool School of Tropical Medicine; 2020)
• A Simulation Model for the Appliances of Lancashire Fire and Rescue Service (with Lancashire Fire and Rescue Service; 2021)

Optimisation under Uncertainty:

• Optimisation of Inventory Management in a Multi-store Environment (2024)
• Using Value Iteration and Q-learning to Study an Inventory Control Problem (2024)
• Investigating the Optimal Inventory Cost Policy Utilizing Reinforcement Learning Algorithms for Markov Decision Processes (2023)
• MDPs and Reinforcement Learning for Intelligent Control of Automated Vehicles (2023)
• Optimisation of Total Aviation Cost and Flight Delays at Heathrow Airport through Rationalising Flight Capacity (2021)
• Optimisation of Delayed Flights and Operational Costs at London Heathrow Airport by Implementing Ground Delay Programs (2021)
• Research on the Optimal Policy of Inventory Cost-Based on Reinforcement Learning Algorithm for MDPs (2021)
• Revenue Management: Inventory Management in the Fashion Industry with Sustainability (2020)
• Optimal Graph Patrol Problem Using Index-based Heuristics (2020)
• Markov Decision Processes for Queueing Systems with Different Types of Customers (2020)

Learning from Experimentation:

• A/B testing and beyond (2023)
• Multi-Arm Bandits in Thompson Sampling and AB Testing: An Overview and Comparison (2023)
• Exploring the Effects of the Design of E-commerce Websites on the Number of Customers Visiting Them through A/B Testing (2022)
• A/B Testing and beyond (2022)
• Football Player Value Prediction: Comparing Machine Learning Models (2021)
• The Evaluation of Dynamic Pricing in Hotel Industry using Machine Learning (2021)
• Dynamic Pricing on E- Retail using Machine Learning (2021)
• A/B Testing Simulation and Time Series Forecasting on the MOOC Platform (2021)
• Real-time Demand Learning with Q-learning Approach for Optimising Dynamic Pricing in Electronic Retail Setting (2020)
• Dynamic Pricing on Airbnb Using Machine Learning Techniques (2020)
• Comparative Long-Term Effect Forecasting of Group Sequential Designs for A/B Testing (2020)
• Digital Marketing Analytics: Simulated A/B Tests on the Homepage of Health Organisation (2020)
• A/B Test for Recommendation System Based on Machine Learning (2020)

Queueing and Random Systems:

• Improving Patient Flow between Acute, Community and Social Care (with NHS Bristol, North Somerset and South Gloucestershire CCG; 2021)
• Modelling Outpatient/Inpatient Flows (with Wrightington, Wigan, and Leigh NHS Foundation Trust; 2021)
• Improving Hospital Performance through Waiting List Modelling (with NHS Bristol, North Somerset and South Gloucestershire CCG; 2021)
• Modelling Short-term Bed Occupancy (with Blackpool Teaching Hospital NHS Foundation Trust; 2021)
• Using Queueing Theory to Model Operational Delays at Airports (2020)
• An Analytic Infinite-Server Queueing Network Model to Analyse Bed Occupancy in Hospital: The Case of Two-Node Systems (with Rotherham NHS Foundation Trust; 2020)
• Social Network Analysis: The Case of UK Companies Before and After Brexit (2020)
• Securing Domiciliary Care Homes: Legal and Ethical Requirements Modelling (2020)

Undergraduate: The group members typically lead modules in BSc Business Analytics, BSc MORSE and those offered to other students from the Management School or other faculties covering topics such as decision theory, risk theory, queueing theory, simulation, business intelligence, probability & statistics for business and management, spreadsheet modelling, and analytics computing (e.g., R, Python, VBA).