Integrative capstone
Simulation Capstone
A substantial computational model of your own choosing, taken from problem statement to accessible presentation.
§ Project brief
The capstone is an integrative modelling project. You will select a system or question of interest, formulate a computational model, implement it, verify and validate it, analyse its sensitivity and uncertainty, run a designed scenario experiment, and communicate the results to both a technical and a non-technical audience.
The capstone is assessed on the rigour of the modelling process and the clarity of the communication, not on the novelty or sophistication of the underlying model. A simple model with complete verification, careful validation, and honest limitations is worth more than a sophisticated model with incomplete evidence.
You should aim for a project that is ambitious enough to exercise the full fourteen-step lifecycle and modest enough to be completed with rigour in the time available. Typical successful capstones involve models of moderate size with a clear question and a careful treatment of uncertainty.
Process over product
The purpose of the capstone is to demonstrate that you can build a model that another analyst could trust. The most important deliverable is the credibility dossier — the evidence that the model is what it says it is, and that it can support the claims you make about it.
§ Learning outcomes addressed
The capstone assesses the full set of course-level learning outcomes. By completing it, you will demonstrate that you can:
Model formulation
- Translate a real-world system into a computational model specification.
- State the purpose, boundary, variables, parameters, units, and assumptions.
- Write a claim-support statement that follows from the evidence.
Method and implementation
- Select an appropriate numerical or simulation method.
- Design a transparent three-layer spreadsheet or code-based architecture.
- Implement the model reproducibly, with documented inputs and outputs.
- Handle the boundary conditions, step sizes, and initial conditions correctly.
Analysis and evidence
- Verify the implementation against analytical solutions, limiting cases, and conservation laws.
- Validate against held-out evidence, with disconfirming criteria stated in advance.
- Conduct sensitivity and uncertainty analyses and interpret their implications.
- Design and run scenario experiments rather than one-off trials.
- Assess the robustness of the model's conclusions.
Communication
- Produce a technical report that another analyst could review and reproduce.
- Produce a plain-language executive summary for a decision-maker.
- Deliver an accessible presentation to a mixed audience.
- State the model's assumptions and limitations clearly and honestly.
§ Application areas
You may choose any system or question that can be modelled using the methods covered in the course. The following areas are offered as starting points; you are not limited to them.
| Area | Typical methods | Typical question |
|---|---|---|
| Health-service queues | Discrete-event simulation, Markov chains | How many staff are needed to keep waiting times below a target? |
| Inventory systems | Discrete-event simulation, Monte Carlo | What reorder policy minimises cost subject to a service level? |
| Financial risk | Monte Carlo, sensitivity analysis | What is the Value at Risk of a portfolio under assumed return distributions? |
| Energy storage | ODE models, optimisation | What storage capacity is required to smooth a variable supply? |
| Population or epidemic dynamics | ODE models, sensitivity analysis | How do parameter uncertainties affect predicted peak infection? |
| Diffusion or heat transfer | Finite-difference PDE schemes | What is the temperature profile of a rod under given boundary conditions? |
| Transportation flows | Discrete-event simulation, optimisation | What routing scheme minimises average travel time? |
| Supply chains | Discrete-event simulation, Monte Carlo | How does supplier uncertainty propagate through a multi-stage supply chain? |
| Reliability systems | Markov chains, Monte Carlo | What is the long-run availability of a redundant system? |
| Resource allocation | Linear programming, sensitivity analysis | How should a fixed budget be allocated across competing activities? |
| Environmental uncertainty | Monte Carlo, sensitivity analysis | What range of outcomes is plausible under uncertain environmental inputs? |
| Emergency-service operations | Discrete-event simulation | How do response times depend on station location and fleet size? |
Choosing a topic
Choose something you know or can learn about quickly. A model of a system you understand well is easier to validate than a model of a system you have read about once. If you have access to data — even a small amount — that is a strong signal that the topic is a good fit.
§ Deliverables
The capstone has two assessed components: the capstone report (45%) and the capstone presentation (5%). The report contains a set of required sub-deliverables, each of which must be present for the report to be complete.
Capstone report
The main deliverable. Includes the model, the evidence, the results, and the documentation.
Capstone presentation
An accessible presentation of the model, its results, and its limitations, delivered to a mixed audience.
Required sub-deliverables
The following elements must appear in the capstone report. Each is assessed under the rubric in the next section.
| # | Sub-deliverable | What it should contain |
|---|---|---|
| 1 | Project proposal | The question, the system, the intended method, and the success criteria. |
| 2 | Problem and stakeholder statement | Who cares about the answer, and what decision it supports. |
| 3 | Model-purpose statement | What the model is meant to do, and what it is not meant to do. |
| 4 | Variables, parameters, units, and assumptions | A complete table with sources for each value. |
| 5 | Conceptual model diagram | A figure showing the components of the system and their relationships. |
| 6 | Mathematical formulation | Equations, initial conditions, boundary conditions, and constraints. |
| 7 | Numerical or simulation method | The method, the step size or replication scheme, and the justification. |
| 8 | Model implementation | Three-layer architecture, documented inputs and outputs. |
| 9 | Verification evidence | Five or more tests with criteria stated in advance. |
| 10 | Validation evidence | Held-out data, disconfirming evidence stated in advance, results. |
| 11 | Numerical error analysis | Convergence study, step-size sensitivity, or replication error. |
| 12 | Sensitivity and uncertainty analysis | One-at-a-time sensitivity, joint uncertainty propagation, robustness. |
| 13 | Scenario experiments | A designed experiment comparing alternatives. |
| 14 | Results and visualizations | Charts, tables, and the interpretation of each. |
| 15 | Limitations and ethical considerations | What the model does not address; ethical issues raised by its use. |
| 16 | Reproducible spreadsheet or code files | Model files, data, seeds, and a readme sufficient to rerun. |
| 17 | Technical report | The full report itself, written for a technical reviewer. |
| 18 | Plain-language executive summary | One page for a non-technical reader. Answers the five questions. |
| 19 | Accessible presentation | Slides or equivalent, usable by the full audience. |
§ Timeline and milestones
The capstone is undertaken in the final weeks of the course, after Module 7. The following is a suggested schedule. Adjust it to your own pace, but keep the milestones.
- Week 14 — Topic selection and proposal Choose a topic. Write and submit the project proposal. Confirm the topic with the course tutor.
- Week 15 — Formulation and implementation Write the specification. Build the three-layer spreadsheet or code. Get the model running on a small case.
- Week 16 — Verification and validation Run the verification tests. Design and execute the validation exercise. Address any failures.
- Week 17 — Analysis and results Conduct sensitivity and uncertainty analyses. Run the scenario experiments. Prepare the figures.
- Week 17 (end) — Draft review Submit a draft of the report to the course tutor for feedback.
- Week 18 — Revisions and submission Incorporate feedback. Finalise the report, the summary, and the presentation. Submit through the LMS.
Do not leave everything to the last week
The capstone is a substantial piece of work. Students who attempt to complete it in the final week almost always submit something incomplete. Start early, work steadily, and use the draft review milestone.
§ Proposal guidelines
The project proposal is a one- to two-page document submitted before the main work begins. It establishes the scope of the project and confirms that the topic is appropriate.
The proposal must answer six questions
- What is the question? State the decision or understanding the model is meant to support.
- What is the system? Describe the system you will model and the boundary you will draw around it.
- What method will you use? Name the modelling approach (ODE, PDE, Monte Carlo, DES, LP) and the numerical method.
- What data do you have? Describe the data you will use to calibrate and validate the model.
- How will you verify and validate? State the tests you intend to run and the criteria you will use.
- What will success look like? State the deliverable and the claim-support scope you expect.
§ Report structure
The technical report is the primary deliverable. It should be written for a technical reviewer who is familiar with the course material but not with your specific project. The following structure is recommended.
| Section | Purpose |
|---|---|
| Title page | Course number, project title, your name and student ID, submission date. |
| Executive summary | One page. Question, approach, finding, recommendation, caveats. |
| 1. Introduction and purpose | The decision the model supports. The question it answers. |
| 2. System and boundary | What is inside the model and what is outside. |
| 3. Model specification | Variables, parameters, units, assumptions, claim-support scope. |
| 4. Conceptual model | Diagram and its explanation. |
| 5. Mathematical formulation | Equations and conditions in full. |
| 6. Data | Sources, treatment, calibration and validation split. |
| 7. Method | Method chosen, parameters, and justification. |
| 8. Implementation | Architecture, software, files delivered. |
| 9. Verification | Tests performed, criteria, results. |
| 10. Validation | Held-out data, disconfirming evidence, results, verdict. |
| 11. Sensitivity and uncertainty | One-at-a-time and joint analyses, robustness assessment. |
| 12. Scenario experiments | Design, results, interpretation. |
| 13. Results and discussion | Principal findings with confidence intervals. |
| 14. Limitations and ethical considerations | What the model does not address. Responsible-use issues. |
| 15. Recommendation | The action the model supports, conditional on its assumptions. |
| 16. Claim-support statement | A precise statement of what the model can and cannot support. |
| References | IEEE style. Every cited source verified. |
| Appendix A — Model files | List of delivered files with a short description of each. |
| Appendix B — Reproducibility instructions | The readme and step-by-step rerun procedure. |
Length
A complete capstone report is typically 20–30 pages including figures, tables, and appendices. The length is not a criterion for assessment; completeness and clarity are. Do not pad the report, and do not omit required elements to shorten it.
§ Presentation
The capstone presentation is a short talk delivered to a mixed audience. It is worth 5% of the course grade and is assessed separately from the report. The purpose of the presentation is to communicate the finding to a non-specialist audience, and to answer questions.
Format
- Duration: 10–15 minutes, plus 5 minutes for questions.
- Audience: a mixed audience of peers and the course tutor.
- Slides: 8–12 slides, one idea per slide.
- Delivery: in person or recorded, as arranged with the tutor.
Content
- The question What decision or understanding does the model support?
- The system and the model What system is modelled? What method was used?
- The finding What did the model say? Include uncertainty.
- The recommendation What action does the model support?
- The caveats What the model does not address. What could change the answer.
Accessibility
- Large, high-contrast text; readable from the back of a room.
- Plain-language labels on every chart; no unexplained acronyms.
- Colour is not the only signal; use shape and position as well.
- Text descriptions of key charts, provided verbally and in handouts.
- One idea per slide; the message is the point.
§ Rubric
The capstone is assessed against ten criteria. The weights sum to 100 percent.
| Criterion | Weight | What is assessed |
|---|---|---|
| Problem definition and conceptual model | 8% | The question, the system, the boundary, and the conceptual diagram are clear and justified. |
| Mathematical formulation | 12% | Equations, variables, parameters, units, and assumptions are stated correctly and completely. |
| Method selection | 10% | The method is appropriate to the problem and its choice is justified. |
| Implementation quality | 15% | Three-layer architecture; no hidden hard-coded constants; formula correctness; boundary handling. |
| Verification and numerical testing | 12% | Multiple diverse tests; criteria stated in advance; convergence and error analysis. |
| Validation | 10% | Held-out data; disconfirming evidence stated in advance; scope of validation. |
| Sensitivity and uncertainty analysis | 10% | Sensitivity to each input; joint uncertainty propagated; robustness of the conclusions assessed. |
| Results and interpretation | 8% | Results are presented with confidence intervals and interpreted correctly. |
| Reproducibility and documentation | 8% | Model files, data, seeds, software versions, and a readme sufficient for a rerun. |
| Communication and accessibility | 7% | Technical report, executive summary, and presentation are clear, accurate, and accessible. |
| Total | 100% |
In addition to the weighted rubric, the following minimum requirements must be met for the capstone to be considered complete:
- The capstone report is submitted on time.
- All 19 required sub-deliverables are present.
- The capstone presentation is delivered.
- Functioning model files are included in the submission.
- The submission meets academic-integrity requirements.
- The overall capstone grade is at least 50 percent.
§ Ethical considerations
A model is not neutral. It encodes assumptions, prioritises some outcomes over others, and may be used to justify decisions that affect people. The capstone requires you to address the ethical dimensions of your model alongside the technical ones.
Data privacy
If your model uses data about individuals — patients, customers, employees, students — you must handle it responsibly. Do not include personally identifiable information in the submission. Anonymise or aggregate as appropriate. If the data were provided under an agreement, respect the terms of that agreement.
Bias in inputs and assumptions
Models inherit the biases of their inputs. Historical data may reflect past discrimination or unequal treatment. Assumptions about behaviour may embed stereotypes. Part of your discussion should address where bias could enter the model and how it might affect the conclusions.
Stakeholder impacts
Identify who is affected by the decisions your model supports. Consider whether the model's conclusions are likely to benefit some groups more than others. Where the answer is uncertain, state so.
Transparent reporting
Report the results you obtained, including those that complicate the story. Do not omit a sensitivity result because it undermines the recommendation. Do not present a point estimate as if it were a certainty. Communicate uncertainty honestly.
Responsible use of optimisation
If your model involves optimisation, consider what is being optimised and for whom. An optimal solution according to one objective may be poor according to another. The choice of objective is a value judgement, not a technical one.
Responsible use of generative AI
If you use generative AI tools in the preparation of your capstone, disclose this in the submission. Do not use AI to generate content that you do not understand. Do not cite sources you have not verified. Verify that any code produced by AI actually works and actually does what you intend.
Do not skip this section
The ethical considerations are not decoration. They are part of what it means to build a model responsibly, and they are assessed under the rubric's "Limitations and ethical considerations" sub-deliverable.
§ Common pitfalls
Based on past capstones, the following are the most common causes of a disappointing result. Watch for each one.
Watch for these
- Choosing a topic that is too large. A project that cannot be completed with rigour is worse than a modest one that is completed thoroughly.
- Skipping the specification. Without a clear specification, nothing downstream can be justified.
- Building the model before writing the purpose statement. The purpose determines the method, not the other way around.
- Verifying against the implementation itself. Convergence checks are not correctness checks. Use an external standard.
- Validating on calibration data. The held-out discipline is essential.
- Setting acceptance criteria after seeing the result. The criteria must be stated in advance.
- Reporting a point estimate without a confidence interval. Uncertainty is part of the result.
- Confusing simulation precision with model validity. A narrow interval does not imply a correct model.
- Leaving the report until the last week. The capstone is too large to complete in a few days.
- Writing only for the technical audience. The executive summary and presentation are required deliverables.
- Overclaiming the model's scope. The claim-support statement should follow from the evidence.
- Forgetting to document the seeds. A stochastic model without recorded seeds is not reproducible.
§ Submission
What to submit
A single ZIP archive named
MATH4810-capstone-studentID.zip containing:
- The capstone report as a PDF.
- The executive summary as a one-page PDF.
- The model files — spreadsheet or code, in their native format.
- The data files used for calibration and validation.
- The readme with the reproducibility instructions.
- The presentation — slides in PDF format, and, if recorded, the video file or a link.
- The AI-use disclosure, if any AI tool was used.
How to submit
Submit through the course LMS by the deadline listed in the course schedule. Late submissions are subject to the penalty described in the syllabus. Extensions must be requested from the course tutor before the deadline.
After submission
The capstone is marked against the rubric by the course tutor. Written feedback is provided within two weeks of submission. Students who wish to appeal the grade should follow the university's grade-appeal procedure.
Final note
The capstone is the most demanding piece of work in the course. It is also, for many students, the most satisfying. If you have read this page carefully, prepared in advance, and used the milestones as intended, you are ready to begin.