You have been hired as the scheduling analyst for the Blue Ridge Summer League. The league commissioner needs a schedule that is fair, compact, and accounts for team rest. Your job is to build the optimization model, evaluate whether AI tools can replicate your work, and redesign the model under new league priorities.
This project is designed as a multi-phase decision-modeling exercise. Across the semester, you will move from baseline model construction to model extension, AI-assisted evaluation, and structural redesign under changing managerial priorities. The purpose of the project is not only to practice optimization techniques, but also to develop the ability to explain, evaluate, and defend modeling choices in a realistic decision context.
You will:
The objective is not merely to construct a feasible schedule. Rather, the project is designed to examine how modeling decisions, constraint interaction, objective selection, and managerial priorities influence optimization behavior. Later phases explicitly evaluate the reliability and limitations of AI-generated optimization models.
All models must be implemented in Microsoft Excel using Solver and must remain within the 200 decision variable limit and 100 constraint limit of the standard Solver configuration.
Facilities and time slots are not explicitly modeled. The schedule is formulated at the day level.
Before solving, you should verify several implied bounds:
Failure to verify these structural bounds often leads to infeasible or logically inconsistent models.
To verify your understanding of the variable structure, consider a simplified version of the problem.
Setup: 2 teams (A, B), 3 days, at most 1 game per day, and the pair must play at least 1 and at most 2 games.
The single decision variable for each day is:
| Day 1 | Day 2 | Day 3 | |
|---|---|---|---|
| A vs B | $x_1$ | $x_2$ | $x_3$ |
where $x_d \in \{0, 1\}$ indicates whether the pair plays on day $d$.
Valid schedule: $x_1 = 1, x_2 = 0, x_3 = 1$
Infeasible schedule: $x_1 = 1, x_2 = 1, x_3 = 1$
In the full problem, you will have 6 pairs and 10 days. The variable structure scales accordingly.
| Week | Phase | Deliverable |
|---|---|---|
| Week 9 | Phase 1 | Baseline formulation |
| Week 10 | Phase 2 | Schedule quality and constraint interaction |
| Week 11 | Feedback and review | Instructor feedback on Phases 1–2; prepare for AI evaluation |
| Week 12 | Phase 3 | AI-assisted formulation, equivalence, and model responsibility |
| Week 13 | Phase 4a | Structural redesign under a new league priority |
| Week 14 | Phase 4b | AI redesign evaluation and comparative analysis |
| Week 15 | Final reflection | Synthesis |
In this phase, you will build a baseline scheduling model for the Blue Ridge Summer League. The goal is to translate the league’s basic rules and requirements into a workable optimization model.
This phase establishes the foundation for the rest of the project. Your objective is not only to produce a correct baseline formulation, but also to begin thinking carefully about what the model includes, what it leaves out, and what assumptions make the formulation possible.
Maximize the total number of games scheduled over the 10-day horizon.
Your model must enforce:
Checkpoint
- How many binary decision variables does your model have?
- What is the theoretical maximum number of games? What is the minimum?
- Does your constraint count match the number of structural requirements listed above?
In Phase 2, you will extend your baseline model to account for schedule quality through rest considerations. The goal is to move beyond simple feasibility and begin evaluating what makes a schedule more desirable from a managerial perspective.
This phase asks you to examine the tradeoff between schedule quantity and schedule quality. In doing so, you should begin to think not only about how to modify the model, but also about what values your formulation is prioritizing.
All Phase 1 constraints remain in force.
Minimize total rest violations.
A rest violation occurs when a team is scheduled to play on two consecutive days (i.e., day $t$ and day $t+1$). Each such occurrence counts as one violation.
Note: A team can play at most one game per day, so a rest violation only depends on whether the team plays on adjacent days, not on the number of games.
Hint: In addition to the Phase 1 constraints, you will need to introduce new variables and constraints to track when a team plays on consecutive days.
This typically requires:
- Defining whether each team plays on each day, and
- Defining whether a rest violation occurs between consecutive days
These variables must be properly linked so that a rest violation is counted if and only if a team plays on both day $t$ and day $t+1$.
You should explicitly consider:
Superficial rest-counting approaches without correct logical linkage will receive reduced credit.
Checkpoint
- Is zero rest violations feasible? Write your argument before solving.
- How many new variables did you introduce? Are they correctly linked to the game variables?
- Did you preserve all Phase 1 constraints without modification?
A fully correct linearization of the Phase 2 model will likely exceed Excel Solver’s 200-variable and 100-constraint limits. You have two paths:
You are not required to pursue either path. If your model hits the solver limit, document what happened and reflect on the trade-off between model form, solver choice, and solution quality.
By the end of Phase 2, you have already constructed and extended a workable scheduling model. The second half of the project shifts the focus from model construction alone to model evaluation, model responsibility, and model redesign.
In Phase 3, you will examine whether a publicly available AI system can meaningfully reproduce the structure and logic of your model. In Phase 4, you will redesign the model under a changed league priority and evaluate how that shift alters the tradeoffs and recommendations. Across both phases, the goal is not merely to obtain a feasible model, but to determine which model version you are willing to defend and why.
In Phase 2, you extended your model to account for schedule quality through rest considerations. In this phase, you will examine whether a publicly available AI system can produce a formulation that is equivalent to, or meaningfully different from, your Phase 2 model.
The purpose of this phase is not simply to show that AI makes mistakes. In some cases, the AI-generated model may be largely correct. Your task is to determine whether the AI-generated formulation is truly equivalent to your Phase 2 model, whether it is preferable in any meaningful way, and which version you are ultimately willing to defend.
Do not correct the AI-generated model before analyzing it.
Note on linearity and solver compatibility: Your prompt to the AI must explicitly require a linear formulation. AI tools often produce nonlinear formulations (e.g., products of binary variables) that are incompatible with Excel Solver’s Simplex LP method. If the AI-generated model is nonlinear despite your instruction, revise your prompt until a linear formulation is obtained. If the resulting linear model exceeds Excel Solver’s 200-variable or 100-constraint limit, use LibreOffice Calc’s solver, which supports larger models and provides a spreadsheet experience similar to Excel. You are also encouraged to use AI to generate scaffolding code to solve the model with other solvers such as PuLP.
Use the following comparison structure:
| Dimension | Your Phase 2 Model | AI-Generated Model | Final Responsible Model |
|---|---|---|---|
| Decision variables | |||
| Objective function | |||
| Constraint structure | |||
| Logical correctness | |||
| Solver feasibility | |||
| 200-variable limit compliance | |||
| 100-constraint limit compliance | |||
| Interpretability / compactness | |||
| Extensibility for future redesign | |||
| Which version you would defend and why |
A strong submission does not require the AI-generated model to be wrong. High-quality work may show that the AI-generated model is largely correct, while still carefully comparing formulation quality, assumptions, interpretability, and defensibility across versions.
Briefly address the following:
| Criterion | Points |
|---|---|
| Accurate implementation of the AI-generated model | 5 |
| Evaluation of correctness and equivalence | 10 |
| Quality of comparison across model versions | 10 |
| Analysis of formulation quality, interpretability, and extensibility | 10 |
| Evidence of model ownership and responsible judgment | 10 |
| Clarity, specificity, and supporting evidence | 5 |
| Total | 50 |
In this phase, the league commissioner has introduced a new managerial priority. Your task is not simply to add another constraint. Instead, you must redesign the model so that it reflects a meaningful change in what the league values.
The purpose of this phase is to evaluate your ability to revise a model when managerial priorities shift, and to assess whether AI can meaningfully support that redesign. A strong redesign should do more than make the model more complicated. It should make clear what value is being protected, what tradeoff is being introduced, and what new limitations arise.
Select one substantive structural redesign that reflects a realistic new league priority. Examples include, but are not limited to:
Merely changing numerical parameter values does not count as a structural redesign.
Note on linearity and solver compatibility: Your prompt to the AI must explicitly require a linear formulation. AI tools often produce nonlinear formulations (e.g., products of binary variables) that are incompatible with Excel Solver’s Simplex LP method. If the AI-generated redesign is nonlinear despite your instruction, revise your prompt until a linear formulation is obtained. If the resulting linear model exceeds Excel Solver’s 200-variable or 100-constraint limit, use LibreOffice Calc’s solver, which supports larger models and provides a spreadsheet experience similar to Excel. You are also encouraged to use AI to generate scaffolding code to solve the model with other solvers such as PuLP.
A strong submission will focus not only on technical changes, but also on the managerial consequences of the redesign.
Write a short executive recommendation (200–300 words) to the league commissioner that addresses:
| Criterion | Points |
|---|---|
| Quality and justification of the structural redesign | 15 |
| Correctness of the redesigned formulation | 10 |
| Analysis of tradeoffs and managerial consequences | 10 |
| Evaluation of the AI-generated redesign | 10 |
| Comparison of defensibility, interpretability, and extensibility across redesigns | 10 |
| Clarity, organization, and supporting evidence | 5 |
| Total | 60 |
Maximum length: 1 page.
This reflection should synthesize your per-phase observations into broader insights. Revisit your brief reflections from Phases 1–4 and address:
Your responses must reference specific experiences from the project. General statements without connection to your modeling work will receive reduced credit.
| Component | Points |
|---|---|
| Phase 1 | 25 |
| Phase 2 | 45 |
| Phase 3 | 50 |
| Phase 4 | 60 |
| Final reflection | 20 |
| Total | 200 |
This project assesses:
There is no requirement that AI must fail.
There is an expectation that you can explain how structural complexity, modeling assumptions, and changing priorities alter feasibility, optimality, and model robustness.