Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:26:34

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: school_finance

```sql
CREATE TABLE School (
  School_id TEXT,
  School_name TEXT,
  Location TEXT,
  Mascot TEXT,
  Enrollment NUMBER,
  IHSAA_Class TEXT,
  IHSAA_Football_Class TEXT,
  County TEXT
);
```

```sql
CREATE TABLE budget (
  School_id NUMBER,
  Year NUMBER,
  Budgeted NUMBER,
  total_budget_percent_budgeted NUMBER,
  Invested NUMBER,
  total_budget_percent_invested NUMBER,
  Budget_invested_percent TEXT
);
```

```sql
CREATE TABLE endowment (
  endowment_id NUMBER,
  School_id NUMBER,
  donator_name TEXT,
  amount NUMBER
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "school_finance",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing", 
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "school_finance",
  "iteration": 0,
  "business_context": "A school district aims to allocate its budget across multiple schools to maximize the total educational impact while staying within the total budget and ensuring a minimum investment in each school.",
  "optimization_problem_description": "The district needs to decide how much to invest in each school to maximize the total educational impact, measured by the sum of weighted investments, while ensuring that the total investment does not exceed the total budget and that each school receives a minimum investment.",
  "optimization_formulation": {
    "objective": "maximize \u2211(weight_school_i \u00d7 investment_school_i)",
    "decision_variables": "investment_school_i (continuous)",
    "constraints": [
      "\u2211(investment_school_i) \u2264 total_budget",
      "investment_school_i \u2265 minimum_investment_school_i for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "weight_school_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "weight representing the educational impact per dollar invested in school i"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "budget.Budgeted",
        "mapping_adequacy": "partial",
        "description": "total budget available for investment across all schools"
      },
      "minimum_investment_school_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum investment required for school i"
      }
    },
    "decision_variables": {
      "investment_school_i": {
        "currently_mapped_to": "budget.Invested",
        "mapping_adequacy": "partial",
        "description": "amount invested in school i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "weights for educational impact per dollar invested in each school",
    "minimum investment required for each school"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define weights for educational impact and minimum investment requirements for each school"
  }
}
