Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:29:19

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_bus

```sql
CREATE TABLE driver (
  Driver_ID NUMBER,
  Name TEXT,
  Party TEXT,
  Home_city TEXT,
  Age NUMBER
);
```

```sql
CREATE TABLE school (
  School_ID NUMBER,
  Grade TEXT,
  School TEXT,
  Location TEXT,
  Type TEXT
);
```

```sql
CREATE TABLE school_bus (
  School_ID NUMBER,
  Driver_ID NUMBER,
  Years_Working NUMBER,
  If_full_time OTHERS
);
```



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_bus",
  "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_bus",
  "iteration": 0,
  "business_context": "Optimize the assignment of drivers to schools to minimize total travel distance while ensuring each school is assigned exactly one driver and each driver is assigned to at most one school.",
  "optimization_problem_description": "The goal is to minimize the total travel distance between drivers' home cities and schools' locations. Each school must be assigned exactly one driver, and each driver can be assigned to at most one school. The problem is formulated as a linear assignment problem.",
  "optimization_formulation": {
    "objective": "minimize \u2211(distance[Driver_ID, School_ID] \u00d7 assign[Driver_ID, School_ID])",
    "decision_variables": "assign[Driver_ID, School_ID] (binary: 1 if driver is assigned to school, 0 otherwise)",
    "constraints": [
      "\u2211(assign[Driver_ID, School_ID]) = 1 for each School_ID (each school must have exactly one driver)",
      "\u2211(assign[Driver_ID, School_ID]) \u2264 1 for each Driver_ID (each driver can be assigned to at most one school)",
      "assign[Driver_ID, School_ID] \u2208 {0, 1} for all Driver_ID, School_ID (binary decision variables)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "distance[Driver_ID, School_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Travel distance between driver's home city and school's location"
      }
    },
    "constraint_bounds": {
      "constraint_1[School_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Each school must have exactly one driver"
      },
      "constraint_2[Driver_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Each driver can be assigned to at most one school"
      }
    },
    "decision_variables": {
      "assign[Driver_ID, School_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating assignment of driver to school",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Distance matrix between drivers' home cities and schools' locations",
    "Mapping of drivers' home cities and schools' locations to calculate distances"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Obtain or calculate the distance matrix between drivers' home cities and schools' locations to complete the optimization model."
  }
}
