Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:35:24

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: architecture

```sql
CREATE TABLE architect (
  id TEXT,
  name TEXT,
  nationality TEXT,
  gender TEXT
);
```

```sql
CREATE TABLE bridge (
  architect_id NUMBER,
  id NUMBER,
  name TEXT,
  location TEXT,
  length_meters NUMBER,
  length_feet NUMBER
);
```

```sql
CREATE TABLE mill (
  architect_id NUMBER,
  id NUMBER,
  location TEXT,
  name TEXT,
  type TEXT,
  built_year NUMBER,
  notes TEXT
);
```



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": "architecture",
  "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": "architecture",
  "iteration": 0,
  "business_context": "A construction company wants to minimize the total length of bridges and mills built by architects while ensuring that each architect is assigned to at least one project and no architect is overburdened with more than three projects.",
  "optimization_problem_description": "The company aims to minimize the total length of bridges and mills built by architects, subject to constraints on the number of projects each architect can handle and ensuring each architect is assigned to at least one project.",
  "optimization_formulation": {
    "objective": "minimize \u2211(length_meters[i] * x[i] + length_feet[j] * y[j]) where x[i] and y[j] are binary decision variables indicating whether bridge i or mill j is built",
    "decision_variables": "x[i] (binary, 1 if bridge i is built, 0 otherwise), y[j] (binary, 1 if mill j is built, 0 otherwise)",
    "constraints": [
      "\u2211(x[i] + y[j]) >= 1 for each architect k (each architect must be assigned to at least one project)",
      "\u2211(x[i] + y[j]) <= 3 for each architect k (no architect can be assigned to more than three projects)",
      "x[i] \u2208 {0, 1} for all bridges i (binary decision variable for bridges)",
      "y[j] \u2208 {0, 1} for all mills j (binary decision variable for mills)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "length_meters[i]": {
        "currently_mapped_to": "bridge.length_meters",
        "mapping_adequacy": "good",
        "description": "length of bridge i in meters"
      },
      "length_feet[j]": {
        "currently_mapped_to": "bridge.length_feet",
        "mapping_adequacy": "good",
        "description": "length of bridge j in feet"
      }
    },
    "constraint_bounds": {
      "constraint_1[k]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "each architect k must be assigned to at least one project"
      },
      "constraint_2[k]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "no architect k can be assigned to more than three projects"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary decision variable for bridge i",
        "variable_type": "binary"
      },
      "y[j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary decision variable for mill j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Data on the number of projects each architect is currently handling",
    "Mapping of architects to their respective bridges and mills",
    "Binary decision variables for bridges and mills"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine constraints and decision variables to better align with the schema and business requirements"
  }
}
