Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:55:08

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": "An architectural firm wants to optimize the allocation of architects to bridge and mill projects to maximize the total length of bridges and the number of mills designed, considering constraints on the number of projects an architect can handle.",
  "optimization_problem_description": "The firm aims to maximize the total length of bridges and the number of mills designed by allocating architects to projects, subject to constraints on the maximum number of projects an architect can handle and ensuring each project is assigned to exactly one architect.",
  "optimization_formulation": {
    "objective": "maximize total_length_of_bridges + total_number_of_mills",
    "decision_variables": "x_ij: binary variable indicating if architect i is assigned to bridge j; y_ik: binary variable indicating if architect i is assigned to mill k",
    "constraints": [
      "sum(x_ij for all j) + sum(y_ik for all k) <= max_projects_per_architect for each architect i",
      "sum(x_ij for all i) = 1 for each bridge j",
      "sum(y_ik for all i) = 1 for each mill k"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "length_of_bridge[j]": {
        "currently_mapped_to": "bridge.length_meters",
        "mapping_adequacy": "good",
        "description": "length of bridge j in meters"
      },
      "number_of_mills[k]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "indicator for mill k being designed"
      }
    },
    "constraint_bounds": {
      "max_projects_per_architect[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of projects architect i can handle"
      }
    },
    "decision_variables": {
      "x_ij": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating if architect i is assigned to bridge j",
        "variable_type": "binary"
      },
      "y_ik": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating if architect i is assigned to mill k",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Data on the maximum number of projects each architect can handle",
    "Indicator or count for each mill being designed"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data on project handling capacity and mill indicators"
  }
}
