Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:35:24

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain 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
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


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



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "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": "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.",
  "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",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for decision variables and constraints, modifying existing tables to align with optimization requirements, and adding business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints and decision variables to better align with the schema and business requirements",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraints, modifying existing tables to align with optimization requirements, and adding business configuration logic for scalar parameters and formulas.

CREATE TABLE architect_project_assignments (
  architect_id INTEGER,
  project_id INTEGER,
  min_projects INTEGER,
  max_projects INTEGER
);

CREATE TABLE decision_variables (
  bridge_decision BOOLEAN,
  mill_decision BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "architect_project_assignments": {
      "business_purpose": "Mapping of architects to their respective bridges and mills",
      "optimization_role": "constraint_bounds",
      "columns": {
        "architect_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each architect",
          "optimization_purpose": "Links architects to projects",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "project_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each project",
          "optimization_purpose": "Links projects to architects",
          "sample_values": [
            101,
            102,
            103
          ]
        },
        "min_projects": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum number of projects an architect must handle",
          "optimization_purpose": "Lower bound for constraint",
          "sample_values": [
            1,
            1,
            1
          ]
        },
        "max_projects": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of projects an architect can handle",
          "optimization_purpose": "Upper bound for constraint",
          "sample_values": [
            3,
            3,
            3
          ]
        }
      }
    },
    "decision_variables": {
      "business_purpose": "Binary decision variables for bridges and mills",
      "optimization_role": "decision_variables",
      "columns": {
        "bridge_decision": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates whether a bridge is built",
          "optimization_purpose": "Binary decision variable for bridges",
          "sample_values": [
            true,
            false,
            true
          ]
        },
        "mill_decision": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates whether a mill is built",
          "optimization_purpose": "Binary decision variable for mills",
          "sample_values": [
            false,
            true,
            false
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_projects_per_architect": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of projects an architect can handle",
    "optimization_role": "Upper bound for constraint on project assignments",
    "configuration_type": "scalar_parameter"
  },
  "min_projects_per_architect": {
    "sample_value": 1,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of projects an architect must handle",
    "optimization_role": "Lower bound for constraint on project assignments",
    "configuration_type": "scalar_parameter"
  },
  "project_assignment_formula": {
    "formula_expression": "IF(architect_project_count <= max_projects_per_architect, TRUE, FALSE)",
    "data_type": "STRING",
    "business_meaning": "Ensures architects are not overburdened with projects",
    "optimization_role": "Constraint enforcement",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "architecture",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 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 still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "architecture",
  "iteration": 1,
  "business_context": "A construction company aims to minimize the total length of bridges and mills built by architects while ensuring each architect is assigned to at least one project and no architect is overburdened with more than three projects.",
  "optimization_problem_description": "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 decision variable for bridge i, y[j]: binary decision variable for mill j",
    "constraints": "\u2211(x[i] + y[j]) >= min_projects_per_architect for each architect, \u2211(x[i] + y[j]) <= max_projects_per_architect for each architect"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "length_meters[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Length of bridge i in meters"
      },
      "length_feet[j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Length of mill j in feet"
      }
    },
    "constraint_bounds": {
      "min_projects_per_architect": {
        "currently_mapped_to": "business_configuration_logic.min_projects_per_architect",
        "mapping_adequacy": "good",
        "description": "Minimum number of projects an architect must handle"
      },
      "max_projects_per_architect": {
        "currently_mapped_to": "business_configuration_logic.max_projects_per_architect",
        "mapping_adequacy": "good",
        "description": "Maximum number of projects an architect can handle"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "decision_variables.bridge_decision",
        "mapping_adequacy": "good",
        "description": "Binary decision variable for bridge i",
        "variable_type": "binary"
      },
      "y[j]": {
        "currently_mapped_to": "decision_variables.mill_decision",
        "mapping_adequacy": "good",
        "description": "Binary decision variable for mill j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "length_meters[i]",
    "length_feet[j]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine objective coefficients to include length data for bridges and mills"
  }
}
