Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:29:24

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 company wants to optimize the assignment of technicians to machine repairs to minimize the total value points of machines being repaired, ensuring that each repair is assigned to exactly one technician and each technician can handle a limited number of repairs.",
  "optimization_problem": "The goal is to minimize the total value points of machines assigned to technicians for repair, subject to constraints on technician availability and repair requirements.",
  "objective": "minimize sum(value_points[machine_id] * x[technician_id, repair_id])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include adding a new table for constraint bounds, modifying existing tables for better mapping, and updating configuration logic for missing parameters."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine the maximum number of repairs each technician can handle and ensure all necessary data is available for constraints",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a new table for constraint bounds, modifying existing tables for better mapping, and updating configuration logic for missing parameters.

CREATE TABLE machine (
  machine_id INTEGER,
  value_points INTEGER
);

CREATE TABLE repair_assignment (
  technician_id INTEGER,
  repair_id INTEGER,
  is_assigned BOOLEAN
);

CREATE TABLE constraint_bounds (
  technician_id INTEGER,
  max_repairs INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "machine": {
      "business_purpose": "Stores information about machines needing repair",
      "optimization_role": "objective_coefficients",
      "columns": {
        "machine_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each machine",
          "optimization_purpose": "Index for value points",
          "sample_values": "1, 2, 3"
        },
        "value_points": {
          "data_type": "INTEGER",
          "business_meaning": "Value points of the machine",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "10, 20, 30"
        }
      }
    },
    "repair_assignment": {
      "business_purpose": "Tracks which technician is assigned to which repair",
      "optimization_role": "decision_variables",
      "columns": {
        "technician_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for technician",
          "optimization_purpose": "Index for decision variable",
          "sample_values": "1, 2, 3"
        },
        "repair_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for repair task",
          "optimization_purpose": "Index for decision variable",
          "sample_values": "101, 102, 103"
        },
        "is_assigned": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a technician is assigned to a repair",
          "optimization_purpose": "Binary decision variable",
          "sample_values": "true, false"
        }
      }
    },
    "constraint_bounds": {
      "business_purpose": "Stores constraint bounds for optimization",
      "optimization_role": "constraint_bounds",
      "columns": {
        "technician_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for technician",
          "optimization_purpose": "Index for constraint",
          "sample_values": "1, 2, 3"
        },
        "max_repairs": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum repairs a technician can handle",
          "optimization_purpose": "Constraint bound",
          "sample_values": "5, 5, 5"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_repairs_per_technician": {
    "sample_value": "5",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of repairs a technician can handle",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  }
}


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

JSON STRUCTURE REQUIRED:

{
  "database_id": "machine_repair",
  "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": "machine_repair",
  "iteration": 1,
  "business_context": "A company wants to optimize the assignment of technicians to machine repairs to minimize the total value points of machines being repaired, ensuring that each repair is assigned to exactly one technician and each technician can handle a limited number of repairs.",
  "optimization_problem_description": "The goal is to minimize the total value points of machines assigned to technicians for repair, subject to constraints on technician availability and repair requirements.",
  "optimization_formulation": {
    "objective": "minimize sum(value_points[machine_id] * x[technician_id, repair_id])",
    "decision_variables": "x[technician_id, repair_id] are binary variables indicating if a technician is assigned to a repair",
    "constraints": [
      "sum(x[technician_id, repair_id] for all repair_id) <= max_repairs[technician_id] for all technician_id",
      "sum(x[technician_id, repair_id] for all technician_id) = 1 for all repair_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "value_points[machine_id]": {
        "currently_mapped_to": "machine.value_points",
        "mapping_adequacy": "good",
        "description": "Value points of the machine, used as coefficients in the objective function"
      }
    },
    "constraint_bounds": {
      "max_repairs[technician_id]": {
        "currently_mapped_to": "constraint_bounds.max_repairs",
        "mapping_adequacy": "good",
        "description": "Maximum number of repairs a technician can handle"
      }
    },
    "decision_variables": {
      "x[technician_id, repair_id]": {
        "currently_mapped_to": "repair_assignment.is_assigned",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if a technician is assigned to a repair",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
