Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:45:44

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 repair shop aims to optimize the assignment of technicians to machine repairs to minimize the total repair time while considering technician expertise and machine priority.",
  "optimization_problem": "The objective is to minimize the total repair time by assigning technicians to machine repairs efficiently. Constraints include ensuring each repair is assigned to one technician, each technician is not overloaded, and high-priority machines are repaired first.",
  "objective": "minimize \u2211(repair_time[technician_id, repair_ID] \u00d7 assignment[technician_id, repair_ID])",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating new tables for repair time, technician capacity, and machine priority. Configuration logic updates include scalar parameters for max repairs per technician and min priority, and a formula for repair time calculation."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data for repair time, technician capacity, and machine priority.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for repair time, technician capacity, and machine priority. Configuration logic updates include scalar parameters for max repairs per technician and min priority, and a formula for repair time calculation.

CREATE TABLE repair_time (
  technician_id INTEGER,
  repair_ID INTEGER,
  repair_time FLOAT
);

CREATE TABLE technician_capacity (
  technician_id INTEGER,
  max_repairs INTEGER
);

CREATE TABLE machine_priority (
  Machine_ID INTEGER,
  priority INTEGER
);

CREATE TABLE repair_assignment (
  technician_id INTEGER,
  repair_ID INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "repair_time": {
      "business_purpose": "time taken by a technician to complete a repair",
      "optimization_role": "objective_coefficients",
      "columns": {
        "technician_id": {
          "data_type": "INTEGER",
          "business_meaning": "identifier for the technician",
          "optimization_purpose": "links to technician in repair assignment",
          "sample_values": "1, 2, 3"
        },
        "repair_ID": {
          "data_type": "INTEGER",
          "business_meaning": "identifier for the repair",
          "optimization_purpose": "links to repair in repair assignment",
          "sample_values": "101, 102, 103"
        },
        "repair_time": {
          "data_type": "FLOAT",
          "business_meaning": "time taken to complete the repair",
          "optimization_purpose": "coefficient in the objective function",
          "sample_values": "2.5, 3.0, 4.0"
        }
      }
    },
    "technician_capacity": {
      "business_purpose": "maximum number of repairs a technician can handle",
      "optimization_role": "constraint_bounds",
      "columns": {
        "technician_id": {
          "data_type": "INTEGER",
          "business_meaning": "identifier for the technician",
          "optimization_purpose": "links to technician in repair assignment",
          "sample_values": "1, 2, 3"
        },
        "max_repairs": {
          "data_type": "INTEGER",
          "business_meaning": "maximum number of repairs the technician can handle",
          "optimization_purpose": "bound in the constraint",
          "sample_values": "5, 6, 7"
        }
      }
    },
    "machine_priority": {
      "business_purpose": "priority level for machine repairs",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Machine_ID": {
          "data_type": "INTEGER",
          "business_meaning": "identifier for the machine",
          "optimization_purpose": "links to repair in repair assignment",
          "sample_values": "201, 202, 203"
        },
        "priority": {
          "data_type": "INTEGER",
          "business_meaning": "priority level of the machine",
          "optimization_purpose": "bound in the constraint",
          "sample_values": "1, 2, 3"
        }
      }
    },
    "repair_assignment": {
      "business_purpose": "assignment of technicians to repairs",
      "optimization_role": "decision_variables",
      "columns": {
        "technician_id": {
          "data_type": "INTEGER",
          "business_meaning": "identifier for the technician",
          "optimization_purpose": "decision variable in the optimization model",
          "sample_values": "1, 2, 3"
        },
        "repair_ID": {
          "data_type": "INTEGER",
          "business_meaning": "identifier for the repair",
          "optimization_purpose": "decision variable in the optimization model",
          "sample_values": "101, 102, 103"
        }
      }
    }
  }
}


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": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "min_priority": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "minimum priority level for machine repairs",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "repair_time_formula": {
    "formula_expression": "repair_time[technician_id, repair_ID] = base_time + (complexity_factor * machine_complexity)",
    "data_type": "STRING",
    "business_meaning": "calculation of repair time based on technician and machine complexity",
    "optimization_role": "objective coefficient",
    "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": "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 repair shop aims to optimize the assignment of technicians to machine repairs to minimize the total repair time while considering technician expertise and machine priority.",
  "optimization_problem_description": "Minimize the total repair time by assigning technicians to machine repairs efficiently. Constraints include ensuring each repair is assigned to one technician, each technician is not overloaded, and high-priority machines are repaired first.",
  "optimization_formulation": {
    "objective": "minimize \u2211(repair_time[technician_id, repair_ID] \u00d7 assignment[technician_id, repair_ID])",
    "decision_variables": "assignment[technician_id, repair_ID] \u2208 {0, 1} (binary decision variable indicating if a technician is assigned to a repair)",
    "constraints": [
      "\u2211(assignment[technician_id, repair_ID] for all technicians) = 1 for each repair_ID (each repair is assigned to one technician)",
      "\u2211(assignment[technician_id, repair_ID] for all repairs) \u2264 max_repairs[technician_id] for each technician_id (technician capacity constraint)",
      "priority[repair_ID] \u2265 min_priority for high-priority repairs (priority constraint)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "repair_time[technician_id, repair_ID]": {
        "currently_mapped_to": "repair_time.repair_time",
        "mapping_adequacy": "good",
        "description": "time taken by a technician to complete a repair"
      }
    },
    "constraint_bounds": {
      "max_repairs[technician_id]": {
        "currently_mapped_to": "technician_capacity.max_repairs",
        "mapping_adequacy": "good",
        "description": "maximum number of repairs a technician can handle"
      },
      "min_priority": {
        "currently_mapped_to": "business_configuration_logic.min_priority",
        "mapping_adequacy": "good",
        "description": "minimum priority level for machine repairs"
      }
    },
    "decision_variables": {
      "assignment[technician_id, repair_ID]": {
        "currently_mapped_to": "repair_assignment.technician_id, repair_assignment.repair_ID",
        "mapping_adequacy": "good",
        "description": "binary decision 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"
  }
}
