Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:48:29

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "A company aims to minimize the total cost of handling customer complaints by optimally assigning staff to complaints based on their efficiency and the severity of the complaints. The cost is determined by the time each staff member spends on each complaint and their hourly wage.",
  "optimization_problem": "The objective is to minimize the total cost of handling complaints, which is a linear function of the time each staff member spends on each complaint and their hourly wage. The constraints ensure that each complaint is assigned to exactly one staff member and that no staff member exceeds their maximum working hours.",
  "objective": "minimize \u2211(time_spent[staff_id, complaint_id] * hourly_wage[staff_id])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for the missing decision variable 'time_spent[staff_id, complaint_id]'. Configuration logic remains unchanged as no additional scalar parameters or formulas were identified."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map the missing decision variable 'time_spent[staff_id, complaint_id]' to complete the linear optimization formulation.",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for the missing decision variable 'time_spent[staff_id, complaint_id]'. Configuration logic remains unchanged as no additional scalar parameters or formulas were identified.

CREATE TABLE staff_wages (
  staff_id INTEGER,
  hourly_wage FLOAT
);

CREATE TABLE complaint_time_constraints (
  complaint_id INTEGER,
  min_time FLOAT,
  max_time FLOAT
);

CREATE TABLE staff_working_hours (
  staff_id INTEGER,
  max_hours FLOAT
);

CREATE TABLE time_spent (
  staff_id INTEGER,
  complaint_id INTEGER,
  time_spent FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "staff_wages": {
      "business_purpose": "Hourly wage of each staff member",
      "optimization_role": "objective_coefficients",
      "columns": {
        "staff_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each staff member",
          "optimization_purpose": "Index for staff in the optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "hourly_wage": {
          "data_type": "FLOAT",
          "business_meaning": "Hourly wage of the staff member",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": [
            25.0,
            30.0,
            35.0
          ]
        }
      }
    },
    "complaint_time_constraints": {
      "business_purpose": "Minimum and maximum time required to handle each complaint",
      "optimization_role": "constraint_bounds",
      "columns": {
        "complaint_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each complaint",
          "optimization_purpose": "Index for complaints in the optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "min_time": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum time required to handle the complaint",
          "optimization_purpose": "Lower bound in the time constraint",
          "sample_values": [
            1.0,
            1.5,
            2.0
          ]
        },
        "max_time": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum time allowed to handle the complaint",
          "optimization_purpose": "Upper bound in the time constraint",
          "sample_values": [
            3.0,
            4.0,
            5.0
          ]
        }
      }
    },
    "staff_working_hours": {
      "business_purpose": "Maximum working hours for each staff member",
      "optimization_role": "constraint_bounds",
      "columns": {
        "staff_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each staff member",
          "optimization_purpose": "Index for staff in the optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "max_hours": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum working hours for the staff member",
          "optimization_purpose": "Upper bound in the working hours constraint",
          "sample_values": [
            40.0,
            45.0,
            50.0
          ]
        }
      }
    },
    "time_spent": {
      "business_purpose": "Time spent by each staff member on each complaint",
      "optimization_role": "decision_variables",
      "columns": {
        "staff_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each staff member",
          "optimization_purpose": "Index for staff in the optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "complaint_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each complaint",
          "optimization_purpose": "Index for complaints in the optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "time_spent": {
          "data_type": "FLOAT",
          "business_meaning": "Time spent by the staff member on the complaint",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": [
            1.5,
            2.0,
            2.5
          ]
        }
      }
    }
  }
}



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

JSON STRUCTURE REQUIRED:

{
  "database_id": "customer_complaints",
  "iteration": 2,
  "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": "customer_complaints",
  "iteration": 2,
  "business_context": "A company aims to minimize the total cost of handling customer complaints by optimally assigning staff to complaints based on their efficiency and the severity of the complaints. The cost is determined by the time each staff member spends on each complaint and their hourly wage.",
  "optimization_problem_description": "The objective is to minimize the total cost of handling complaints, which is a linear function of the time each staff member spends on each complaint and their hourly wage. The constraints ensure that each complaint is assigned to exactly one staff member, the time spent on each complaint is within the specified bounds, and no staff member exceeds their maximum working hours.",
  "optimization_formulation": {
    "objective": "minimize \u2211(time_spent[staff_id, complaint_id] * hourly_wage[staff_id])",
    "decision_variables": "time_spent[staff_id, complaint_id] (continuous)",
    "constraints": [
      "\u2211(time_spent[staff_id, complaint_id]) = 1 for each complaint_id",
      "min_time[complaint_id] \u2264 time_spent[staff_id, complaint_id] \u2264 max_time[complaint_id] for each staff_id, complaint_id",
      "\u2211(time_spent[staff_id, complaint_id]) \u2264 max_hours[staff_id] for each staff_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "hourly_wage[staff_id]": {
        "currently_mapped_to": "staff_wages.hourly_wage",
        "mapping_adequacy": "good",
        "description": "Hourly wage of each staff member, used as a coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "min_time[complaint_id]": {
        "currently_mapped_to": "complaint_time_constraints.min_time",
        "mapping_adequacy": "good",
        "description": "Minimum time required to handle each complaint, used as a lower bound in the time constraint"
      },
      "max_time[complaint_id]": {
        "currently_mapped_to": "complaint_time_constraints.max_time",
        "mapping_adequacy": "good",
        "description": "Maximum time allowed to handle each complaint, used as an upper bound in the time constraint"
      },
      "max_hours[staff_id]": {
        "currently_mapped_to": "staff_working_hours.max_hours",
        "mapping_adequacy": "good",
        "description": "Maximum working hours for each staff member, used as an upper bound in the working hours constraint"
      }
    },
    "decision_variables": {
      "time_spent[staff_id, complaint_id]": {
        "currently_mapped_to": "time_spent.time_spent",
        "mapping_adequacy": "good",
        "description": "Time spent by each staff member on each complaint, used as a decision variable in the optimization model",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
