Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:26:53

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 news agency wants to optimize the assignment of journalists to events to maximize the total coverage quality, considering factors like journalist experience and event attendance.",
  "optimization_problem": "The goal is to maximize the total coverage quality by assigning journalists to events. The coverage quality is a linear function of the journalist's years of experience and the event's attendance. Constraints include ensuring each event is covered by at least one journalist and each journalist is assigned to no more than a specified number of events.",
  "objective": "maximize \u2211(Years_working_journalist \u00d7 Event_Attendance_event \u00d7 x_journalist_event)",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for journalist-event assignments and adding a column for maximum assignments per journalist. Configuration logic updates include adding scalar parameters for maximum assignments and a formula for coverage quality calculation."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map the maximum number of assignments per journalist and the binary decision variables for journalist-event assignments.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for journalist-event assignments and adding a column for maximum assignments per journalist. Configuration logic updates include adding scalar parameters for maximum assignments and a formula for coverage quality calculation.

CREATE TABLE journalist (
  Years_working INTEGER,
  max_assignments INTEGER
);

CREATE TABLE event (
  Event_Attendance INTEGER
);

CREATE TABLE journalist_event_assignment (
  assignment BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "journalist": {
      "business_purpose": "Stores information about journalists",
      "optimization_role": "business_data",
      "columns": {
        "Years_working": {
          "data_type": "INTEGER",
          "business_meaning": "Years of experience of the journalist",
          "optimization_purpose": "Objective coefficient",
          "sample_values": "5, 10, 15"
        },
        "max_assignments": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of events the journalist can be assigned to",
          "optimization_purpose": "Constraint bound",
          "sample_values": "3, 4, 5"
        }
      }
    },
    "event": {
      "business_purpose": "Stores information about events",
      "optimization_role": "business_data",
      "columns": {
        "Event_Attendance": {
          "data_type": "INTEGER",
          "business_meaning": "Attendance of the event",
          "optimization_purpose": "Objective coefficient",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "journalist_event_assignment": {
      "business_purpose": "Stores binary assignments of journalists to events",
      "optimization_role": "decision_variables",
      "columns": {
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary variable indicating if a journalist is assigned to an event",
          "optimization_purpose": "Decision variable",
          "sample_values": "0, 1"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_assignments": {
    "sample_value": 3,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of events a journalist can be assigned to",
    "optimization_role": "Constraint bound for journalist assignments",
    "configuration_type": "scalar_parameter"
  },
  "coverage_quality_formula": {
    "formula_expression": "Years_working_journalist * Event_Attendance_event",
    "data_type": "STRING",
    "business_meaning": "Calculation of coverage quality based on journalist experience and event attendance",
    "optimization_role": "Objective coefficient calculation",
    "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": "news_report",
  "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": "news_report",
  "iteration": 1,
  "business_context": "A news agency wants to optimize the assignment of journalists to events to maximize the total coverage quality, considering factors like journalist experience and event attendance. The optimization problem is linear, ensuring each event is covered by at least one journalist and each journalist is assigned to no more than a specified number of events.",
  "optimization_problem_description": "Maximize the total coverage quality by assigning journalists to events. The coverage quality is a linear function of the journalist's years of experience and the event's attendance. Constraints include ensuring each event is covered by at least one journalist and each journalist is assigned to no more than a specified number of events.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Years_working_journalist \u00d7 Event_Attendance_event \u00d7 x_journalist_event)",
    "decision_variables": "x_journalist_event: binary variable indicating if journalist j is assigned to event e",
    "constraints": "1. \u2211(x_journalist_event) \u2265 1 for each event e, 2. \u2211(x_journalist_event) \u2264 max_assignments_j for each journalist j"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Years_working_journalist": {
        "currently_mapped_to": "journalist.Years_working",
        "mapping_adequacy": "good",
        "description": "Years of experience of the journalist"
      },
      "Event_Attendance_event": {
        "currently_mapped_to": "event.Event_Attendance",
        "mapping_adequacy": "good",
        "description": "Attendance of the event"
      }
    },
    "constraint_bounds": {
      "max_assignments_j": {
        "currently_mapped_to": "journalist.max_assignments",
        "mapping_adequacy": "good",
        "description": "Maximum number of events a journalist can be assigned to"
      }
    },
    "decision_variables": {
      "x_journalist_event": {
        "currently_mapped_to": "journalist_event_assignment.assignment",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if a journalist is assigned to an event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
