Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-28 00:21:27

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 allocation of journalists to events to maximize the total event attendance covered by journalists, considering constraints on the number of events a journalist can cover and the total number of journalists available.",
  "optimization_problem": "The goal is to maximize the total event attendance covered by journalists. Each journalist can cover a limited number of events, and there is a limited number of journalists available. The decision is which journalist covers which event to maximize the total attendance covered.",
  "objective": "maximize \u2211(Event_Attendance[Event_ID] \u00d7 x[journalist_ID, Event_ID])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for missing constraint bounds and modifying existing tables to better map decision variables. Configuration logic updates include moving scalar parameters to JSON for better management."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine the mapping of decision variables and ensure all necessary parameters are available",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing constraint bounds and modifying existing tables to better map decision variables. Configuration logic updates include moving scalar parameters to JSON for better management.

CREATE TABLE event (
  Event_ID INTEGER,
  Event_Attendance INTEGER
);

CREATE TABLE journalist_event_assignment (
  journalist_ID INTEGER,
  Event_ID INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "event": {
      "business_purpose": "Stores information about events including attendance",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Event_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each event",
          "optimization_purpose": "Index for objective coefficients",
          "sample_values": "1, 2, 3"
        },
        "Event_Attendance": {
          "data_type": "INTEGER",
          "business_meaning": "Number of attendees expected at the event",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "journalist_event_assignment": {
      "business_purpose": "Tracks assignments of journalists to events",
      "optimization_role": "decision_variables",
      "columns": {
        "journalist_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each journalist",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "Event_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each event",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_events_per_journalist": {
    "sample_value": "5",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of events a journalist can cover",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "total_journalists": {
    "sample_value": "10",
    "data_type": "INTEGER",
    "business_meaning": "Total number of journalists available",
    "optimization_role": "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": "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 allocation of journalists to events to maximize the total event attendance covered by journalists, considering constraints on the number of events a journalist can cover and the total number of journalists available.",
  "optimization_problem_description": "Maximize the total event attendance covered by journalists, subject to constraints on the number of events each journalist can cover and the total number of journalists available.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Event_Attendance[Event_ID] \u00d7 x[journalist_ID, Event_ID])",
    "decision_variables": "x[journalist_ID, Event_ID] are binary variables indicating if journalist covers the event",
    "constraints": [
      "\u2211(x[journalist_ID, Event_ID]) <= max_events_per_journalist for each journalist_ID",
      "\u2211(x[journalist_ID, Event_ID]) <= total_journalists for each Event_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Event_Attendance[Event_ID]": {
        "currently_mapped_to": "event.Event_Attendance",
        "mapping_adequacy": "good",
        "description": "Number of attendees expected at the event"
      }
    },
    "constraint_bounds": {
      "max_events_per_journalist": {
        "currently_mapped_to": "business_configuration_logic.max_events_per_journalist",
        "mapping_adequacy": "good",
        "description": "Maximum number of events a journalist can cover"
      },
      "total_journalists": {
        "currently_mapped_to": "business_configuration_logic.total_journalists",
        "mapping_adequacy": "good",
        "description": "Total number of journalists available"
      }
    },
    "decision_variables": {
      "x[journalist_ID, Event_ID]": {
        "currently_mapped_to": "journalist_event_assignment.journalist_ID, journalist_event_assignment.Event_ID",
        "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"
  }
}
