Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-27 22:41:29

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 political organization is optimizing the allocation of its members to various party events to maximize the overall effectiveness of the events. Each member has a certain effectiveness score for each event, and the goal is to assign members to events in a way that maximizes the total effectiveness while respecting constraints such as the number of members per event and availability.",
  "optimization_problem": "The problem is to maximize the total effectiveness of party events by optimally assigning members to events. Each member has a specific effectiveness score for each event, and the assignment must respect constraints such as the maximum number of members per event and the availability of members.",
  "objective": "maximize total_effectiveness = sum(efficiency_score[member_id, event_id] * x[member_id, event_id])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for decision variables, modifying existing tables to better map decision variables, and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine the mapping of decision variables and ensure all necessary data is available for linear optimization",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for decision variables, modifying existing tables to better map decision variables, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE effectiveness_scores (
  member_id INTEGER,
  event_id INTEGER,
  efficiency_score FLOAT
);

CREATE TABLE member_availability (
  member_id INTEGER,
  event_id INTEGER,
  is_available BOOLEAN
);

CREATE TABLE party_events (
  event_id INTEGER,
  Member_in_charge_ID INTEGER,
  max_members_per_event INTEGER
);

CREATE TABLE member_event_assignments (
  member_id INTEGER,
  event_id INTEGER,
  assignment BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "effectiveness_scores": {
      "business_purpose": "Stores effectiveness scores of members for each event",
      "optimization_role": "objective_coefficients",
      "columns": {
        "member_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member",
          "optimization_purpose": "Index for effectiveness scores",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for an event",
          "optimization_purpose": "Index for effectiveness scores",
          "sample_values": "101, 102, 103"
        },
        "efficiency_score": {
          "data_type": "FLOAT",
          "business_meaning": "Effectiveness score of a member for a specific event",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "0.8, 0.9, 1.0"
        }
      }
    },
    "member_availability": {
      "business_purpose": "Indicates availability of members for events",
      "optimization_role": "constraint_bounds",
      "columns": {
        "member_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member",
          "optimization_purpose": "Index for availability",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for an event",
          "optimization_purpose": "Index for availability",
          "sample_values": "101, 102, 103"
        },
        "is_available": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a member is available for an event",
          "optimization_purpose": "Constraint in optimization model",
          "sample_values": "true, false"
        }
      }
    },
    "party_events": {
      "business_purpose": "Stores information about party events",
      "optimization_role": "business_data",
      "columns": {
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for an event",
          "optimization_purpose": "Index for event data",
          "sample_values": "101, 102, 103"
        },
        "Member_in_charge_ID": {
          "data_type": "INTEGER",
          "business_meaning": "ID of the member in charge of the event",
          "optimization_purpose": "Decision variable mapping",
          "sample_values": "1, 2, 3"
        },
        "max_members_per_event": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of members that can be assigned to the event",
          "optimization_purpose": "Constraint bound",
          "sample_values": "50, 100, 150"
        }
      }
    },
    "member_event_assignments": {
      "business_purpose": "Stores binary decision variables indicating member assignments to events",
      "optimization_role": "decision_variables",
      "columns": {
        "member_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for an event",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "101, 102, 103"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary variable indicating if a member is assigned to an event",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_members_per_event": {
    "sample_value": "100",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of members that can be assigned to a single event",
    "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": "party_people",
  "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": "party_people",
  "iteration": 2,
  "business_context": "A political organization is optimizing the allocation of its members to various party events to maximize the overall effectiveness of the events. Each member has a certain effectiveness score for each event, and the goal is to assign members to events in a way that maximizes the total effectiveness while respecting constraints such as the number of members per event and availability.",
  "optimization_problem_description": "The problem is to maximize the total effectiveness of party events by optimally assigning members to events. Each member has a specific effectiveness score for each event, and the assignment must respect constraints such as the maximum number of members per event and the availability of members.",
  "optimization_formulation": {
    "objective": "maximize total_effectiveness = sum(efficiency_score[member_id, event_id] * assignment[member_id, event_id])",
    "decision_variables": "assignment[member_id, event_id] are binary variables indicating if a member is assigned to an event",
    "constraints": [
      "sum(assignment[member_id, event_id]) <= max_members_per_event for each event_id",
      "assignment[member_id, event_id] <= is_available[member_id, event_id] for each member_id, event_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "efficiency_score[member_id, event_id]": {
        "currently_mapped_to": "effectiveness_scores.efficiency_score",
        "mapping_adequacy": "good",
        "description": "Effectiveness score of a member for a specific event"
      }
    },
    "constraint_bounds": {
      "max_members_per_event[event_id]": {
        "currently_mapped_to": "party_events.max_members_per_event",
        "mapping_adequacy": "good",
        "description": "Maximum number of members that can be assigned to the event"
      },
      "is_available[member_id, event_id]": {
        "currently_mapped_to": "member_availability.is_available",
        "mapping_adequacy": "good",
        "description": "Indicates if a member is available for an event"
      }
    },
    "decision_variables": {
      "assignment[member_id, event_id]": {
        "currently_mapped_to": "member_event_assignments.assignment",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if a member is assigned to an event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
