Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:55:13

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": "The local government in Alabama is organizing various community events and wants to optimize the allocation of participants to these events to maximize the overall satisfaction score. Each participant has a satisfaction score for attending a specific event, and the goal is to assign participants to events in a way that maximizes the total satisfaction score while respecting capacity constraints for each event.",
  "optimization_problem": "Maximize the total satisfaction score by optimally assigning participants to events, considering each participant's satisfaction score for attending specific events and the capacity constraints of each event.",
  "objective": "maximize \u2211(satisfaction_score[participant_id, event_id] \u00d7 x[participant_id, event_id])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for satisfaction scores and event capacities, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data on satisfaction scores and event capacities to complete the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for satisfaction scores and event capacities, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE SatisfactionScores (
  participant_id INTEGER,
  event_id INTEGER,
  satisfaction_score FLOAT
);

CREATE TABLE EventCapacities (
  event_id INTEGER,
  capacity_limit INTEGER
);

CREATE TABLE Participants_in_Events (
  participant_id INTEGER,
  event_id INTEGER,
  participant_event_assignment BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "SatisfactionScores": {
      "business_purpose": "Stores satisfaction scores for each participant-event pair",
      "optimization_role": "objective_coefficients",
      "columns": {
        "participant_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each participant",
          "optimization_purpose": "Index for satisfaction scores",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each event",
          "optimization_purpose": "Index for satisfaction scores",
          "sample_values": "101, 102, 103"
        },
        "satisfaction_score": {
          "data_type": "FLOAT",
          "business_meaning": "Satisfaction score of a participant attending an event",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "0.5, 0.8, 1.0"
        }
      }
    },
    "EventCapacities": {
      "business_purpose": "Stores capacity limits for each event",
      "optimization_role": "constraint_bounds",
      "columns": {
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each event",
          "optimization_purpose": "Index for capacity constraints",
          "sample_values": "101, 102, 103"
        },
        "capacity_limit": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of participants allowed for the event",
          "optimization_purpose": "Constraint bound in the optimization model",
          "sample_values": "50, 100, 150"
        }
      }
    },
    "Participants_in_Events": {
      "business_purpose": "Tracks participant assignments to events",
      "optimization_role": "decision_variables",
      "columns": {
        "participant_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each participant",
          "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": "101, 102, 103"
        },
        "participant_event_assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a participant is assigned to an event",
          "optimization_purpose": "Binary decision variable",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "event_capacity_limit": {
    "sample_value": "100",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of participants allowed per event",
    "optimization_role": "Used as a constraint in the 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": "local_govt_in_alabama",
  "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": "local_govt_in_alabama",
  "iteration": 1,
  "business_context": "The local government in Alabama is organizing various community events and wants to optimize the allocation of participants to these events to maximize the overall satisfaction score. Each participant has a satisfaction score for attending a specific event, and the goal is to assign participants to events in a way that maximizes the total satisfaction score while respecting capacity constraints for each event.",
  "optimization_problem_description": "Maximize the total satisfaction score by optimally assigning participants to events, considering each participant's satisfaction score for attending specific events and the capacity constraints of each event.",
  "optimization_formulation": {
    "objective": "maximize \u2211(satisfaction_score[participant_id, event_id] \u00d7 x[participant_id, event_id])",
    "decision_variables": "x[participant_id, event_id] are binary variables indicating if a participant is assigned to an event",
    "constraints": [
      "\u2211(x[participant_id, event_id]) \u2264 capacity_limit[event_id] for each event_id",
      "x[participant_id, event_id] \u2208 {0, 1} for each participant_id, event_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "satisfaction_score[participant_id, event_id]": {
        "currently_mapped_to": "SatisfactionScores.satisfaction_score",
        "mapping_adequacy": "good",
        "description": "Satisfaction score of a participant attending an event"
      }
    },
    "constraint_bounds": {
      "capacity_limit[event_id]": {
        "currently_mapped_to": "EventCapacities.capacity_limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of participants allowed for the event"
      }
    },
    "decision_variables": {
      "x[participant_id, event_id]": {
        "currently_mapped_to": "Participants_in_Events.participant_event_assignment",
        "mapping_adequacy": "good",
        "description": "Indicates if a participant is assigned to an event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
