Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-28 00:16:30

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 conference organizer wants to maximize the number of high-quality submissions accepted into various workshops while respecting venue capacity constraints and ensuring a balanced distribution of submissions across workshops.",
  "optimization_problem": "Maximize the total score of accepted submissions across all workshops, subject to venue capacity constraints and ensuring each workshop has a minimum number of accepted submissions.",
  "objective": "maximize total_score = \u2211(Scores[i] * x[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include adding tables for venue capacity and minimum submissions per workshop, modifying existing tables to improve mapping adequacy, and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data on venue capacities and minimum submission requirements for workshops",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding tables for venue capacity and minimum submissions per workshop, modifying existing tables to improve mapping adequacy, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE submission (
  Scores FLOAT
);

CREATE TABLE VenueCapacity (
  workshop_id INTEGER,
  capacity INTEGER
);

CREATE TABLE WorkshopSubmissions (
  workshop_id INTEGER,
  min_submissions INTEGER
);

CREATE TABLE Acceptance (
  Result BOOLEAN,
  workshop_id INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "submission": {
      "business_purpose": "Stores information about each submission",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Scores": {
          "data_type": "FLOAT",
          "business_meaning": "Quality score of each submission",
          "optimization_purpose": "Used to calculate the total score of accepted submissions",
          "sample_values": "0.0 to 10.0"
        }
      }
    },
    "VenueCapacity": {
      "business_purpose": "Stores the maximum capacity for each workshop",
      "optimization_role": "constraint_bounds",
      "columns": {
        "workshop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each workshop",
          "optimization_purpose": "Links capacity to specific workshops",
          "sample_values": "1, 2, 3"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of submissions that can be accepted",
          "optimization_purpose": "Used as a constraint in optimization",
          "sample_values": "50, 100, 150"
        }
      }
    },
    "WorkshopSubmissions": {
      "business_purpose": "Stores the minimum required submissions for each workshop",
      "optimization_role": "constraint_bounds",
      "columns": {
        "workshop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each workshop",
          "optimization_purpose": "Links minimum submissions to specific workshops",
          "sample_values": "1, 2, 3"
        },
        "min_submissions": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum number of submissions required",
          "optimization_purpose": "Used as a constraint in optimization",
          "sample_values": "3, 5, 7"
        }
      }
    },
    "Acceptance": {
      "business_purpose": "Tracks acceptance status of submissions",
      "optimization_role": "decision_variables",
      "columns": {
        "Result": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a submission is accepted",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": "true, false"
        },
        "workshop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the workshop to which the submission is linked",
          "optimization_purpose": "Associates submissions with specific workshops",
          "sample_values": "1, 2, 3"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "min_submissions_per_workshop": {
    "sample_value": "3",
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of submissions required per workshop",
    "optimization_role": "Used as a constraint in the optimization model",
    "configuration_type": "scalar_parameter"
  },
  "venue_capacity": {
    "sample_value": "100",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of submissions that can be accepted in each workshop",
    "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": "workshop_paper",
  "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": "workshop_paper",
  "iteration": 1,
  "business_context": "A conference organizer aims to maximize the total score of accepted submissions across various workshops, ensuring each workshop meets its minimum submission requirement and does not exceed its venue capacity.",
  "optimization_problem_description": "Maximize the total score of accepted submissions while respecting venue capacity and ensuring a minimum number of submissions per workshop.",
  "optimization_formulation": {
    "objective": "maximize total_score = \u2211(submission.Scores[i] * Acceptance.Result[i])",
    "decision_variables": {
      "Acceptance.Result[i]": {
        "currently_mapped_to": "Acceptance.Result",
        "mapping_adequacy": "good",
        "description": "Indicates if a submission is accepted",
        "variable_type": "binary"
      }
    },
    "constraints": {
      "venue_capacity_constraint[workshop_id]": {
        "currently_mapped_to": "VenueCapacity.capacity",
        "mapping_adequacy": "good",
        "description": "Total accepted submissions for each workshop must not exceed its capacity",
        "constraint": "\u2211(Acceptance.Result[i]) \u2264 VenueCapacity.capacity[workshop_id]"
      },
      "min_submissions_constraint[workshop_id]": {
        "currently_mapped_to": "WorkshopSubmissions.min_submissions",
        "mapping_adequacy": "good",
        "description": "Each workshop must have at least a minimum number of accepted submissions",
        "constraint": "\u2211(Acceptance.Result[i]) \u2265 WorkshopSubmissions.min_submissions[workshop_id]"
      }
    }
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Scores[i]": {
        "currently_mapped_to": "submission.Scores",
        "mapping_adequacy": "good",
        "description": "Quality score of each submission"
      }
    },
    "constraint_bounds": {
      "capacity[workshop_id]": {
        "currently_mapped_to": "VenueCapacity.capacity",
        "mapping_adequacy": "good",
        "description": "Maximum number of submissions that can be accepted in each workshop"
      },
      "min_submissions[workshop_id]": {
        "currently_mapped_to": "WorkshopSubmissions.min_submissions",
        "mapping_adequacy": "good",
        "description": "Minimum number of submissions required for each workshop"
      }
    },
    "decision_variables": {
      "Acceptance.Result[i]": {
        "currently_mapped_to": "Acceptance.Result",
        "mapping_adequacy": "good",
        "description": "Indicates if a submission is accepted",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
