Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:28:22

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": "Optimize the selection of workshop submissions to maximize the overall quality of accepted papers while respecting workshop capacity constraints.",
  "optimization_problem": "The goal is to maximize the total score of accepted submissions across all workshops, ensuring that the number of accepted submissions does not exceed the capacity of each workshop.",
  "objective": "maximize \u2211(Scores[i] * x[i]) where x[i] is a binary decision variable indicating whether submission i is accepted.",
  "table_count": 2,
  "key_changes": [
    "Schema changes include adding workshop_capacity and submission_workshop_mapping tables to address missing data requirements. Business configuration logic updated with scalar parameters for workshop capacities and formulas for optimization constraints."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Obtain workshop capacity data and submission-to-workshop assignment information.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding workshop_capacity and submission_workshop_mapping tables to address missing data requirements. Business configuration logic updated with scalar parameters for workshop capacities and formulas for optimization constraints.

CREATE TABLE workshop_capacity (
  workshop_id INTEGER,
  capacity INTEGER
);

CREATE TABLE submission_workshop_mapping (
  submission_id INTEGER,
  workshop_id INTEGER,
  accepted BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "workshop_capacity": {
      "business_purpose": "Maximum number of submissions that can be accepted for each workshop.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "workshop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the workshop.",
          "optimization_purpose": "Index for workshop capacity constraint.",
          "sample_values": "1, 2, 3"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of submissions that can be accepted.",
          "optimization_purpose": "Bound for workshop capacity constraint.",
          "sample_values": "10, 15, 20"
        }
      }
    },
    "submission_workshop_mapping": {
      "business_purpose": "Mapping of submissions to workshops.",
      "optimization_role": "business_data",
      "columns": {
        "submission_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the submission.",
          "optimization_purpose": "Index for submission decision variable.",
          "sample_values": "1, 2, 3"
        },
        "workshop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the workshop.",
          "optimization_purpose": "Index for workshop capacity constraint.",
          "sample_values": "1, 2, 3"
        },
        "accepted": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the submission is accepted.",
          "optimization_purpose": "Decision variable in optimization model.",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "workshop_capacity": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of submissions that can be accepted for a workshop.",
    "optimization_role": "Constraint bound for workshop capacity.",
    "configuration_type": "scalar_parameter"
  },
  "optimization_constraint": {
    "formula_expression": "sum(x[i] for all submissions assigned to workshop j) <= Capacity[j]",
    "data_type": "STRING",
    "business_meaning": "Constraint ensuring the number of accepted submissions does not exceed workshop capacity.",
    "optimization_role": "Constraint in optimization model.",
    "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": "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": "Optimize the selection of workshop submissions to maximize the overall quality of accepted papers while respecting workshop capacity constraints.",
  "optimization_problem_description": "Maximize the total score of accepted submissions across all workshops, ensuring that the number of accepted submissions does not exceed the capacity of each workshop.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Scores[i] * x[i]) where x[i] is a binary decision variable indicating whether submission i is accepted.",
    "decision_variables": "x[i] \u2208 {0,1} for each submission i, indicating acceptance (1) or rejection (0).",
    "constraints": "\u2211(x[i] for all submissions assigned to workshop j) \u2264 Capacity[j] for each workshop j."
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Scores[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Score representing the quality of submission i."
      }
    },
    "constraint_bounds": {
      "Capacity[j]": {
        "currently_mapped_to": "workshop_capacity.capacity",
        "mapping_adequacy": "good",
        "description": "Maximum number of submissions that can be accepted for workshop j."
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "submission_workshop_mapping.accepted",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether submission i is accepted.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Scores[i] for each submission i"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Obtain submission scores to complete the objective function mapping."
  }
}
