Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:04:41

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 decoration competition is held among various colleges. Each college sends members to participate in different rounds with specific decoration themes. The goal is to optimize the allocation of members to rounds to maximize the overall rank performance of the college.",
  "optimization_problem": "The objective is to maximize the total rank points obtained by college members across all rounds. Each member can participate in one or more rounds, and the rank in each round contributes to the college's total score. The optimization will decide which members participate in which rounds to achieve the highest possible total rank score.",
  "objective": "maximize total_rank_points = \u2211(rank_points[round_id, member_id] * x[round_id, member_id])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for decision variables and objective coefficients, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine the mapping of decision variables and ensure all necessary data for rank points conversion is available",
  "mapping_adequacy_summary": "partially_adequate"
}

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

CREATE TABLE DecisionVariables (
  round_id INTEGER,
  member_id INTEGER,
  participation BOOLEAN
);

CREATE TABLE ObjectiveCoefficients (
  round_id INTEGER,
  member_id INTEGER,
  rank_points FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "DecisionVariables": {
      "business_purpose": "Tracks member participation in rounds",
      "optimization_role": "decision_variables",
      "columns": {
        "round_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the round",
          "optimization_purpose": "Index for decision variable",
          "sample_values": "1, 2, 3"
        },
        "member_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the member",
          "optimization_purpose": "Index for decision variable",
          "sample_values": "101, 102, 103"
        },
        "participation": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a member participates in a round",
          "optimization_purpose": "Binary decision variable",
          "sample_values": "true, false"
        }
      }
    },
    "ObjectiveCoefficients": {
      "business_purpose": "Stores rank points for optimization objective",
      "optimization_role": "objective_coefficients",
      "columns": {
        "round_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the round",
          "optimization_purpose": "Index for objective coefficient",
          "sample_values": "1, 2, 3"
        },
        "member_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the member",
          "optimization_purpose": "Index for objective coefficient",
          "sample_values": "101, 102, 103"
        },
        "rank_points": {
          "data_type": "FLOAT",
          "business_meaning": "Rank points earned by a member in a round",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "10.0, 20.0, 30.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_rounds_per_member": {
    "sample_value": "3",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of rounds a member can participate in",
    "optimization_role": "Constraint parameter for member participation",
    "configuration_type": "scalar_parameter"
  },
  "rank_points_conversion": {
    "formula_expression": "rank_points = 100 / rank_position",
    "data_type": "STRING",
    "business_meaning": "Formula to convert rank position to rank points",
    "optimization_role": "Objective coefficient calculation",
    "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": "decoration_competition",
  "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": "decoration_competition",
  "iteration": 1,
  "business_context": "A decoration competition is held among various colleges. Each college sends members to participate in different rounds with specific decoration themes. The goal is to optimize the allocation of members to rounds to maximize the overall rank performance of the college.",
  "optimization_problem_description": "The objective is to maximize the total rank points obtained by college members across all rounds. Each member can participate in one or more rounds, and the rank in each round contributes to the college's total score. The optimization will decide which members participate in which rounds to achieve the highest possible total rank score.",
  "optimization_formulation": {
    "objective": "maximize total_rank_points = \u2211(rank_points[round_id, member_id] * participation[round_id, member_id])",
    "decision_variables": "participation[round_id, member_id] is a binary variable indicating if a member participates in a round",
    "constraints": [
      "\u2211(participation[round_id, member_id]) <= max_rounds_per_member for each member_id",
      "participation[round_id, member_id] \u2208 {0, 1} for all round_id, member_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "rank_points[round_id, member_id]": {
        "currently_mapped_to": "ObjectiveCoefficients.rank_points",
        "mapping_adequacy": "good",
        "description": "Rank points earned by a member in a round"
      }
    },
    "constraint_bounds": {
      "max_rounds_per_member": {
        "currently_mapped_to": "business_configuration_logic.max_rounds_per_member",
        "mapping_adequacy": "good",
        "description": "Maximum number of rounds a member can participate in"
      }
    },
    "decision_variables": {
      "participation[round_id, member_id]": {
        "currently_mapped_to": "DecisionVariables.participation",
        "mapping_adequacy": "good",
        "description": "Indicates if a member participates in a round",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
