Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:54:26

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": "An investor wants to allocate funds to different entrepreneurs to maximize the potential return on investment while staying within a budget limit.",
  "optimization_problem": "The goal is to maximize the total expected return from investing in various entrepreneurs, subject to a budget constraint and individual investment limits.",
  "objective": "maximize total_expected_return = \u2211(expected_return_coefficient[i] * investment[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine expected return rates and total budget 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 missing optimization data, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Expected_Return_Coefficients (
  entrepreneur_id INTEGER,
  expected_return_rate FLOAT
);

CREATE TABLE Investments (
  entrepreneur_id INTEGER,
  amount FLOAT
);

CREATE TABLE Entrepreneur (
  entrepreneur_id INTEGER,
  Money_Requested FLOAT,
  expected_return_coefficient FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Expected_Return_Coefficients": {
      "business_purpose": "Stores expected return rates for each entrepreneur",
      "optimization_role": "objective_coefficients",
      "columns": {
        "entrepreneur_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each entrepreneur",
          "optimization_purpose": "Links return rates to specific entrepreneurs",
          "sample_values": "1, 2, 3"
        },
        "expected_return_rate": {
          "data_type": "FLOAT",
          "business_meaning": "Expected return rate for the entrepreneur",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "0.1, 0.15, 0.2"
        }
      }
    },
    "Investments": {
      "business_purpose": "Tracks the amount of money invested in each entrepreneur",
      "optimization_role": "decision_variables",
      "columns": {
        "entrepreneur_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each entrepreneur",
          "optimization_purpose": "Links investments to specific entrepreneurs",
          "sample_values": "1, 2, 3"
        },
        "amount": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of money invested in the entrepreneur",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "5000, 10000, 15000"
        }
      }
    },
    "Entrepreneur": {
      "business_purpose": "Stores information about each entrepreneur",
      "optimization_role": "business_data",
      "columns": {
        "entrepreneur_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each entrepreneur",
          "optimization_purpose": "Primary key",
          "sample_values": "1, 2, 3"
        },
        "Money_Requested": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum amount requested by the entrepreneur",
          "optimization_purpose": "Constraint bound",
          "sample_values": "20000, 25000, 30000"
        },
        "expected_return_coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Expected return rate for the entrepreneur",
          "optimization_purpose": "Objective coefficient",
          "sample_values": "0.1, 0.15, 0.2"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_budget": {
    "sample_value": "100000",
    "data_type": "FLOAT",
    "business_meaning": "Total budget available for investment",
    "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": "entrepreneur",
  "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": "entrepreneur",
  "iteration": 1,
  "business_context": "An investor aims to allocate a fixed budget across multiple entrepreneurs to maximize the expected return on investment, considering individual investment limits.",
  "optimization_problem_description": "Maximize the total expected return from investments in various entrepreneurs, subject to a total budget constraint and individual investment limits.",
  "optimization_formulation": {
    "objective": "maximize total_expected_return = \u2211(expected_return_coefficient[i] * investment[i])",
    "decision_variables": "investment[i] for each entrepreneur i, representing the amount of money invested in entrepreneur i (continuous)",
    "constraints": [
      "\u2211(investment[i]) <= total_budget",
      "investment[i] <= Money_Requested[i] for each entrepreneur i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "expected_return_coefficient[i]": {
        "currently_mapped_to": "Expected_Return_Coefficients.expected_return_rate",
        "mapping_adequacy": "good",
        "description": "Expected return rate for each entrepreneur, used as a coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "business_configuration_logic.total_budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for investment"
      },
      "Money_Requested[i]": {
        "currently_mapped_to": "Entrepreneur.Money_Requested",
        "mapping_adequacy": "good",
        "description": "Maximum amount requested by each entrepreneur, used as an upper bound for individual investments"
      }
    },
    "decision_variables": {
      "investment[i]": {
        "currently_mapped_to": "Investments.amount",
        "mapping_adequacy": "good",
        "description": "Amount of money invested in each entrepreneur",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
