Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:24:49

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 a fixed budget across multiple entrepreneurs to maximize the total expected return on investment, while ensuring that no single entrepreneur receives more than a specified maximum amount and that the total investment does not exceed the budget.",
  "optimization_problem": "The goal is to maximize the total expected return on investment by deciding how much money to allocate to each entrepreneur. The constraints include not exceeding the total budget and ensuring that no entrepreneur receives more than a predefined maximum amount.",
  "objective": "maximize \u2211(Return_Rate_i \u00d7 Investment_i)",
  "table_count": 1,
  "key_changes": [
    "Schema changes and configuration logic updates implemented to address missing optimization requirements and mapping gaps identified by the OR expert."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map the missing data/parameters required for the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes and configuration logic updates implemented to address missing optimization requirements and mapping gaps identified by the OR expert.

CREATE TABLE entrepreneurs (
  entrepreneur_id INTEGER,
  return_rate FLOAT,
  investment FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "entrepreneurs": {
      "business_purpose": "List of entrepreneurs with their expected return rates and investment allocations",
      "optimization_role": "business_data",
      "columns": {
        "entrepreneur_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each entrepreneur",
          "optimization_purpose": "Index for decision variables and constraints",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "return_rate": {
          "data_type": "FLOAT",
          "business_meaning": "Expected return rate for the entrepreneur",
          "optimization_purpose": "Objective coefficient for optimization",
          "sample_values": [
            0.1,
            0.15,
            0.2
          ]
        },
        "investment": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of money allocated to the entrepreneur",
          "optimization_purpose": "Decision variable for optimization",
          "sample_values": [
            100000,
            150000,
            200000
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Budget": {
    "sample_value": 1000000,
    "data_type": "FLOAT",
    "business_meaning": "Total available budget for investment",
    "optimization_role": "Constraint bound for total investment",
    "configuration_type": "scalar_parameter"
  },
  "Max_Investment_i": {
    "sample_value": 200000,
    "data_type": "FLOAT",
    "business_meaning": "Maximum amount that can be allocated to each entrepreneur",
    "optimization_role": "Constraint bound for individual investment",
    "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 total expected return on investment, while ensuring that no single entrepreneur receives more than a specified maximum amount and that the total investment does not exceed the budget.",
  "optimization_problem_description": "Maximize the total expected return on investment by deciding how much money to allocate to each entrepreneur, subject to constraints on the total budget and maximum investment per entrepreneur.",
  "optimization_formulation": {
    "objective": "maximize \u2211(return_rate_i \u00d7 investment_i)",
    "decision_variables": "investment_i: continuous variable representing the amount allocated to entrepreneur i",
    "constraints": [
      "\u2211(investment_i) \u2264 Total_Budget",
      "investment_i \u2264 Max_Investment_i for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "return_rate_i": {
        "currently_mapped_to": "entrepreneurs.return_rate",
        "mapping_adequacy": "good",
        "description": "Expected return rate for each entrepreneur"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Budget",
        "mapping_adequacy": "good",
        "description": "Total available budget for investment"
      },
      "Max_Investment_i": {
        "currently_mapped_to": "business_configuration_logic.Max_Investment_i",
        "mapping_adequacy": "good",
        "description": "Maximum amount that can be allocated to each entrepreneur"
      }
    },
    "decision_variables": {
      "investment_i": {
        "currently_mapped_to": "entrepreneurs.investment",
        "mapping_adequacy": "good",
        "description": "Amount of money allocated to each entrepreneur",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
