Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:21:16

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 gas company wants to optimize the allocation of its gas stations to different companies to maximize overall market value while considering constraints on sales, profits, and assets.",
  "optimization_problem": "The goal is to maximize the total market value of the companies that operate the gas stations, subject to constraints on the total sales, profits, and assets of these companies. Each gas station can be allocated to one company, and the allocation should respect the company's capacity to manage the station based on its rank.",
  "objective": "maximize sum of (Market_Value[i] * x[i]) for all companies i",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for constraint bounds and modifying existing tables to fill mapping gaps. Configuration logic updated for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints and ensure all necessary data for limits are available",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for constraint bounds and modifying existing tables to fill mapping gaps. Configuration logic updated for scalar parameters and formulas.

CREATE TABLE company (
  Company_ID INTEGER,
  Market_Value FLOAT
);

CREATE TABLE station_company (
  Station_ID INTEGER,
  Company_ID INTEGER
);

CREATE TABLE constraint_bounds (
  Constraint_Name STRING,
  Bound_Value FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "company": {
      "business_purpose": "Stores information about companies",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Company_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each company",
          "optimization_purpose": "Used to link companies with decision variables",
          "sample_values": "1, 2, 3"
        },
        "Market_Value": {
          "data_type": "FLOAT",
          "business_meaning": "Market value of the company",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "10.5, 20.0, 15.0"
        }
      }
    },
    "station_company": {
      "business_purpose": "Links gas stations to companies",
      "optimization_role": "decision_variables",
      "columns": {
        "Station_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each gas station",
          "optimization_purpose": "Used to allocate stations to companies",
          "sample_values": "101, 102, 103"
        },
        "Company_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the company managing the station",
          "optimization_purpose": "Binary decision variable for allocation",
          "sample_values": "1, 2, 3"
        }
      }
    },
    "constraint_bounds": {
      "business_purpose": "Stores bounds for optimization constraints",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Constraint_Name": {
          "data_type": "STRING",
          "business_meaning": "Name of the constraint",
          "optimization_purpose": "Identifies the constraint type",
          "sample_values": "Total_Sales_Limit, Minimum_Profits_Requirement"
        },
        "Bound_Value": {
          "data_type": "FLOAT",
          "business_meaning": "Value of the constraint bound",
          "optimization_purpose": "Used in constraint formulation",
          "sample_values": "100.0, 50.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Sales_Limit": {
    "sample_value": "100.0",
    "data_type": "FLOAT",
    "business_meaning": "Upper limit on total sales for allocated companies",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "Minimum_Profits_Requirement": {
    "sample_value": "50.0",
    "data_type": "FLOAT",
    "business_meaning": "Minimum required total profits for allocated companies",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "Total_Assets_Limit": {
    "sample_value": "200.0",
    "data_type": "FLOAT",
    "business_meaning": "Upper limit on total assets for allocated companies",
    "optimization_role": "Used as a constraint bound in 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": "gas_company",
  "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": "gas_company",
  "iteration": 1,
  "business_context": "A gas company wants to optimize the allocation of its gas stations to different companies to maximize overall market value while considering constraints on sales, profits, and assets.",
  "optimization_problem_description": "The goal is to maximize the total market value of the companies that operate the gas stations, subject to constraints on the total sales, profits, and assets of these companies. Each gas station can be allocated to one company, and the allocation should respect the company's capacity to manage the station based on its rank.",
  "optimization_formulation": {
    "objective": "maximize sum of (Market_Value[i] * x[i]) for all companies i",
    "decision_variables": "x[i] is a binary variable indicating if company i is allocated a gas station",
    "constraints": [
      "sum of (Sales[i] * x[i]) <= Total_Sales_Limit",
      "sum of (Profits[i] * x[i]) >= Minimum_Profits_Requirement",
      "sum of (Assets[i] * x[i]) <= Total_Assets_Limit"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Market_Value[i]": {
        "currently_mapped_to": "company.Market_Value",
        "mapping_adequacy": "good",
        "description": "Market value of company i used as a coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "Total_Sales_Limit": {
        "currently_mapped_to": "business_configuration_logic.Total_Sales_Limit",
        "mapping_adequacy": "good",
        "description": "Upper limit on total sales for allocated companies"
      },
      "Minimum_Profits_Requirement": {
        "currently_mapped_to": "business_configuration_logic.Minimum_Profits_Requirement",
        "mapping_adequacy": "good",
        "description": "Minimum required total profits for allocated companies"
      },
      "Total_Assets_Limit": {
        "currently_mapped_to": "business_configuration_logic.Total_Assets_Limit",
        "mapping_adequacy": "good",
        "description": "Upper limit on total assets for allocated companies"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "station_company.Company_ID",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if company i is allocated a gas station",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
