Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:23:30

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 global logistics company wants to optimize the distribution of goods across various cities in different countries to minimize transportation costs while ensuring demand is met in each city.",
  "optimization_problem": "The company needs to minimize the total transportation cost of distributing goods from a central warehouse to various cities. The objective is to determine the optimal quantity of goods to be shipped to each city, considering the demand in each city and the transportation cost per unit.",
  "objective": "minimize total_transportation_cost = sum(transportation_cost_per_unit[i] * quantity_shipped[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine mapping of transportation costs and capacity constraints",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas.

CREATE TABLE TransportationCosts (
  city_id INTEGER,
  cost_per_unit FLOAT
);

CREATE TABLE CityCapacities (
  city_id INTEGER,
  max_capacity INTEGER
);

CREATE TABLE City (
  city_id INTEGER,
  city_demand INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "TransportationCosts": {
      "business_purpose": "Stores transportation cost per unit for each city",
      "optimization_role": "objective_coefficients",
      "columns": {
        "city_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each city",
          "optimization_purpose": "Links cost to specific city",
          "sample_values": "1, 2, 3"
        },
        "cost_per_unit": {
          "data_type": "FLOAT",
          "business_meaning": "Cost to transport one unit of goods to the city",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "5.0, 10.0, 15.0"
        }
      }
    },
    "CityCapacities": {
      "business_purpose": "Stores maximum capacity of goods that can be shipped to each city",
      "optimization_role": "constraint_bounds",
      "columns": {
        "city_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each city",
          "optimization_purpose": "Links capacity to specific city",
          "sample_values": "1, 2, 3"
        },
        "max_capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of goods that can be shipped to the city",
          "optimization_purpose": "Constraint bound in optimization",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "City": {
      "business_purpose": "Stores information about each city",
      "optimization_role": "business_data",
      "columns": {
        "city_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each city",
          "optimization_purpose": "Primary key for city data",
          "sample_values": "1, 2, 3"
        },
        "city_demand": {
          "data_type": "INTEGER",
          "business_meaning": "Demand for goods in the city",
          "optimization_purpose": "Constraint bound in optimization",
          "sample_values": "50, 150, 250"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_available_goods": {
    "sample_value": "10000",
    "data_type": "INTEGER",
    "business_meaning": "Total number of goods available for distribution",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "transportation_cost_formula": {
    "formula_expression": "transportation_cost_per_unit[i] * quantity_shipped[i]",
    "data_type": "STRING",
    "business_meaning": "Calculates total transportation cost for goods shipped to city i",
    "optimization_role": "Used in the objective function of the 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": "world_1",
  "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": "world_1",
  "iteration": 1,
  "business_context": "A global logistics company is optimizing the distribution of goods from a central warehouse to various cities to minimize transportation costs while meeting each city's demand.",
  "optimization_problem_description": "The company aims to minimize the total transportation cost of distributing goods from a central warehouse to various cities. The objective is to determine the optimal quantity of goods to be shipped to each city, considering the demand in each city, the transportation cost per unit, and the maximum capacity that can be shipped to each city.",
  "optimization_formulation": {
    "objective": "minimize total_transportation_cost = sum(TransportationCosts.cost_per_unit[i] * quantity_shipped[i])",
    "decision_variables": "quantity_shipped[i] for each city i, representing the number of goods shipped to city i (continuous)",
    "constraints": [
      "sum(quantity_shipped[i]) <= total_available_goods",
      "quantity_shipped[i] <= CityCapacities.max_capacity[i] for each city i",
      "quantity_shipped[i] >= City.city_demand[i] for each city i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "transportation_cost_per_unit[i]": {
        "currently_mapped_to": "TransportationCosts.cost_per_unit",
        "mapping_adequacy": "good",
        "description": "Cost to transport one unit of goods to city i"
      }
    },
    "constraint_bounds": {
      "total_available_goods": {
        "currently_mapped_to": "business_configuration_logic.total_available_goods",
        "mapping_adequacy": "good",
        "description": "Total number of goods available for distribution"
      },
      "max_capacity[i]": {
        "currently_mapped_to": "CityCapacities.max_capacity",
        "mapping_adequacy": "good",
        "description": "Maximum number of goods that can be shipped to city i"
      },
      "city_demand[i]": {
        "currently_mapped_to": "City.city_demand",
        "mapping_adequacy": "good",
        "description": "Demand for goods in city i"
      }
    },
    "decision_variables": {
      "quantity_shipped[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of goods shipped to city i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "quantity_shipped[i] decision variable mapping"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Map decision variables for quantity_shipped[i] and ensure all constraints are correctly implemented"
  }
}
