Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:48:14

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 manufacturing company wants to optimize the allocation of production resources to maximize revenue from product sales while considering production capacity and manufacturer-specific constraints.",
  "optimization_problem": "The goal is to maximize the total revenue from selling products produced by different manufacturers, subject to constraints on production capacity and manufacturer-specific production limits.",
  "objective": "maximize total_revenue = \u2211(Price[product] \u00d7 ProductionQuantity[product])",
  "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": "Gather missing data on production capacities and refine 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 Products (
  Price FLOAT,
  ProductionQuantity FLOAT
);

CREATE TABLE ProductionQuantities (
  ProductID INTEGER,
  Quantity FLOAT
);

CREATE TABLE Manufacturers (
  ManufacturerID INTEGER,
  Capacity INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Products": {
      "business_purpose": "Stores product information including prices and production quantities",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Price": {
          "data_type": "FLOAT",
          "business_meaning": "The selling price of each product",
          "optimization_purpose": "Used in calculating total revenue",
          "sample_values": "10.99, 15.49, 20.00"
        },
        "ProductionQuantity": {
          "data_type": "FLOAT",
          "business_meaning": "The number of units to produce for each product",
          "optimization_purpose": "Decision variable for production planning",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "ProductionQuantities": {
      "business_purpose": "Stores production quantities for each product",
      "optimization_role": "decision_variables",
      "columns": {
        "ProductID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each product",
          "optimization_purpose": "Links production quantity to specific product",
          "sample_values": "1, 2, 3"
        },
        "Quantity": {
          "data_type": "FLOAT",
          "business_meaning": "The number of units to produce for each product",
          "optimization_purpose": "Decision variable for production planning",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "Manufacturers": {
      "business_purpose": "Stores manufacturer-specific data including production capacities",
      "optimization_role": "business_data",
      "columns": {
        "ManufacturerID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each manufacturer",
          "optimization_purpose": "Links capacity data to specific manufacturer",
          "sample_values": "1, 2, 3"
        },
        "Capacity": {
          "data_type": "INTEGER",
          "business_meaning": "The maximum production capacity for each manufacturer",
          "optimization_purpose": "Constraint bound for production planning",
          "sample_values": "5000, 7000, 8000"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "TotalProductionCapacity": {
    "sample_value": "10000",
    "data_type": "INTEGER",
    "business_meaning": "The total production capacity available across all manufacturers",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "ManufacturerCapacity": {
    "sample_value": "5000",
    "data_type": "INTEGER",
    "business_meaning": "The maximum production capacity for each manufacturer",
    "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": "manufactory_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": "manufactory_1",
  "iteration": 1,
  "business_context": "A manufacturing company aims to optimize the allocation of production resources to maximize revenue from product sales while considering production capacity and manufacturer-specific constraints.",
  "optimization_problem_description": "Maximize total revenue from product sales by optimizing production quantities, subject to production capacity constraints and manufacturer-specific limits.",
  "optimization_formulation": {
    "objective": "maximize total_revenue = \u2211(Price[product] \u00d7 ProductionQuantity[product])",
    "decision_variables": {
      "ProductionQuantity[product]": {
        "currently_mapped_to": "Products.ProductionQuantity",
        "mapping_adequacy": "good",
        "description": "The number of units to produce for each product",
        "variable_type": "continuous"
      }
    },
    "constraints": {
      "TotalProductionCapacity": {
        "currently_mapped_to": "business_configuration_logic.TotalProductionCapacity",
        "mapping_adequacy": "good",
        "description": "The total production capacity available across all manufacturers"
      },
      "ManufacturerCapacity[manufacturer]": {
        "currently_mapped_to": "Manufacturers.Capacity",
        "mapping_adequacy": "good",
        "description": "The maximum production capacity for each manufacturer"
      }
    }
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Price[product]": {
        "currently_mapped_to": "Products.Price",
        "mapping_adequacy": "good",
        "description": "The selling price of each product"
      }
    },
    "constraint_bounds": {
      "TotalProductionCapacity": {
        "currently_mapped_to": "business_configuration_logic.TotalProductionCapacity",
        "mapping_adequacy": "good",
        "description": "The total production capacity available across all manufacturers"
      },
      "ManufacturerCapacity[manufacturer]": {
        "currently_mapped_to": "Manufacturers.Capacity",
        "mapping_adequacy": "good",
        "description": "The maximum production capacity for each manufacturer"
      }
    },
    "decision_variables": {
      "ProductionQuantity[product]": {
        "currently_mapped_to": "Products.ProductionQuantity",
        "mapping_adequacy": "good",
        "description": "The number of units to produce for each product",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
