Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:29:20

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 furniture manufacturer aims to maximize its profit by determining the optimal number of each furniture type to produce, considering production costs, market rates, and factory capacity constraints.",
  "optimization_problem": "The manufacturer needs to decide how many units of each furniture type to produce to maximize profit, given the production costs, market rates, and limited factory capacity. The objective is to maximize the total profit, which is the difference between the revenue from selling the furniture and the production costs.",
  "objective": "maximize \u2211(Market_Rate \u00d7 Quantity_Produced - Price_in_Dollar \u00d7 Quantity_Produced)",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating tables for decision variables and constraint bounds, and updating business configuration logic to include scalar parameters and formulas for missing optimization requirements."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map the missing constraints and decision variables to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraint bounds, and updating business configuration logic to include scalar parameters and formulas for missing optimization requirements.

CREATE TABLE production_plan (
  Furniture_ID INTEGER,
  Quantity_Produced INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "production_plan": {
      "business_purpose": "Number of units to produce for each furniture type",
      "optimization_role": "decision_variables",
      "columns": {
        "Furniture_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each furniture type",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "Quantity_Produced": {
          "data_type": "INTEGER",
          "business_meaning": "Number of units to produce for each furniture type",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "10, 20, 30"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Factory_Capacity": {
    "sample_value": 1000,
    "data_type": "INTEGER",
    "business_meaning": "Total production capacity of all factories",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "Budget_Limit": {
    "sample_value": 50000,
    "data_type": "FLOAT",
    "business_meaning": "Total budget available for production",
    "optimization_role": "constraint bound",
    "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": "manufacturer",
  "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": "manufacturer",
  "iteration": 1,
  "business_context": "A furniture manufacturer aims to maximize its profit by determining the optimal number of each furniture type to produce, considering production costs, market rates, and factory capacity constraints.",
  "optimization_problem_description": "The manufacturer needs to decide how many units of each furniture type to produce to maximize profit, given the production costs, market rates, and limited factory capacity. The objective is to maximize the total profit, which is the difference between the revenue from selling the furniture and the production costs.",
  "optimization_formulation": {
    "objective": "maximize \u2211((Market_Rate - Price_in_Dollar) \u00d7 Quantity_Produced)",
    "decision_variables": "Quantity_Produced[Furniture_ID]: Number of units to produce for each furniture type",
    "constraints": "1. \u2211(Quantity_Produced) \u2264 Total_Factory_Capacity, 2. \u2211(Price_in_Dollar \u00d7 Quantity_Produced) \u2264 Budget_Limit"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Market_Rate[Furniture_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Market rate for each furniture type"
      },
      "Price_in_Dollar[Furniture_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Production cost for each furniture type"
      }
    },
    "constraint_bounds": {
      "Total_Factory_Capacity": {
        "currently_mapped_to": "business_configuration_logic.Total_Factory_Capacity",
        "mapping_adequacy": "good",
        "description": "Total production capacity of all factories"
      },
      "Budget_Limit": {
        "currently_mapped_to": "business_configuration_logic.Budget_Limit",
        "mapping_adequacy": "good",
        "description": "Total budget available for production"
      }
    },
    "decision_variables": {
      "Quantity_Produced[Furniture_ID]": {
        "currently_mapped_to": "production_plan.Quantity_Produced",
        "mapping_adequacy": "good",
        "description": "Number of units to produce for each furniture type",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Market_Rate[Furniture_ID]",
    "Price_in_Dollar[Furniture_ID]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map the missing objective coefficients (Market_Rate and Price_in_Dollar) to complete the optimization model."
  }
}
