Iteration 3 - OR_EXPERT_REFINEMENT
Sequence: 7
Timestamp: 2025-07-25 22:31:54

Prompt:
You are an Operations Research (OR) expert in iteration 3 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.


CONVERGENCE PRESSURE (Iteration 3/5):
- Focus on finalizing the linear optimization model
- Set complete=true if formulation is mathematically sound and linear
- Minimize further schema change requests


CURRENT STATE (iteration 2):
{
  "iteration": 3,
  "converged": false,
  "business_context": "A publisher aims to maximize revenue from book sales while adhering to budget constraints and production limits. The publisher must decide how many copies of each book to produce, considering the price, production costs, and demand.",
  "optimization_problem": "Maximize total revenue from book sales, subject to constraints on the total production budget, the maximum number of issues per book, and the minimum number of copies to meet demand.",
  "objective": "maximize \u2211(Price_i \u00d7 Copies_i) where Price_i is the price of book i and Copies_i is the number of copies produced for book i",
  "table_count": 2,
  "key_changes": [
    "Added tables for Total_Budget and Max_Issues_i, updated business configuration logic to include scalar parameters and formulas, and ensured schema aligns with OR expert's requirements."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data such as the total production budget and the maximum number of issues per book to complete the optimization model.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 3 Database Schema
-- Objective: Added tables for Total_Budget and Max_Issues_i, updated business configuration logic to include scalar parameters and formulas, and ensured schema aligns with OR expert's requirements.

CREATE TABLE production_budget (
  Copies INTEGER
);

CREATE TABLE minimum_demand (
  Min_Demand INTEGER
);

CREATE TABLE production_costs (
  Cost FLOAT
);

CREATE TABLE book_prices (
  Price FLOAT
);

CREATE TABLE total_budget (
  Total_Budget INTEGER
);

CREATE TABLE max_issues (
  Max_Issues INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "production_budget": {
      "business_purpose": "Total production budget available for book production",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Copies": {
          "data_type": "INTEGER",
          "business_meaning": "Number of copies produced for each book",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": [
            1000,
            1500,
            2000
          ]
        }
      }
    },
    "minimum_demand": {
      "business_purpose": "Minimum demand for each book to meet market requirements",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Min_Demand": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum number of copies required for each book",
          "optimization_purpose": "Constraint bound in optimization model",
          "sample_values": [
            500,
            600,
            700
          ]
        }
      }
    },
    "production_costs": {
      "business_purpose": "Production cost per book",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Cost": {
          "data_type": "FLOAT",
          "business_meaning": "Production cost per book",
          "optimization_purpose": "Coefficient in production cost constraint",
          "sample_values": [
            10.0,
            12.0,
            15.0
          ]
        }
      }
    },
    "book_prices": {
      "business_purpose": "Price of each book to calculate revenue in optimization model",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Price": {
          "data_type": "FLOAT",
          "business_meaning": "Price of each book",
          "optimization_purpose": "Coefficient in revenue calculation",
          "sample_values": [
            20.0,
            25.0,
            30.0
          ]
        }
      }
    },
    "total_budget": {
      "business_purpose": "Total production budget available for book production",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Total_Budget": {
          "data_type": "INTEGER",
          "business_meaning": "Total production budget available for book production",
          "optimization_purpose": "Constraint bound in optimization model",
          "sample_values": [
            100000,
            150000,
            200000
          ]
        }
      }
    },
    "max_issues": {
      "business_purpose": "Maximum number of issues per book",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Max_Issues": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of issues per book",
          "optimization_purpose": "Constraint bound in optimization model",
          "sample_values": [
            5000,
            6000,
            7000
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Budget": {
    "sample_value": 100000,
    "data_type": "INTEGER",
    "business_meaning": "Total production budget available for book production",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "Max_Issues_i": {
    "sample_value": 5000,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of issues per book",
    "optimization_role": "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": "book_2",
  "iteration": 3,
  "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": "book_2",
  "iteration": 3,
  "business_context": "A publisher aims to maximize revenue from book sales while adhering to budget constraints and production limits. The publisher must decide how many copies of each book to produce, considering the price, production costs, and demand.",
  "optimization_problem_description": "Maximize total revenue from book sales, subject to constraints on the total production budget, the maximum number of issues per book, and the minimum number of copies to meet demand.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Price_i \u00d7 Copies_i) where Price_i is the price of book i and Copies_i is the number of copies produced for book i",
    "decision_variables": "Copies_i: number of copies produced for book i (integer)",
    "constraints": [
      "\u2211(Cost_i \u00d7 Copies_i) \u2264 Total_Budget: Total production cost must not exceed the budget",
      "Copies_i \u2264 Max_Issues_i: Number of copies produced for each book must not exceed the maximum issues",
      "Copies_i \u2265 Min_Demand_i: Number of copies produced for each book must meet the minimum demand"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Price_i": {
        "currently_mapped_to": "book_prices.Price",
        "mapping_adequacy": "good",
        "description": "Price of each book used in revenue calculation"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "total_budget.Total_Budget",
        "mapping_adequacy": "good",
        "description": "Total production budget available for book production"
      },
      "Max_Issues_i": {
        "currently_mapped_to": "max_issues.Max_Issues",
        "mapping_adequacy": "good",
        "description": "Maximum number of issues per book"
      },
      "Min_Demand_i": {
        "currently_mapped_to": "minimum_demand.Min_Demand",
        "mapping_adequacy": "good",
        "description": "Minimum number of copies required for each book"
      }
    },
    "decision_variables": {
      "Copies_i": {
        "currently_mapped_to": "production_budget.Copies",
        "mapping_adequacy": "good",
        "description": "Number of copies produced for each book",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
