Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:31:54

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 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": "The publisher wants to 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": 3,
  "key_changes": [
    "Schema changes include adding tables for missing optimization data (production budget, minimum demand, production costs) and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data such as production budget, minimum demand, and production costs to complete the optimization model.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding tables for missing optimization data (production budget, minimum demand, production costs) and updating configuration logic for scalar parameters and formulas.

CREATE TABLE production_budget (
  Copies INTEGER
);

CREATE TABLE minimum_demand (
  Min_Demand INTEGER
);

CREATE TABLE production_costs (
  Cost FLOAT
);


```

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
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Budget": {
    "sample_value": 100000,
    "data_type": "INTEGER",
    "business_meaning": "Total production budget available for book production",
    "optimization_role": "Constraint bound for total production cost",
    "configuration_type": "scalar_parameter"
  },
  "Min_Demand_i": {
    "sample_value": 500,
    "data_type": "INTEGER",
    "business_meaning": "Minimum demand for each book to meet market requirements",
    "optimization_role": "Constraint bound for minimum copies produced",
    "configuration_type": "scalar_parameter"
  },
  "Cost_i": {
    "sample_value": 10,
    "data_type": "FLOAT",
    "business_meaning": "Production cost per book",
    "optimization_role": "Coefficient in production cost constraint",
    "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": 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": "book_2",
  "iteration": 1,
  "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: integer, number of copies produced for book i",
    "constraints": "1. \u2211(Cost_i \u00d7 Copies_i) \u2264 Budget (total production cost constraint), 2. Copies_i \u2265 Min_Demand_i (minimum demand constraint for each book)"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Price_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Price of book i"
      }
    },
    "constraint_bounds": {
      "Budget": {
        "currently_mapped_to": "business_configuration_logic.Budget",
        "mapping_adequacy": "good",
        "description": "Total production budget available for book production"
      },
      "Min_Demand_i": {
        "currently_mapped_to": "business_configuration_logic.Min_Demand_i",
        "mapping_adequacy": "good",
        "description": "Minimum demand for each book to meet market requirements"
      }
    },
    "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": [
    "Price_i: Price of book i"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify and map missing data such as the price of each book to complete the optimization model."
  }
}
