Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:30:15

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either 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
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: cre_Doc_Template_Mgt

```sql
CREATE TABLE Ref_Template_Types (
  Template_Type_Code TEXT,
  Template_Type_Description TEXT
);
```

```sql
CREATE TABLE Templates (
  Template_ID NUMBER,
  Version_Number NUMBER,
  Template_Type_Code TEXT,
  Date_Effective_From TIME,
  Date_Effective_To TIME,
  Template_Details TEXT
);
```

```sql
CREATE TABLE Documents (
  Document_ID NUMBER,
  Template_ID NUMBER,
  Document_Name TEXT,
  Document_Description TEXT,
  Other_Details TEXT
);
```

```sql
CREATE TABLE Paragraphs (
  Paragraph_ID NUMBER,
  Document_ID NUMBER,
  Paragraph_Text TEXT,
  Other_Details TEXT
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "cre_Doc_Template_Mgt",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 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 needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "cre_Doc_Template_Mgt",
  "iteration": 0,
  "business_context": "A company manages multiple document templates and needs to optimize the allocation of templates to documents to minimize the total cost of document creation while ensuring that each document uses a valid template and meets specific content requirements.",
  "optimization_problem_description": "The goal is to minimize the total cost of document creation by selecting the most cost-effective templates for each document, ensuring that each document uses a valid template and meets specific content requirements such as minimum paragraph count.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_of_template[Template_ID] \u00d7 use_template[Template_ID, Document_ID])",
    "decision_variables": "use_template[Template_ID, Document_ID] (binary: 1 if template is used for document, 0 otherwise)",
    "constraints": [
      "Each document must use exactly one template: \u2211(use_template[Template_ID, Document_ID]) = 1 for each Document_ID",
      "Each template must be valid: use_template[Template_ID, Document_ID] \u2264 valid_template[Template_ID] for each Template_ID, Document_ID",
      "Each document must have at least a minimum number of paragraphs: \u2211(paragraph_count[Document_ID]) \u2265 min_paragraphs for each Document_ID",
      "The total cost of templates used must not exceed the budget: \u2211(cost_of_template[Template_ID] \u00d7 use_template[Template_ID, Document_ID]) \u2264 budget"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_of_template[Template_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Cost associated with using a specific template"
      }
    },
    "constraint_bounds": {
      "valid_template[Template_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Indicates whether a template is valid"
      },
      "min_paragraphs": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of paragraphs required for a document"
      },
      "budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total budget for document creation"
      }
    },
    "decision_variables": {
      "use_template[Template_ID, Document_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if a template is used for a document",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Cost associated with each template (cost_of_template[Template_ID])",
    "Validity status of each template (valid_template[Template_ID])",
    "Minimum number of paragraphs required for each document (min_paragraphs)",
    "Total budget for document creation (budget)"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "low",
    "next_focus": "Identify and map missing data required for the optimization model, such as template costs, validity status, and paragraph requirements."
  }
}
