Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:15:31

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 wants to optimize the assignment of templates to documents to minimize the total number of templates used while ensuring each document has a valid template assigned. This is crucial for reducing maintenance costs and ensuring consistency across documents.",
  "optimization_problem_description": "The goal is to minimize the number of unique templates used across all documents while ensuring each document is assigned exactly one template. This involves selecting templates for documents such that the total number of different templates is minimized.",
  "optimization_formulation": {
    "objective": "minimize sum of y_t over all templates t, where y_t is a binary variable indicating if template t is used",
    "decision_variables": "x_dt: binary variable indicating if template t is assigned to document d; y_t: binary variable indicating if template t is used",
    "constraints": [
      "sum of x_dt over all templates t for each document d = 1 (each document must have exactly one template)",
      "x_dt <= y_t for all documents d and templates t (a template can only be assigned if it is used)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "y_t": {
        "currently_mapped_to": "Templates.Template_ID",
        "mapping_adequacy": "good",
        "description": "binary variable indicating if template t is used"
      }
    },
    "constraint_bounds": {
      "document_assignment[document_id]": {
        "currently_mapped_to": "Documents.Document_ID",
        "mapping_adequacy": "good",
        "description": "ensures each document is assigned exactly one template"
      }
    },
    "decision_variables": {
      "x_dt[document_id, template_id]": {
        "currently_mapped_to": "Documents.Document_ID and Templates.Template_ID",
        "mapping_adequacy": "good",
        "description": "binary variable indicating if template t is assigned to document d",
        "variable_type": "binary"
      },
      "y_t[template_id]": {
        "currently_mapped_to": "Templates.Template_ID",
        "mapping_adequacy": "good",
        "description": "binary variable indicating if template t is used",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Cost or penalty associated with using each template to refine the objective function"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Incorporate cost data for templates to refine the objective function"
  }
}
