Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:15:31

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 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": "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.",
  "objective": "minimize sum of y_t over all templates t, where y_t is a binary variable indicating if template t is used",
  "table_count": 1,
  "key_changes": [
    "Schema changes include adding a new table for template costs, modifying existing tables to include necessary fields, and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Incorporate cost data for templates to refine the objective function",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a new table for template costs, modifying existing tables to include necessary fields, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE Templates (
  Template_ID INTEGER,
  Cost FLOAT
);

CREATE TABLE Documents (
  Document_ID INTEGER
);

CREATE TABLE Template_Costs (
  Template_ID INTEGER,
  Cost FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Templates": {
      "business_purpose": "Stores information about document templates",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Template_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each template",
          "optimization_purpose": "Used as an index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "Cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost associated with using the template",
          "optimization_purpose": "Refines the objective function",
          "sample_values": "50.0, 75.0, 100.0"
        }
      }
    },
    "Documents": {
      "business_purpose": "Stores information about documents",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Document_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each document",
          "optimization_purpose": "Ensures each document is assigned a template",
          "sample_values": "101, 102, 103"
        }
      }
    },
    "Template_Costs": {
      "business_purpose": "Stores cost data for each template",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Template_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each template",
          "optimization_purpose": "Links cost to templates",
          "sample_values": "1, 2, 3"
        },
        "Cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost associated with using the template",
          "optimization_purpose": "Used in the objective function",
          "sample_values": "50.0, 75.0, 100.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "template_cost": {
    "sample_value": "100",
    "data_type": "FLOAT",
    "business_meaning": "Cost associated with using a template",
    "optimization_role": "Used to refine the objective function by incorporating cost",
    "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": "cre_Doc_Template_Mgt",
  "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": "cre_Doc_Template_Mgt",
  "iteration": 1,
  "business_context": "A company aims to optimize the assignment of templates to documents to minimize the total number of templates used while considering the cost associated with each template. This is crucial for reducing maintenance costs and ensuring consistency across documents.",
  "optimization_problem_description": "The goal is to minimize the total cost of templates used across all documents while ensuring each document is assigned exactly one template. This involves selecting templates for documents such that the total cost is minimized.",
  "optimization_formulation": {
    "objective": "minimize sum of Cost[t] * y_t over all templates t, where y_t is a binary variable indicating if template t is used",
    "decision_variables": {
      "y_t": {
        "description": "Binary variable indicating if template t is used",
        "variable_type": "binary"
      },
      "x_dt": {
        "description": "Binary variable indicating if document d is assigned to template t",
        "variable_type": "binary"
      }
    },
    "constraints": {
      "document_assignment": {
        "description": "Ensure each document is assigned exactly one template",
        "expression": "sum of x_dt over all templates t for each document d = 1"
      },
      "template_usage": {
        "description": "Link template usage to document assignment",
        "expression": "x_dt <= y_t for all documents d and templates t"
      }
    }
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Cost[t]": {
        "currently_mapped_to": "Templates.Cost",
        "mapping_adequacy": "good",
        "description": "Cost associated with using template t"
      }
    },
    "constraint_bounds": {
      "document_assignment": {
        "currently_mapped_to": "Documents.Document_ID",
        "mapping_adequacy": "good",
        "description": "Ensures each document is assigned exactly one template"
      }
    },
    "decision_variables": {
      "y_t": {
        "currently_mapped_to": "Templates.Template_ID",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if template t is used",
        "variable_type": "binary"
      },
      "x_dt": {
        "currently_mapped_to": "Documents.Document_ID and Templates.Template_ID",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if document d is assigned to template t",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
