Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:30:15

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 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": "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.",
  "objective": "minimize \u2211(cost_of_template[Template_ID] \u00d7 use_template[Template_ID, Document_ID])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for template costs and validity, and updating configuration logic for minimum paragraphs and budget. Business configuration logic now includes scalar parameters and formulas for optimization."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data required for the optimization model, such as template costs, validity status, and paragraph requirements.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for template costs and validity, and updating configuration logic for minimum paragraphs and budget. Business configuration logic now includes scalar parameters and formulas for optimization.

CREATE TABLE template_costs (
  template_id INTEGER,
  cost FLOAT
);

CREATE TABLE template_validity (
  template_id INTEGER,
  is_valid BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "template_costs": {
      "business_purpose": "Cost associated with using a specific template",
      "optimization_role": "objective_coefficients",
      "columns": {
        "template_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the template",
          "optimization_purpose": "Index for template cost",
          "sample_values": "1, 2, 3"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost of using the template",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "10.5, 20.0, 15.75"
        }
      }
    },
    "template_validity": {
      "business_purpose": "Indicates whether a template is valid",
      "optimization_role": "constraint_bounds",
      "columns": {
        "template_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the template",
          "optimization_purpose": "Index for template validity",
          "sample_values": "1, 2, 3"
        },
        "is_valid": {
          "data_type": "BOOLEAN",
          "business_meaning": "Validity status of the template",
          "optimization_purpose": "Constraint bound for template usage",
          "sample_values": "true, false, true"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "min_paragraphs": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "Minimum number of paragraphs required for a document",
    "optimization_role": "Constraint bound for document paragraph count",
    "configuration_type": "scalar_parameter"
  },
  "budget": {
    "sample_value": 1000,
    "data_type": "FLOAT",
    "business_meaning": "Total budget for document creation",
    "optimization_role": "Constraint bound for total cost of templates used",
    "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 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": [
      "\u2211(use_template[Template_ID, Document_ID]) = 1 for each Document_ID (each document must use exactly one template)",
      "use_template[Template_ID, Document_ID] \u2264 is_valid[Template_ID] for each Template_ID, Document_ID (only valid templates can be used)",
      "\u2211(cost_of_template[Template_ID] \u00d7 use_template[Template_ID, Document_ID]) \u2264 budget (total cost must be within budget)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_of_template[Template_ID]": {
        "currently_mapped_to": "template_costs.cost",
        "mapping_adequacy": "good",
        "description": "Cost of using a specific template"
      }
    },
    "constraint_bounds": {
      "is_valid[Template_ID]": {
        "currently_mapped_to": "template_validity.is_valid",
        "mapping_adequacy": "good",
        "description": "Validity status of a template"
      },
      "budget": {
        "currently_mapped_to": "business_configuration_logic.budget",
        "mapping_adequacy": "good",
        "description": "Total budget for document creation"
      }
    },
    "decision_variables": {
      "use_template[Template_ID, Document_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating whether a template is used for a document",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Decision variable use_template[Template_ID, Document_ID]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify and map the missing decision variable use_template[Template_ID, Document_ID]"
  }
}
