Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:12:03

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 music streaming service wants to optimize the allocation of its storage resources to maximize the total rating of songs available on the platform, considering the file size and resolution of each song.",
  "optimization_problem": "The goal is to maximize the total rating of songs stored on the platform while respecting storage capacity and resolution quality constraints. Each song has a file size and resolution, and the platform has a limited storage capacity.",
  "objective": "maximize total_rating = \u2211(rating[i] * x[i])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include adding tables for missing data requirements and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine mapping of decision variables and ensure all necessary parameters are available",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding tables for missing data requirements and updating configuration logic for scalar parameters and formulas.

CREATE TABLE song (
  f_id INTEGER,
  rating FLOAT,
  file_size INTEGER
);

CREATE TABLE song_file_data (
  song_id INTEGER,
  resolution INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "song": {
      "business_purpose": "Stores metadata about each song",
      "optimization_role": "objective_coefficients",
      "columns": {
        "f_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each song",
          "optimization_purpose": "Used as a decision variable in optimization",
          "sample_values": "1, 2, 3"
        },
        "rating": {
          "data_type": "FLOAT",
          "business_meaning": "The rating of each song",
          "optimization_purpose": "Used to calculate the total rating of stored songs",
          "sample_values": "4.5, 3.8, 5.0"
        },
        "file_size": {
          "data_type": "INTEGER",
          "business_meaning": "The file size of each song",
          "optimization_purpose": "Used in storage capacity constraint",
          "sample_values": "5000, 3000, 7000"
        }
      }
    },
    "song_file_data": {
      "business_purpose": "Stores file size and resolution data for each song",
      "optimization_role": "business_data",
      "columns": {
        "song_id": {
          "data_type": "INTEGER",
          "business_meaning": "References the unique identifier of a song",
          "optimization_purpose": "Links file data to songs",
          "sample_values": "1, 2, 3"
        },
        "resolution": {
          "data_type": "INTEGER",
          "business_meaning": "The resolution quality of each song",
          "optimization_purpose": "Used in resolution quality constraint",
          "sample_values": "1080, 720, 480"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_storage_capacity": {
    "sample_value": "100000",
    "data_type": "INTEGER",
    "business_meaning": "The total storage capacity available for storing songs",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "minimum_total_resolution": {
    "sample_value": "720",
    "data_type": "INTEGER",
    "business_meaning": "The minimum total resolution quality required for stored songs",
    "optimization_role": "Used as a constraint bound in optimization model",
    "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": "music_1",
  "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": "music_1",
  "iteration": 1,
  "business_context": "A music streaming service aims to optimize its storage allocation to maximize the total rating of songs available on the platform, considering the file size and resolution of each song, while adhering to storage capacity and resolution quality constraints.",
  "optimization_problem_description": "Maximize the total rating of songs stored on the platform, subject to storage capacity and resolution quality constraints. Each song has a file size and resolution, and the platform has a limited storage capacity.",
  "optimization_formulation": {
    "objective": "maximize total_rating = \u2211(rating[i] * x[i])",
    "decision_variables": "x[i] is a binary variable indicating whether song i is stored (1) or not (0)",
    "constraints": [
      "\u2211(file_size[i] * x[i]) <= total_storage_capacity",
      "\u2211(resolution[i] * x[i]) >= minimum_total_resolution"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "rating[i]": {
        "currently_mapped_to": "song.rating",
        "mapping_adequacy": "good",
        "description": "The rating of each song used to calculate the total rating of stored songs"
      }
    },
    "constraint_bounds": {
      "total_storage_capacity": {
        "currently_mapped_to": "business_configuration_logic.total_storage_capacity",
        "mapping_adequacy": "good",
        "description": "The total storage capacity available for storing songs"
      },
      "minimum_total_resolution": {
        "currently_mapped_to": "business_configuration_logic.minimum_total_resolution",
        "mapping_adequacy": "good",
        "description": "The minimum total resolution quality required for stored songs"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "song.f_id",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating whether song i is stored",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
