Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-28 00:05:02

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 TV network wants to optimize its programming schedule to maximize viewership across different channels while considering constraints such as air time slots, channel capacity, and viewer demographics.",
  "optimization_problem": "The goal is to maximize the total viewership by selecting the optimal combination of TV series and cartoons to air on different channels, considering constraints like available time slots, channel-specific content restrictions, and target audience demographics.",
  "objective": "maximize total_viewership = \u2211(Viewers_m[i] * x[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data, modifying existing tables to fill mapping gaps, and moving certain parameters to configuration logic for better management."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine mapping of constraints and decision variables to existing schema or identify additional data sources",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data, modifying existing tables to fill mapping gaps, and moving certain parameters to configuration logic for better management.

CREATE TABLE TV_series (
  Viewers_m INTEGER,
  Air_Time INTEGER,
  Content_Type STRING,
  Demographic_Target INTEGER,
  selected BOOLEAN
);

CREATE TABLE Channel (
  Total_Available_Time INTEGER,
  Content_Capacity INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "TV_series": {
      "business_purpose": "Stores TV series and cartoon data for scheduling optimization",
      "optimization_role": "business_data",
      "columns": {
        "Viewers_m": {
          "data_type": "INTEGER",
          "business_meaning": "Number of viewers in millions",
          "optimization_purpose": "Objective coefficient for maximizing viewership",
          "sample_values": "1, 2, 3"
        },
        "Air_Time": {
          "data_type": "INTEGER",
          "business_meaning": "Air time required for the series or cartoon",
          "optimization_purpose": "Constraint for total available time",
          "sample_values": "30, 60, 90"
        },
        "Content_Type": {
          "data_type": "STRING",
          "business_meaning": "Type of content (e.g., series, cartoon)",
          "optimization_purpose": "Constraint for channel content capacity",
          "sample_values": "series, cartoon"
        },
        "Demographic_Target": {
          "data_type": "INTEGER",
          "business_meaning": "Target demographic viewership",
          "optimization_purpose": "Constraint for minimum demographic target",
          "sample_values": "50000, 100000, 150000"
        },
        "selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the series or cartoon is selected to air",
          "optimization_purpose": "Decision variable for optimization",
          "sample_values": "true, false"
        }
      }
    },
    "Channel": {
      "business_purpose": "Stores channel data for scheduling optimization",
      "optimization_role": "business_data",
      "columns": {
        "Total_Available_Time": {
          "data_type": "INTEGER",
          "business_meaning": "Total available air time for the channel",
          "optimization_purpose": "Constraint for total available time",
          "sample_values": "24, 48, 72"
        },
        "Content_Capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum allowable content type per channel",
          "optimization_purpose": "Constraint for channel content capacity",
          "sample_values": "10, 20, 30"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Available_Time": {
    "sample_value": "24",
    "data_type": "INTEGER",
    "business_meaning": "Total available air time for each channel",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "Channel_Content_Capacity": {
    "sample_value": "10",
    "data_type": "INTEGER",
    "business_meaning": "Maximum allowable content type per channel",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "Minimum_Demographic_Target": {
    "sample_value": "100000",
    "data_type": "INTEGER",
    "business_meaning": "Minimum required viewership from specific demographic groups",
    "optimization_role": "Used as a constraint 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": "tvshow",
  "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": "tvshow",
  "iteration": 1,
  "business_context": "A TV network aims to optimize its programming schedule to maximize viewership across different channels, considering constraints such as air time slots, channel capacity, and viewer demographics.",
  "optimization_problem_description": "The objective is to maximize total viewership by selecting the optimal combination of TV series and cartoons to air on different channels, subject to constraints like available time slots, channel-specific content restrictions, and target audience demographics.",
  "optimization_formulation": {
    "objective": "maximize total_viewership = \u2211(Viewers_m[i] * selected[i])",
    "decision_variables": "selected[i]: binary variable indicating if TV series/cartoon i is selected to air",
    "constraints": [
      "\u2211(Air_Time[i] * selected[i]) \u2264 Total_Available_Time for each channel",
      "\u2211(Content_Type[i] * selected[i]) \u2264 Content_Capacity for each channel",
      "\u2211(Demographic_Target[i] * selected[i]) \u2265 Minimum_Demographic_Target"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Viewers_m[i]": {
        "currently_mapped_to": "TV_series.Viewers_m",
        "mapping_adequacy": "good",
        "description": "Number of viewers in millions for TV series/cartoon i"
      }
    },
    "constraint_bounds": {
      "Total_Available_Time": {
        "currently_mapped_to": "Channel.Total_Available_Time",
        "mapping_adequacy": "good",
        "description": "Total available air time for each channel"
      },
      "Content_Capacity": {
        "currently_mapped_to": "Channel.Content_Capacity",
        "mapping_adequacy": "good",
        "description": "Maximum allowable content type per channel"
      },
      "Minimum_Demographic_Target": {
        "currently_mapped_to": "business_configuration_logic.Minimum_Demographic_Target",
        "mapping_adequacy": "good",
        "description": "Minimum required viewership from specific demographic groups"
      }
    },
    "decision_variables": {
      "selected[i]": {
        "currently_mapped_to": "TV_series.selected",
        "mapping_adequacy": "good",
        "description": "Indicates if the series or cartoon is selected to air",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
