Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-28 00:05:02

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: tvshow

```sql
CREATE TABLE TV_Channel (
  id TEXT,
  series_name TEXT,
  Country TEXT,
  Language TEXT,
  Content TEXT,
  Pixel_aspect_ratio_PAR TEXT,
  Hight_definition_TV TEXT,
  Pay_per_view_PPV TEXT,
  Package_Option TEXT
);
```

```sql
CREATE TABLE TV_series (
  id NUMBER,
  Episode TEXT,
  Air_Date TEXT,
  Rating TEXT,
  Share NUMBER,
  18_49_Rating_Share TEXT,
  Viewers_m TEXT,
  Weekly_Rank NUMBER,
  Channel TEXT
);
```

```sql
CREATE TABLE Cartoon (
  id NUMBER,
  Title TEXT,
  Directed_by TEXT,
  Written_by TEXT,
  Original_air_date TEXT,
  Production_code NUMBER,
  Channel 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": "tvshow",
  "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": "tvshow",
  "iteration": 0,
  "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_description": "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.",
  "optimization_formulation": {
    "objective": "maximize total_viewership = \u2211(Viewers_m[i] * x[i])",
    "decision_variables": "x[i] = 1 if TV series or cartoon i is selected to air, 0 otherwise (binary)",
    "constraints": [
      "\u2211(Air_Time[i] * x[i]) \u2264 Total_Available_Time for each channel",
      "\u2211(x[i] * Content_Type[i]) \u2264 Channel_Content_Capacity for each content type",
      "\u2211(x[i] * Demographic_Target[i]) \u2265 Minimum_Demographic_Target for each demographic group"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Viewers_m[i]": {
        "currently_mapped_to": "TV_series.Viewers_m",
        "mapping_adequacy": "good",
        "description": "represents the number of viewers in millions for each TV series or cartoon"
      }
    },
    "constraint_bounds": {
      "Total_Available_Time": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the total available air time for each channel"
      },
      "Channel_Content_Capacity": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the maximum allowable content type per channel"
      },
      "Minimum_Demographic_Target": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the minimum required viewership from specific demographic groups"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating if a TV series or cartoon is selected to air",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Air_Time for each TV series or cartoon",
    "Content_Type for each TV series or cartoon",
    "Demographic_Target for each TV series or cartoon",
    "Total_Available_Time for each channel",
    "Channel_Content_Capacity for each content type",
    "Minimum_Demographic_Target for each demographic group"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine mapping of constraints and decision variables to existing schema or identify additional data sources"
  }
}
