Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:41:39

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: program_share

```sql
CREATE TABLE program (
  Program_ID NUMBER,
  Name TEXT,
  Origin TEXT,
  Launch NUMBER,
  Owner TEXT
);
```

```sql
CREATE TABLE channel (
  Channel_ID NUMBER,
  Name TEXT,
  Owner TEXT,
  Share_in_percent NUMBER,
  Rating_in_percent NUMBER
);
```

```sql
CREATE TABLE broadcast (
  Channel_ID NUMBER,
  Program_ID NUMBER,
  Time_of_day TEXT
);
```

```sql
CREATE TABLE broadcast_share (
  Channel_ID NUMBER,
  Program_ID NUMBER,
  Date TEXT,
  Share_in_percent NUMBER
);
```



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": "program_share",
  "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": "program_share",
  "iteration": 0,
  "business_context": "A media company wants to optimize the allocation of programs to channels to maximize the total share percentage across all broadcasts, considering the constraints on channel capacities and program availability.",
  "optimization_problem_description": "The goal is to maximize the total share percentage of programs broadcasted on various channels. The decision involves selecting which programs to broadcast on which channels, subject to constraints on the maximum share a channel can handle and the availability of programs.",
  "optimization_formulation": {
    "objective": "maximize total_share = \u2211(broadcast_share.Share_in_percent * x[channel_id, program_id])",
    "decision_variables": "x[channel_id, program_id] = 1 if program is broadcasted on channel, 0 otherwise (binary)",
    "constraints": [
      "\u2211(x[channel_id, program_id]) <= 1 for each program_id (a program can be broadcasted on at most one channel)",
      "\u2211(broadcast_share.Share_in_percent * x[channel_id, program_id]) <= channel.Share_in_percent for each channel_id (channel capacity constraint)",
      "x[channel_id, program_id] \u2208 {0, 1} for all channel_id, program_id (binary decision variable)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "broadcast_share.Share_in_percent[channel_id, program_id]": {
        "currently_mapped_to": "broadcast_share.Share_in_percent",
        "mapping_adequacy": "good",
        "description": "represents the share percentage of a program on a channel"
      }
    },
    "constraint_bounds": {
      "channel.Share_in_percent[channel_id]": {
        "currently_mapped_to": "channel.Share_in_percent",
        "mapping_adequacy": "good",
        "description": "represents the maximum share capacity of a channel"
      }
    },
    "decision_variables": {
      "x[channel_id, program_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating if a program is broadcasted on a channel",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Binary decision variable mapping for x[channel_id, program_id]",
    "Data on program availability or constraints on program broadcasting"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine decision variable mapping and ensure all necessary data for constraints are available"
  }
}
