Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:51:52

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 media company wants to maximize the total viewership share across its channels by optimally scheduling programs. The company needs to decide which programs to broadcast on which channels and at what times of day, considering channel ratings and program origins.",
  "optimization_problem": "The goal is to maximize the total viewership share by selecting the best combination of programs, channels, and times of day. The objective is to maximize the sum of the products of program shares and channel ratings. Constraints include ensuring each program is broadcast at most once, each channel has a limited number of time slots, and programs from certain origins are prioritized.",
  "objective": "maximize \u2211(Share_in_percent[Channel_ID, Program_ID] \u00d7 Rating_in_percent[Channel_ID])",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating tables for time slots, program origins, and decision variables. Configuration logic updates include scalar parameters for maximum broadcasts and formulas for priority rules."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints and ensure all necessary data is available for the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for time slots, program origins, and decision variables. Configuration logic updates include scalar parameters for maximum broadcasts and formulas for priority rules.

CREATE TABLE time_slots (
  time_slot_id INTEGER,
  time_of_day STRING
);

CREATE TABLE program_origins (
  program_id INTEGER,
  origin STRING
);

CREATE TABLE broadcast_decisions (
  channel_id INTEGER,
  program_id INTEGER,
  time_slot_id INTEGER,
  x BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "time_slots": {
      "business_purpose": "Available time slots for broadcasting programs",
      "optimization_role": "business_data",
      "columns": {
        "time_slot_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a time slot",
          "optimization_purpose": "Used in decision variables",
          "sample_values": "1, 2, 3"
        },
        "time_of_day": {
          "data_type": "STRING",
          "business_meaning": "Time of day for broadcasting",
          "optimization_purpose": "Used in decision variables",
          "sample_values": "Morning, Afternoon, Evening"
        }
      }
    },
    "program_origins": {
      "business_purpose": "Origin of programs (e.g., local, international)",
      "optimization_role": "business_data",
      "columns": {
        "program_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a program",
          "optimization_purpose": "Used in decision variables",
          "sample_values": "1, 2, 3"
        },
        "origin": {
          "data_type": "STRING",
          "business_meaning": "Origin of the program",
          "optimization_purpose": "Used in constraints",
          "sample_values": "Local, International"
        }
      }
    },
    "broadcast_decisions": {
      "business_purpose": "Binary decisions indicating if a program is broadcast on a channel at a specific time",
      "optimization_role": "decision_variables",
      "columns": {
        "channel_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a channel",
          "optimization_purpose": "Used in decision variables",
          "sample_values": "1, 2, 3"
        },
        "program_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a program",
          "optimization_purpose": "Used in decision variables",
          "sample_values": "1, 2, 3"
        },
        "time_slot_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a time slot",
          "optimization_purpose": "Used in decision variables",
          "sample_values": "1, 2, 3"
        },
        "x": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary decision variable",
          "optimization_purpose": "Used in decision variables",
          "sample_values": "0, 1"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_broadcasts_per_channel": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of times a program can be broadcast on a channel",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "local_program_priority": {
    "formula_expression": "SUM(broadcast_decisions.x WHERE program_origins.Origin = 'Local') >= 1",
    "data_type": "STRING",
    "business_meaning": "Ensures each channel broadcasts at least one local program",
    "optimization_role": "Constraint",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "program_share",
  "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": "program_share",
  "iteration": 1,
  "business_context": "A media company aims to maximize the total viewership share across its channels by optimally scheduling programs. The company needs to decide which programs to broadcast on which channels and at what times of day, considering channel ratings and program origins, while ensuring linearity in the optimization model.",
  "optimization_problem_description": "The goal is to maximize the total viewership share by selecting the best combination of programs, channels, and times of day. The objective is to maximize the sum of the products of program shares and channel ratings. Constraints include ensuring each program is broadcast at most once, each channel has a limited number of time slots, and programs from certain origins are prioritized.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Share_in_percent[Channel_ID, Program_ID] \u00d7 Rating_in_percent[Channel_ID] \u00d7 x[Channel_ID, Program_ID, Time_Slot_ID])",
    "decision_variables": "x[Channel_ID, Program_ID, Time_Slot_ID]: binary decision variable indicating if a program is broadcast on a channel at a specific time",
    "constraints": [
      "\u2211(x[Channel_ID, Program_ID, Time_Slot_ID] for all Time_Slot_ID) \u2264 1 for each Program_ID (each program is broadcast at most once)",
      "\u2211(x[Channel_ID, Program_ID, Time_Slot_ID] for all Program_ID) \u2264 max_broadcasts_per_channel for each Channel_ID (each channel has a limited number of time slots)",
      "\u2211(x[Channel_ID, Program_ID, Time_Slot_ID] for all Program_ID where Origin = 'Local') \u2265 1 for each Channel_ID (each channel broadcasts at least one local program)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Share_in_percent[Channel_ID, Program_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Share of viewership for a program on a channel"
      },
      "Rating_in_percent[Channel_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Rating of a channel"
      }
    },
    "constraint_bounds": {
      "max_broadcasts_per_channel": {
        "currently_mapped_to": "business_configuration_logic.max_broadcasts_per_channel",
        "mapping_adequacy": "good",
        "description": "Maximum number of broadcasts per channel"
      }
    },
    "decision_variables": {
      "x[Channel_ID, Program_ID, Time_Slot_ID]": {
        "currently_mapped_to": "broadcast_decisions.x",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if a program is broadcast on a channel at a specific time",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Share_in_percent[Channel_ID, Program_ID]",
    "Rating_in_percent[Channel_ID]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Obtain data for Share_in_percent[Channel_ID, Program_ID] and Rating_in_percent[Channel_ID] to complete the linear formulation"
  }
}
