Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:41:39

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 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": "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.",
  "objective": "maximize total_share = \u2211(broadcast_share.Share_in_percent * x[channel_id, program_id])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a new table for decision variables, modifying existing tables to ensure all necessary data for constraints are available, and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine decision variable mapping and ensure all necessary data for constraints are available",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for decision variables, modifying existing tables to ensure all necessary data for constraints are available, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE broadcast_share (
  channel_id INTEGER,
  program_id INTEGER,
  Share_in_percent FLOAT
);

CREATE TABLE decision_variables (
  channel_id INTEGER,
  program_id INTEGER,
  x BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "broadcast_share": {
      "business_purpose": "Stores share percentages of programs on channels",
      "optimization_role": "objective_coefficients",
      "columns": {
        "channel_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the channel",
          "optimization_purpose": "Used to link with decision variables",
          "sample_values": "1, 2, 3"
        },
        "program_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the program",
          "optimization_purpose": "Used to link with decision variables",
          "sample_values": "101, 102, 103"
        },
        "Share_in_percent": {
          "data_type": "FLOAT",
          "business_meaning": "Share percentage of the program on the channel",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "10.5, 20.0, 15.0"
        }
      }
    },
    "decision_variables": {
      "business_purpose": "Indicates if a program is broadcasted on a channel",
      "optimization_role": "decision_variables",
      "columns": {
        "channel_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the channel",
          "optimization_purpose": "Part of the decision variable index",
          "sample_values": "1, 2, 3"
        },
        "program_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the program",
          "optimization_purpose": "Part of the decision variable index",
          "sample_values": "101, 102, 103"
        },
        "x": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary decision variable indicating if a program is broadcasted",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": "0, 1"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "channel_capacity_limit": {
    "sample_value": "100",
    "data_type": "INTEGER",
    "business_meaning": "Maximum share capacity a channel can handle",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "program_availability": {
    "sample_value": "1",
    "data_type": "BOOLEAN",
    "business_meaning": "Indicates if a program is available for broadcasting",
    "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": "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 optimize the allocation of programs to channels to maximize the total share percentage across all broadcasts, considering 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 * decision_variables.x[channel_id, program_id])",
    "decision_variables": "x[channel_id, program_id] is a binary variable indicating if program_id is broadcasted on channel_id",
    "constraints": [
      "\u2211(broadcast_share.Share_in_percent * decision_variables.x[channel_id, program_id]) \u2264 business_configuration_logic.channel_capacity_limit for each channel_id",
      "decision_variables.x[channel_id, program_id] \u2264 business_configuration_logic.program_availability for each program_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Share_in_percent[channel_id, program_id]": {
        "currently_mapped_to": "broadcast_share.Share_in_percent",
        "mapping_adequacy": "good",
        "description": "Share percentage of the program on the channel"
      }
    },
    "constraint_bounds": {
      "channel_capacity_limit[channel_id]": {
        "currently_mapped_to": "business_configuration_logic.channel_capacity_limit",
        "mapping_adequacy": "good",
        "description": "Maximum share capacity a channel can handle"
      },
      "program_availability[program_id]": {
        "currently_mapped_to": "business_configuration_logic.program_availability",
        "mapping_adequacy": "good",
        "description": "Indicates if a program is available for broadcasting"
      }
    },
    "decision_variables": {
      "x[channel_id, program_id]": {
        "currently_mapped_to": "decision_variables.x",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if a program is broadcasted",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
