Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-28 00:09:17

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": "Optimize the allocation of promotional tweets to maximize user engagement while respecting user preferences and platform constraints.",
  "optimization_problem": "The goal is to maximize the engagement score of promotional tweets by selecting which users should receive them, considering user preferences and the number of tweets each user can receive.",
  "objective": "maximize \u2211(engagement_coefficient[i] * x[i])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine mapping of coefficients and constraints 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 and updating configuration logic for scalar parameters and formulas.

CREATE TABLE user_profiles (
  uid INTEGER,
  engagement_coefficient FLOAT
);

CREATE TABLE engagement_coefficients (
  user_id INTEGER,
  coefficient FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "user_profiles": {
      "business_purpose": "Stores user information and engagement coefficients",
      "optimization_role": "decision_variables/objective_coefficients",
      "columns": {
        "uid": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each user",
          "optimization_purpose": "Decision variable index",
          "sample_values": "1, 2, 3"
        },
        "engagement_coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Expected engagement score if user receives the promotional tweet",
          "optimization_purpose": "Objective coefficient",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    },
    "engagement_coefficients": {
      "business_purpose": "Stores engagement coefficients for each user",
      "optimization_role": "objective_coefficients",
      "columns": {
        "user_id": {
          "data_type": "INTEGER",
          "business_meaning": "User identifier",
          "optimization_purpose": "Link to decision variable",
          "sample_values": "1, 2, 3"
        },
        "coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Engagement coefficient for user",
          "optimization_purpose": "Objective coefficient",
          "sample_values": "0.5, 0.7, 0.9"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_tweets_per_user": {
    "sample_value": "5",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of promotional tweets a user can receive",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "min_engagement_threshold": {
    "sample_value": "0.1",
    "data_type": "FLOAT",
    "business_meaning": "Minimum engagement score required for a user to receive the promotional tweet",
    "optimization_role": "Constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "total_followers_limit": {
    "sample_value": "1000000",
    "data_type": "INTEGER",
    "business_meaning": "Total number of followers that can be targeted with promotional tweets",
    "optimization_role": "Constraint bound",
    "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": "twitter_1",
  "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": "twitter_1",
  "iteration": 1,
  "business_context": "Optimize the allocation of promotional tweets to maximize user engagement while respecting user preferences and platform constraints.",
  "optimization_problem_description": "Maximize the total engagement score by selecting users to receive promotional tweets, subject to user-specific and platform-wide constraints.",
  "optimization_formulation": {
    "objective": "maximize \u2211(engagement_coefficient[i] * x[i])",
    "decision_variables": "x[i] is a binary variable indicating whether user i receives the promotional tweet",
    "constraints": [
      "\u2211(x[i]) <= total_followers_limit",
      "x[i] * engagement_coefficient[i] >= min_engagement_threshold for all i",
      "x[i] is binary for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "engagement_coefficient[i]": {
        "currently_mapped_to": "user_profiles.engagement_coefficient",
        "mapping_adequacy": "good",
        "description": "Expected engagement score if user receives the promotional tweet"
      }
    },
    "constraint_bounds": {
      "total_followers_limit": {
        "currently_mapped_to": "business_configuration_logic.total_followers_limit",
        "mapping_adequacy": "good",
        "description": "Total number of followers that can be targeted with promotional tweets"
      },
      "min_engagement_threshold": {
        "currently_mapped_to": "business_configuration_logic.min_engagement_threshold",
        "mapping_adequacy": "good",
        "description": "Minimum engagement score required for a user to receive the promotional tweet"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "user_profiles.uid",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if user i receives the tweet",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
