Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-28 00:09:17

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: twitter_1

```sql
CREATE TABLE follows (
  f1 NUMBER,
  f2 NUMBER
);
```

```sql
CREATE TABLE tweets (
  id NUMBER,
  uid NUMBER,
  text TEXT,
  createdate TIME
);
```

```sql
CREATE TABLE user_profiles (
  uid NUMBER,
  name TEXT,
  email TEXT,
  partitionid NUMBER,
  followers 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": "twitter_1",
  "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": "twitter_1",
  "iteration": 0,
  "business_context": "Optimize the allocation of promotional tweets to maximize user engagement while respecting user preferences and platform constraints.",
  "optimization_problem_description": "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.",
  "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 (1 if yes, 0 if no)",
    "constraints": [
      "\u2211(x[i]) \u2264 max_tweets_per_user for each user i",
      "x[i] * engagement_coefficient[i] \u2265 min_engagement_threshold for each user i",
      "\u2211(x[i] * followers[i]) \u2264 total_followers_limit"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "engagement_coefficient[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the expected engagement score if user i receives the promotional tweet"
      }
    },
    "constraint_bounds": {
      "max_tweets_per_user": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of promotional tweets a user can receive"
      },
      "min_engagement_threshold": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum engagement score required for a user to receive the promotional tweet"
      },
      "total_followers_limit": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "total number of followers that can be targeted with promotional tweets"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "user_profiles.uid",
        "mapping_adequacy": "partial",
        "description": "binary decision variable indicating if user i receives the promotional tweet",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Engagement coefficients for each user",
    "Maximum number of promotional tweets per user",
    "Minimum engagement threshold for each user",
    "Total followers limit for promotional tweets"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine mapping of coefficients and constraints to existing schema or identify additional data sources"
  }
}
