Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:43:29

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: network_2

```sql
CREATE TABLE Person (
  name TEXT,
  age NUMBER,
  city TEXT,
  gender TEXT,
  job TEXT
);
```

```sql
CREATE TABLE PersonFriend (
  name TEXT,
  friend TEXT,
  year 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": "network_2",
  "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": "network_2",
  "iteration": 0,
  "business_context": "A social network wants to maximize the number of friendships formed in the network while ensuring that each person has a balanced number of friends across different age groups.",
  "optimization_problem_description": "The objective is to maximize the total number of friendships formed, subject to constraints that ensure each person has a balanced number of friends across different age groups and that no person exceeds a maximum number of friendships.",
  "optimization_formulation": {
    "objective": "maximize \u2211(x_ij) where x_ij is a binary decision variable indicating whether person i is friends with person j",
    "decision_variables": "x_ij: binary variable indicating whether person i is friends with person j",
    "constraints": [
      "\u2211(x_ij) \u2264 max_friendships_per_person for each person i",
      "\u2211(x_ij for j in age_group_k) \u2265 min_friendships_per_age_group for each person i and age group k",
      "x_ij = x_ji for all i, j (friendship is mutual)",
      "x_ii = 0 for all i (no self-friendship)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "x_ij": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating whether person i is friends with person j"
      }
    },
    "constraint_bounds": {
      "max_friendships_per_person": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of friendships allowed per person"
      },
      "min_friendships_per_age_group": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum number of friendships required per age group"
      }
    },
    "decision_variables": {
      "x_ij": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary variable indicating whether person i is friends with person j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "max_friendships_per_person",
    "min_friendships_per_age_group",
    "age group definitions",
    "binary decision variables x_ij"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define age groups and determine appropriate values for max_friendships_per_person and min_friendships_per_age_group"
  }
}
