Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:36:21

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_1

```sql
CREATE TABLE Highschooler (
  ID NUMBER,
  name TEXT,
  grade NUMBER
);
```

```sql
CREATE TABLE Friend (
  student_id NUMBER,
  friend_id NUMBER
);
```

```sql
CREATE TABLE Likes (
  student_id NUMBER,
  liked_id 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_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": "network_1",
  "iteration": 0,
  "business_context": "A high school wants to optimize the social engagement of students by maximizing the number of mutual friendships. Each student can have a limited number of friends, and the goal is to maximize the number of mutual friendships within these constraints.",
  "optimization_problem_description": "Maximize the number of mutual friendships among students, where a mutual friendship is defined as a pair of students who both list each other as friends. Each student can have a limited number of friends, and the optimization will determine the optimal set of friendships to maximize mutual connections.",
  "optimization_formulation": {
    "objective": "maximize \u2211(x_ij + x_ji) for all i, j where x_ij and x_ji are binary variables indicating if student i considers student j a friend and vice versa",
    "decision_variables": "x_ij: binary variable indicating if student i considers student j a friend",
    "constraints": [
      "\u2211(x_ij) \u2264 max_friends for all i",
      "x_ij + x_ji \u2264 1 for all i, j",
      "x_ij is binary for all i, j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "x_ij[i,j]": {
        "currently_mapped_to": "Friend.student_id, Friend.friend_id",
        "mapping_adequacy": "good",
        "description": "binary variable indicating if student i considers student j a friend"
      }
    },
    "constraint_bounds": {
      "max_friends[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of friends a student can have"
      }
    },
    "decision_variables": {
      "x_ij[i,j]": {
        "currently_mapped_to": "Friend.student_id, Friend.friend_id",
        "mapping_adequacy": "good",
        "description": "binary variable indicating if student i considers student j a friend",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Maximum number of friends each student can have (max_friends)"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Determine the maximum number of friends each student can have to complete the model"
  }
}
