Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:42:04

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: game_1

```sql
CREATE TABLE Student (
  StuID NUMBER,
  LName TEXT,
  Fname TEXT,
  Age NUMBER,
  Sex TEXT,
  Major NUMBER,
  Advisor NUMBER,
  city_code TEXT
);
```

```sql
CREATE TABLE Video_Games (
  GameID NUMBER,
  GName TEXT,
  GType TEXT
);
```

```sql
CREATE TABLE Plays_Games (
  StuID NUMBER,
  GameID NUMBER,
  Hours_Played NUMBER
);
```

```sql
CREATE TABLE SportsInfo (
  StuID NUMBER,
  SportName TEXT,
  HoursPerWeek NUMBER,
  GamesPlayed NUMBER,
  OnScholarship TEXT
);
```



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": "game_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": "game_1",
  "iteration": 0,
  "business_context": "A university wants to optimize the allocation of scholarships to students based on their academic performance, sports participation, and gaming habits to maximize overall student satisfaction and performance.",
  "optimization_problem_description": "The objective is to maximize the total weighted sum of student satisfaction, which is influenced by their academic performance, sports participation, and gaming habits. Constraints include budget limits for scholarships, minimum and maximum hours spent on sports and gaming, and ensuring that students with higher academic performance receive more scholarships.",
  "optimization_formulation": {
    "objective": "maximize \u2211(w1 * Academic_Performance[i] + w2 * Sports_Participation[i] + w3 * Gaming_Habits[i])",
    "decision_variables": "Scholarship_Amount[i] (continuous), Hours_Sports[i] (continuous), Hours_Gaming[i] (continuous)",
    "constraints": [
      "\u2211 Scholarship_Amount[i] \u2264 Total_Budget",
      "Hours_Sports[i] \u2264 Max_Hours_Sports",
      "Hours_Sports[i] \u2265 Min_Hours_Sports",
      "Hours_Gaming[i] \u2264 Max_Hours_Gaming",
      "Hours_Gaming[i] \u2265 Min_Hours_Gaming",
      "Scholarship_Amount[i] \u2264 Max_Scholarship_Per_Student",
      "Scholarship_Amount[i] \u2265 Min_Scholarship_Per_Student",
      "Academic_Performance[i] \u2265 Min_Academic_Performance"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "w1": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "weight for academic performance"
      },
      "w2": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "weight for sports participation"
      },
      "w3": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "weight for gaming habits"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "total budget available for scholarships"
      },
      "Max_Hours_Sports": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum hours a student can spend on sports"
      },
      "Min_Hours_Sports": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum hours a student must spend on sports"
      },
      "Max_Hours_Gaming": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum hours a student can spend on gaming"
      },
      "Min_Hours_Gaming": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum hours a student must spend on gaming"
      },
      "Max_Scholarship_Per_Student": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum scholarship amount per student"
      },
      "Min_Scholarship_Per_Student": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum scholarship amount per student"
      },
      "Min_Academic_Performance": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum academic performance required for scholarship"
      }
    },
    "decision_variables": {
      "Scholarship_Amount[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "amount of scholarship allocated to student i",
        "variable_type": "continuous"
      },
      "Hours_Sports[i]": {
        "currently_mapped_to": "SportsInfo.HoursPerWeek",
        "mapping_adequacy": "partial",
        "description": "hours spent on sports by student i",
        "variable_type": "continuous"
      },
      "Hours_Gaming[i]": {
        "currently_mapped_to": "Plays_Games.Hours_Played",
        "mapping_adequacy": "partial",
        "description": "hours spent on gaming by student i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Academic performance data for students",
    "Total budget for scholarships",
    "Maximum and minimum hours for sports and gaming",
    "Maximum and minimum scholarship amounts per student",
    "Weights for academic performance, sports participation, and gaming habits"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map academic performance data and weights for the objective function"
  }
}
