Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:37:12

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: university_basketball

```sql
CREATE TABLE basketball_match (
  Team_ID NUMBER,
  School_ID NUMBER,
  Team_Name TEXT,
  ACC_Regular_Season TEXT,
  ACC_Percent TEXT,
  ACC_Home TEXT,
  ACC_Road TEXT,
  All_Games TEXT,
  All_Games_Percent NUMBER,
  All_Home TEXT,
  All_Road TEXT,
  All_Neutral TEXT
);
```

```sql
CREATE TABLE university (
  School_ID NUMBER,
  School TEXT,
  Location TEXT,
  Founded NUMBER,
  Affiliation TEXT,
  Enrollment NUMBER,
  Nickname TEXT,
  Primary_conference 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": "university_basketball",
  "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": "university_basketball",
  "iteration": 0,
  "business_context": "Optimize the selection of basketball teams for a tournament to maximize the overall win percentage while respecting constraints on team diversity and geographical distribution.",
  "optimization_problem_description": "The objective is to maximize the total win percentage of selected teams for a tournament. Constraints include selecting a specific number of teams, ensuring a minimum number of teams from different conferences, and limiting the number of teams from the same location.",
  "optimization_formulation": {
    "objective": "maximize \u2211(All_Games_Percent \u00d7 Team_Selection)",
    "decision_variables": "Team_Selection[Team_ID] (binary: 1 if team is selected, 0 otherwise)",
    "constraints": [
      "\u2211(Team_Selection) = Total_Teams_Required",
      "\u2211(Team_Selection \u00d7 Conference_Indicator) \u2265 Min_Teams_Per_Conference",
      "\u2211(Team_Selection \u00d7 Location_Indicator) \u2264 Max_Teams_Per_Location"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "All_Games_Percent[Team_ID]": {
        "currently_mapped_to": "basketball_match.All_Games_Percent",
        "mapping_adequacy": "good",
        "description": "Win percentage of each team"
      }
    },
    "constraint_bounds": {
      "Total_Teams_Required": {
        "currently_mapped_to": "business_configuration_logic.key",
        "mapping_adequacy": "missing",
        "description": "Total number of teams to be selected"
      },
      "Min_Teams_Per_Conference": {
        "currently_mapped_to": "business_configuration_logic.key",
        "mapping_adequacy": "missing",
        "description": "Minimum number of teams required from each conference"
      },
      "Max_Teams_Per_Location": {
        "currently_mapped_to": "business_configuration_logic.key",
        "mapping_adequacy": "missing",
        "description": "Maximum number of teams allowed from the same location"
      }
    },
    "decision_variables": {
      "Team_Selection[Team_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating whether a team is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total_Teams_Required",
    "Min_Teams_Per_Conference",
    "Max_Teams_Per_Location",
    "Conference_Indicator",
    "Location_Indicator"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map additional parameters such as Total_Teams_Required, Min_Teams_Per_Conference, and Max_Teams_Per_Location to the business configuration logic."
  }
}
