Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:59:04

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: 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": "A university basketball league wants to optimize the allocation of resources to different teams to maximize their overall performance in the league.",
  "optimization_problem_description": "The goal is to maximize the overall performance of the basketball teams by optimally allocating resources such as training hours, coaching staff, and budget. The performance is measured by the win percentage in all games. Constraints include limits on total resources available and minimum resource allocation requirements for each team.",
  "optimization_formulation": {
    "objective": "maximize \u2211(All_Games_Percent[Team_ID] \u00d7 Resource_Allocation[Team_ID])",
    "decision_variables": "Resource_Allocation[Team_ID] - continuous variable representing the amount of resources allocated to each team",
    "constraints": [
      "\u2211(Resource_Allocation[Team_ID]) \u2264 Total_Resources_Available",
      "Resource_Allocation[Team_ID] \u2265 Minimum_Resource_Allocation[Team_ID] for all Team_ID",
      "Resource_Allocation[Team_ID] \u2264 Maximum_Resource_Allocation[Team_ID] for all Team_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "All_Games_Percent[Team_ID]": {
        "currently_mapped_to": "basketball_match.All_Games_Percent",
        "mapping_adequacy": "good",
        "description": "represents the win percentage of each team in all games"
      }
    },
    "constraint_bounds": {
      "Total_Resources_Available": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "total resources available for allocation across all teams"
      },
      "Minimum_Resource_Allocation[Team_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum resources that must be allocated to each team"
      },
      "Maximum_Resource_Allocation[Team_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum resources that can be allocated to each team"
      }
    },
    "decision_variables": {
      "Resource_Allocation[Team_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "amount of resources allocated to each team",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total_Resources_Available",
    "Minimum_Resource_Allocation for each team",
    "Maximum_Resource_Allocation for each team"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data on resource constraints and refine the model with realistic bounds"
  }
}
