Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-28 00:07:10

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: wrestler

```sql
CREATE TABLE wrestler (
  Wrestler_ID NUMBER,
  Name TEXT,
  Reign TEXT,
  Days_held TEXT,
  Location TEXT,
  Event TEXT
);
```

```sql
CREATE TABLE Elimination (
  Elimination_ID TEXT,
  Wrestler_ID TEXT,
  Team TEXT,
  Eliminated_By TEXT,
  Elimination_Move TEXT,
  Time 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": "wrestler",
  "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": "wrestler",
  "iteration": 0,
  "business_context": "Optimize the assignment of wrestlers to events to maximize the total number of days titles are held, considering constraints on wrestler participation and event scheduling.",
  "optimization_problem_description": "The goal is to maximize the total number of days titles are held by assigning wrestlers to events, ensuring that each wrestler can only participate in a limited number of events and that each event has a limited number of participants.",
  "optimization_formulation": {
    "objective": "maximize total_days_held = \u2211(days_held_coefficient[i] * x[i])",
    "decision_variables": "x[i] is a binary variable indicating whether wrestler i is assigned to an event",
    "constraints": [
      "\u2211(x[i]) \u2264 max_events_per_wrestler for each wrestler i",
      "\u2211(x[i]) \u2264 max_participants_per_event for each event",
      "x[i] \u2208 {0, 1} for each wrestler i and event"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "days_held_coefficient[i]": {
        "currently_mapped_to": "wrestler.Days_held",
        "mapping_adequacy": "good",
        "description": "Number of days a title is held by wrestler i"
      }
    },
    "constraint_bounds": {
      "max_events_per_wrestler": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of events a wrestler can participate in"
      },
      "max_participants_per_event": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of participants allowed per event"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if wrestler i is assigned to an event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Data on maximum number of events a wrestler can participate in",
    "Data on maximum number of participants allowed per event",
    "Mapping of wrestlers to specific events"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping of decision variables and constraints to existing schema or business logic"
  }
}
