Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 21:57:27

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: climbing

```sql
CREATE TABLE mountain (
  Mountain_ID NUMBER,
  Name TEXT,
  Height NUMBER,
  Prominence NUMBER,
  Range TEXT,
  Country TEXT
);
```

```sql
CREATE TABLE climber (
  Climber_ID NUMBER,
  Name TEXT,
  Country TEXT,
  Time TEXT,
  Points NUMBER,
  Mountain_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": "climbing",
  "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": "climbing",
  "iteration": 0,
  "business_context": "A climbing competition organizer wants to allocate climbers to mountains in a way that maximizes the total points scored by climbers, while ensuring that each mountain is climbed by at least one climber and each climber is assigned to exactly one mountain.",
  "optimization_problem_description": "Optimize the assignment of climbers to mountains to maximize the total points scored, subject to constraints on climber assignments and mountain requirements.",
  "optimization_formulation": {
    "objective": "maximize total_points = \u2211(Points[i] * x[i,j])",
    "decision_variables": "x[i,j] = 1 if climber i is assigned to mountain j, 0 otherwise (binary)",
    "constraints": [
      "\u2211(x[i,j]) = 1 for each climber i (each climber is assigned to exactly one mountain)",
      "\u2211(x[i,j]) \u2265 1 for each mountain j (each mountain is climbed by at least one climber)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Points[i]": {
        "currently_mapped_to": "climber.Points",
        "mapping_adequacy": "good",
        "description": "Points scored by climber i"
      }
    },
    "constraint_bounds": {
      "climber_assignment[i]": {
        "currently_mapped_to": "climber.Climber_ID",
        "mapping_adequacy": "good",
        "description": "Ensures each climber is assigned to exactly one mountain"
      },
      "mountain_requirement[j]": {
        "currently_mapped_to": "mountain.Mountain_ID",
        "mapping_adequacy": "good",
        "description": "Ensures each mountain is climbed by at least one climber"
      }
    },
    "decision_variables": {
      "x[i,j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if climber i is assigned to mountain j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Binary decision variable x[i,j] to represent assignment of climbers to mountains"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and integrate binary decision variables for climber assignments"
  }
}
