Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:24:02

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: roller_coaster

```sql
CREATE TABLE roller_coaster (
  Roller_Coaster_ID NUMBER,
  Name TEXT,
  Park TEXT,
  Country_ID NUMBER,
  Length NUMBER,
  Height NUMBER,
  Speed TEXT,
  Opened TEXT,
  Status TEXT
);
```

```sql
CREATE TABLE country (
  Country_ID NUMBER,
  Name TEXT,
  Population NUMBER,
  Area NUMBER,
  Languages 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": "roller_coaster",
  "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": "roller_coaster",
  "iteration": 0,
  "business_context": "A theme park company wants to optimize the allocation of maintenance resources across its roller coasters to minimize downtime while ensuring safety standards are met. The company needs to decide how many maintenance hours to allocate to each roller coaster, considering constraints like maximum available maintenance hours and minimum safety requirements.",
  "optimization_problem_description": "The goal is to minimize the total downtime of roller coasters by optimally allocating maintenance hours. Each roller coaster has a specific maintenance requirement to ensure safety, and there is a limited number of maintenance hours available. The optimization will determine the number of maintenance hours allocated to each roller coaster to minimize downtime while meeting safety requirements.",
  "optimization_formulation": {
    "objective": "minimize total_downtime = \u2211(downtime_coefficient[i] \u00d7 maintenance_hours[i])",
    "decision_variables": "maintenance_hours[i] for each roller coaster, representing the number of maintenance hours allocated (continuous)",
    "constraints": [
      "\u2211(maintenance_hours[i]) \u2264 total_available_hours",
      "maintenance_hours[i] \u2265 minimum_required_hours[i] for each roller coaster",
      "maintenance_hours[i] \u2264 maximum_possible_hours[i] for each roller coaster"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "downtime_coefficient[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the impact of maintenance hours on reducing downtime for each roller coaster"
      }
    },
    "constraint_bounds": {
      "total_available_hours": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "total number of maintenance hours available across all roller coasters"
      },
      "minimum_required_hours[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum maintenance hours required for safety for each roller coaster"
      },
      "maximum_possible_hours[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum maintenance hours that can be allocated to each roller coaster"
      }
    },
    "decision_variables": {
      "maintenance_hours[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "number of maintenance hours allocated to each roller coaster",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Downtime coefficients for each roller coaster",
    "Total available maintenance hours",
    "Minimum required maintenance hours for each roller coaster",
    "Maximum possible maintenance hours for each roller coaster"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data for downtime coefficients and maintenance hour constraints"
  }
}
