Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:52:22

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: bike_1

```sql
CREATE TABLE station (
  id NUMBER,
  name TEXT,
  lat NUMBER,
  long NUMBER,
  dock_count NUMBER,
  city TEXT,
  installation_date TEXT
);
```

```sql
CREATE TABLE status (
  station_id NUMBER,
  bikes_available NUMBER,
  docks_available NUMBER,
  time TEXT
);
```

```sql
CREATE TABLE trip (
  id NUMBER,
  duration NUMBER,
  start_date TEXT,
  start_station_name TEXT,
  start_station_id NUMBER,
  end_date TEXT,
  end_station_name TEXT,
  end_station_id NUMBER,
  bike_id NUMBER,
  subscription_type TEXT,
  zip_code NUMBER
);
```

```sql
CREATE TABLE weather (
  date TEXT,
  max_temperature_f NUMBER,
  mean_temperature_f NUMBER,
  min_temperature_f NUMBER,
  max_dew_point_f NUMBER,
  mean_dew_point_f NUMBER,
  min_dew_point_f NUMBER,
  max_humidity NUMBER,
  mean_humidity NUMBER,
  min_humidity NUMBER,
  max_sea_level_pressure_inches NUMBER,
  mean_sea_level_pressure_inches NUMBER,
  min_sea_level_pressure_inches NUMBER,
  max_visibility_miles NUMBER,
  mean_visibility_miles NUMBER,
  min_visibility_miles NUMBER,
  max_wind_Speed_mph NUMBER,
  mean_wind_speed_mph NUMBER,
  max_gust_speed_mph NUMBER,
  precipitation_inches NUMBER,
  cloud_cover NUMBER,
  events TEXT,
  wind_dir_degrees NUMBER,
  zip_code 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": "bike_1",
  "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": "bike_1",
  "iteration": 0,
  "business_context": "Optimize the allocation of bikes across stations to minimize the number of stations running out of bikes or docks at any given time.",
  "optimization_problem_description": "The goal is to determine the optimal number of bikes to allocate to each station at the start of the day to minimize the likelihood of stations running out of bikes or docks, considering current availability and expected demand.",
  "optimization_formulation": {
    "objective": "minimize \u2211(shortage_penalty[i] * shortage[i] + excess_penalty[i] * excess[i])",
    "decision_variables": "shortage[i]: number of bikes short at station i, excess[i]: number of excess bikes at station i",
    "constraints": [
      "\u2211(bikes_available[i] + shortage[i] - excess[i]) = total_bikes",
      "shortage[i] >= 0",
      "excess[i] >= 0",
      "bikes_available[i] + shortage[i] - excess[i] <= dock_count[i]",
      "bikes_available[i] + shortage[i] - excess[i] >= 0"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "shortage_penalty[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Penalty cost for each bike shortage at station i"
      },
      "excess_penalty[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Penalty cost for each excess bike at station i"
      }
    },
    "constraint_bounds": {
      "total_bikes": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total number of bikes available in the system"
      },
      "dock_count[i]": {
        "currently_mapped_to": "station.dock_count",
        "mapping_adequacy": "good",
        "description": "Maximum number of bikes that can be docked at station i"
      }
    },
    "decision_variables": {
      "shortage[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of bikes short at station i",
        "variable_type": "continuous"
      },
      "excess[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of excess bikes at station i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Penalty costs for shortages and excesses",
    "Total number of bikes available in the system",
    "Expected demand data for each station"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Determine penalty costs and gather expected demand data for each station"
  }
}
