Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:33:14

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: inn_1

```sql
CREATE TABLE Rooms (
  RoomId TEXT,
  roomName TEXT,
  beds NUMBER,
  bedType TEXT,
  maxOccupancy NUMBER,
  basePrice NUMBER,
  decor TEXT
);
```

```sql
CREATE TABLE Reservations (
  Code NUMBER,
  Room TEXT,
  CheckIn TEXT,
  CheckOut TEXT,
  Rate NUMBER,
  LastName TEXT,
  FirstName TEXT,
  Adults NUMBER,
  Kids 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": "inn_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": "inn_1",
  "iteration": 0,
  "business_context": "Optimize room allocation to maximize revenue while respecting room capacities and reservation constraints.",
  "optimization_problem_description": "Maximize total revenue from room reservations by deciding which reservations to accept, ensuring that the number of guests does not exceed room capacities and that each room is not double-booked.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Rate \u00d7 AcceptReservation)",
    "decision_variables": "AcceptReservation[Code] (binary: 1 if reservation is accepted, 0 otherwise)",
    "constraints": [
      "\u2211(Adults[Code] + Kids[Code]) \u00d7 AcceptReservation[Code] \u2264 maxOccupancy[Room] for each Room",
      "\u2211(AcceptReservation[Code] where Room[Code] = Room) \u2264 1 for each Room and overlapping CheckIn/CheckOut dates"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Rate[Code]": {
        "currently_mapped_to": "Reservations.Rate",
        "mapping_adequacy": "good",
        "description": "Revenue generated from each reservation"
      }
    },
    "constraint_bounds": {
      "maxOccupancy[Room]": {
        "currently_mapped_to": "Rooms.maxOccupancy",
        "mapping_adequacy": "good",
        "description": "Maximum number of guests allowed in a room"
      }
    },
    "decision_variables": {
      "AcceptReservation[Code]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Decision to accept or reject a reservation",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "AcceptReservation decision variable",
    "Overlap detection logic for CheckIn/CheckOut dates"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define AcceptReservation variable and implement date overlap constraints"
  }
}
