Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 22:47:35

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain 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
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "business_context": "The inn wants to maximize its revenue by optimizing room pricing while considering occupancy constraints and room availability.",
  "optimization_problem": "Maximize the total revenue from room bookings by adjusting room rates, ensuring that the occupancy does not exceed the maximum capacity of each room and that all reservations are honored.",
  "objective": "maximize total_revenue = \u2211(Rate[Code] \u00d7 (CheckOut[Code] - CheckIn[Code]))",
  "table_count": 1,
  "key_changes": [
    "Schema changes include adding a new table for reservation durations and modifying existing tables to ensure all reservations are mapped to rooms. Configuration logic updated for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine the conversion of CheckIn and CheckOut dates to numerical values and ensure all reservations are valid",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a new table for reservation durations and modifying existing tables to ensure all reservations are mapped to rooms. Configuration logic updated for scalar parameters and formulas.

CREATE TABLE Reservations (
  ReservationId INTEGER,
  Rate FLOAT,
  RoomId INTEGER
);

CREATE TABLE ReservationDurations (
  ReservationId INTEGER,
  LengthOfStay INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Reservations": {
      "business_purpose": "Stores reservation details including rates and room assignments",
      "optimization_role": "decision_variables",
      "columns": {
        "ReservationId": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each reservation",
          "optimization_purpose": "Identifies reservation in optimization model",
          "sample_values": "1, 2, 3"
        },
        "Rate": {
          "data_type": "FLOAT",
          "business_meaning": "Rate charged for the reservation",
          "optimization_purpose": "Decision variable for revenue maximization",
          "sample_values": "120.0, 150.0, 200.0"
        },
        "RoomId": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the room assigned to the reservation",
          "optimization_purpose": "Ensures reservation is mapped to a room",
          "sample_values": "101, 102, 103"
        }
      }
    },
    "ReservationDurations": {
      "business_purpose": "Stores the calculated length of stay for each reservation",
      "optimization_role": "business_data",
      "columns": {
        "ReservationId": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each reservation",
          "optimization_purpose": "Links duration to reservation",
          "sample_values": "1, 2, 3"
        },
        "LengthOfStay": {
          "data_type": "INTEGER",
          "business_meaning": "Number of days for the reservation",
          "optimization_purpose": "Used in revenue calculation",
          "sample_values": "2, 3, 5"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "maxOccupancy": {
    "sample_value": "4",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of people that can occupy a room",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "basePrice": {
    "sample_value": "100.0",
    "data_type": "FLOAT",
    "business_meaning": "Minimum rate that can be charged for a room",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "lengthOfStay": {
    "formula_expression": "DATEDIFF(CheckOut, CheckIn)",
    "data_type": "STRING",
    "business_meaning": "Calculates the number of days for a reservation",
    "optimization_role": "Used in objective function to calculate revenue",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "inn_1",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 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 still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "inn_1",
  "iteration": 1,
  "business_context": "The inn aims to maximize its revenue by optimizing room pricing while ensuring that room occupancy does not exceed capacity and all reservations are honored.",
  "optimization_problem_description": "Maximize total revenue from room bookings by adjusting room rates, ensuring occupancy constraints and room availability are respected.",
  "optimization_formulation": {
    "objective": "maximize total_revenue = \u2211(Rate[ReservationId] \u00d7 LengthOfStay[ReservationId])",
    "decision_variables": {
      "Rate[ReservationId]": {
        "currently_mapped_to": "Reservations.Rate",
        "mapping_adequacy": "good",
        "description": "Rate charged for each reservation",
        "variable_type": "continuous"
      }
    },
    "constraints": {
      "maxOccupancy[RoomId]": {
        "currently_mapped_to": "business_configuration_logic.maxOccupancy",
        "mapping_adequacy": "good",
        "description": "Ensures room occupancy does not exceed maximum capacity"
      },
      "basePrice[ReservationId]": {
        "currently_mapped_to": "business_configuration_logic.basePrice",
        "mapping_adequacy": "good",
        "description": "Ensures rate does not fall below base price"
      }
    }
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Rate[ReservationId]": {
        "currently_mapped_to": "Reservations.Rate",
        "mapping_adequacy": "good",
        "description": "Rate charged for each reservation"
      },
      "LengthOfStay[ReservationId]": {
        "currently_mapped_to": "ReservationDurations.LengthOfStay",
        "mapping_adequacy": "good",
        "description": "Number of days for each reservation"
      }
    },
    "constraint_bounds": {
      "maxOccupancy": {
        "currently_mapped_to": "business_configuration_logic.maxOccupancy",
        "mapping_adequacy": "good",
        "description": "Maximum number of people that can occupy a room"
      },
      "basePrice": {
        "currently_mapped_to": "business_configuration_logic.basePrice",
        "mapping_adequacy": "good",
        "description": "Minimum rate that can be charged for a room"
      }
    },
    "decision_variables": {
      "Rate[ReservationId]": {
        "currently_mapped_to": "Reservations.Rate",
        "mapping_adequacy": "good",
        "description": "Rate charged for each reservation",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
