Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:19:12

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: real_estate_properties

```sql
CREATE TABLE Ref_Feature_Types (
  feature_type_code TEXT,
  feature_type_name TEXT
);
```

```sql
CREATE TABLE Ref_Property_Types (
  property_type_code TEXT,
  property_type_description TEXT
);
```

```sql
CREATE TABLE Other_Available_Features (
  feature_id NUMBER,
  feature_type_code TEXT,
  feature_name TEXT,
  feature_description TEXT
);
```

```sql
CREATE TABLE Properties (
  property_id NUMBER,
  property_type_code TEXT,
  date_on_market TIME,
  date_sold TIME,
  property_name TEXT,
  property_address TEXT,
  room_count NUMBER,
  vendor_requested_price NUMBER,
  buyer_offered_price NUMBER,
  agreed_selling_price NUMBER,
  apt_feature_1 TEXT,
  apt_feature_2 TEXT,
  apt_feature_3 TEXT,
  fld_feature_1 TEXT,
  fld_feature_2 TEXT,
  fld_feature_3 TEXT,
  hse_feature_1 TEXT,
  hse_feature_2 TEXT,
  hse_feature_3 TEXT,
  oth_feature_1 TEXT,
  oth_feature_2 TEXT,
  oth_feature_3 TEXT,
  shp_feature_1 TEXT,
  shp_feature_2 TEXT,
  shp_feature_3 TEXT,
  other_property_details TEXT
);
```

```sql
CREATE TABLE Other_Property_Features (
  property_id NUMBER,
  feature_id NUMBER,
  property_feature_description 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": "real_estate_properties",
  "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": "real_estate_properties",
  "iteration": 0,
  "business_context": "A real estate company wants to maximize its profit from selling properties by optimizing the selection of properties to sell based on their features and market demand.",
  "optimization_problem_description": "The goal is to maximize the total profit from selling properties. The profit is defined as the difference between the agreed selling price and the vendor requested price. The decision variables are which properties to sell, considering constraints such as the number of properties that can be sold, the types of properties, and specific features that are in demand.",
  "optimization_formulation": {
    "objective": "maximize total_profit = sum((agreed_selling_price[i] - vendor_requested_price[i]) * x[i])",
    "decision_variables": "x[i] = 1 if property i is selected to be sold, 0 otherwise (binary)",
    "constraints": [
      "sum(x[i]) <= max_properties_to_sell",
      "sum(room_count[i] * x[i]) <= max_total_rooms",
      "sum((apt_feature_1[i] == 'desired_feature') * x[i]) >= min_desired_features"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "agreed_selling_price[i]": {
        "currently_mapped_to": "Properties.agreed_selling_price",
        "mapping_adequacy": "good",
        "description": "The agreed selling price of property i"
      },
      "vendor_requested_price[i]": {
        "currently_mapped_to": "Properties.vendor_requested_price",
        "mapping_adequacy": "good",
        "description": "The vendor requested price of property i"
      }
    },
    "constraint_bounds": {
      "max_properties_to_sell": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum number of properties that can be sold"
      },
      "max_total_rooms": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum total number of rooms across all selected properties"
      },
      "min_desired_features": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The minimum number of properties with a desired feature"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating if property i is selected to be sold",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "max_properties_to_sell",
    "max_total_rooms",
    "min_desired_features",
    "Binary decision variable mapping for x[i]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine constraints and ensure all necessary data for decision variables and bounds are available"
  }
}
