Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:31:02

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "A company aims to optimize the allocation of office spaces across multiple buildings to minimize the total leasing cost while ensuring each company's space requirements are met based on their sales and assets.",
  "optimization_problem": "The objective is to minimize the total leasing cost of office spaces across different buildings. The decision variables represent the amount of space allocated to each company in each building. Constraints ensure that each company's space requirements are met, the total space in each building is not exceeded, and the allocation is non-negative.",
  "objective": "minimize \u2211(cost_per_sqft[building_id] \u00d7 space_allocated[building_id, company_id])",
  "table_count": 1,
  "key_changes": [
    "Added space_allocated table to map decision variables, updated business configuration logic with scalar parameters and formulas, and ensured schema follows normalization principles."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map the decision variable space_allocated[building_id, company_id] to complete the linear optimization formulation.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Added space_allocated table to map decision variables, updated business configuration logic with scalar parameters and formulas, and ensured schema follows normalization principles.

CREATE TABLE cost_per_sqft (
  building_id INTEGER,
  cost_per_sqft FLOAT
);

CREATE TABLE required_space (
  company_id INTEGER,
  required_space INTEGER
);

CREATE TABLE available_space (
  building_id INTEGER,
  available_space INTEGER
);

CREATE TABLE space_allocated (
  building_id INTEGER,
  company_id INTEGER,
  space_allocated FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "cost_per_sqft": {
      "business_purpose": "Cost per square foot for leasing space in each building",
      "optimization_role": "objective_coefficients",
      "columns": {
        "building_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each building",
          "optimization_purpose": "Index for cost_per_sqft",
          "sample_values": "1, 2, 3"
        },
        "cost_per_sqft": {
          "data_type": "FLOAT",
          "business_meaning": "Cost per square foot for leasing space in the building",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "50.0, 60.0, 70.0"
        }
      }
    },
    "required_space": {
      "business_purpose": "Minimum space required by each company based on sales and assets",
      "optimization_role": "constraint_bounds",
      "columns": {
        "company_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each company",
          "optimization_purpose": "Index for required_space",
          "sample_values": "1, 2, 3"
        },
        "required_space": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum space required by the company",
          "optimization_purpose": "Bound in the constraints",
          "sample_values": "1000, 1500, 2000"
        }
      }
    },
    "available_space": {
      "business_purpose": "Total available space in each building",
      "optimization_role": "constraint_bounds",
      "columns": {
        "building_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each building",
          "optimization_purpose": "Index for available_space",
          "sample_values": "1, 2, 3"
        },
        "available_space": {
          "data_type": "INTEGER",
          "business_meaning": "Total available space in the building",
          "optimization_purpose": "Bound in the constraints",
          "sample_values": "5000, 6000, 7000"
        }
      }
    },
    "space_allocated": {
      "business_purpose": "Amount of space allocated to each company in each building",
      "optimization_role": "decision_variables",
      "columns": {
        "building_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each building",
          "optimization_purpose": "Index for space allocation",
          "sample_values": "1, 2, 3"
        },
        "company_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each company",
          "optimization_purpose": "Index for space allocation",
          "sample_values": "1, 2, 3"
        },
        "space_allocated": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of space allocated to the company in the building",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": "500.0, 600.0, 700.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "cost_per_sqft": {
    "sample_value": 50.0,
    "data_type": "FLOAT",
    "business_meaning": "Cost per square foot for leasing space in each building",
    "optimization_role": "Used in the objective function to minimize total leasing cost",
    "configuration_type": "scalar_parameter"
  },
  "required_space": {
    "sample_value": 1000,
    "data_type": "INTEGER",
    "business_meaning": "Minimum space required by each company based on sales and assets",
    "optimization_role": "Used in constraints to ensure each company's space requirements are met",
    "configuration_type": "scalar_parameter"
  },
  "available_space": {
    "sample_value": 5000,
    "data_type": "INTEGER",
    "business_meaning": "Total available space in each building",
    "optimization_role": "Used in constraints to ensure the total space in each building is not exceeded",
    "configuration_type": "scalar_parameter"
  },
  "total_leasing_cost_formula": {
    "formula_expression": "sum(cost_per_sqft[building_id] * space_allocated[building_id, company_id])",
    "data_type": "STRING",
    "business_meaning": "Total leasing cost calculation",
    "optimization_role": "Objective function to minimize total leasing cost",
    "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": "company_office",
  "iteration": 2,
  "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": "company_office",
  "iteration": 2,
  "business_context": "A company aims to optimize the allocation of office spaces across multiple buildings to minimize the total leasing cost while ensuring each company's space requirements are met based on their sales and assets.",
  "optimization_problem_description": "The objective is to minimize the total leasing cost of office spaces across different buildings. The decision variables represent the amount of space allocated to each company in each building. Constraints ensure that each company's space requirements are met, the total space in each building is not exceeded, and the allocation is non-negative.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_per_sqft[building_id] \u00d7 space_allocated[building_id, company_id])",
    "decision_variables": "space_allocated[building_id, company_id] (continuous)",
    "constraints": [
      "\u2211(space_allocated[building_id, company_id]) \u2265 required_space[company_id] for each company_id",
      "\u2211(space_allocated[building_id, company_id]) \u2264 available_space[building_id] for each building_id",
      "space_allocated[building_id, company_id] \u2265 0 for each building_id and company_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_sqft[building_id]": {
        "currently_mapped_to": "cost_per_sqft.cost_per_sqft",
        "mapping_adequacy": "good",
        "description": "Cost per square foot for leasing space in each building"
      }
    },
    "constraint_bounds": {
      "required_space[company_id]": {
        "currently_mapped_to": "required_space.required_space",
        "mapping_adequacy": "good",
        "description": "Minimum space required by each company"
      },
      "available_space[building_id]": {
        "currently_mapped_to": "available_space.available_space",
        "mapping_adequacy": "good",
        "description": "Total available space in each building"
      }
    },
    "decision_variables": {
      "space_allocated[building_id, company_id]": {
        "currently_mapped_to": "space_allocated.space_allocated",
        "mapping_adequacy": "good",
        "description": "Amount of space allocated to each company in each building",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
