Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:02:51

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: company_office

```sql
CREATE TABLE buildings (
  id NUMBER,
  name TEXT,
  City TEXT,
  Height NUMBER,
  Stories NUMBER,
  Status TEXT
);
```

```sql
CREATE TABLE Companies (
  id NUMBER,
  name TEXT,
  Headquarters TEXT,
  Industry TEXT,
  Sales_billion NUMBER,
  Profits_billion NUMBER,
  Assets_billion NUMBER,
  Market_Value_billion TEXT
);
```

```sql
CREATE TABLE Office_locations (
  building_id NUMBER,
  company_id NUMBER,
  move_in_year 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": "company_office",
  "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": "company_office",
  "iteration": 0,
  "business_context": "A company wants to optimize the allocation of its office spaces across different buildings to maximize its market value while considering constraints like available stories in buildings and the company's sales performance.",
  "optimization_problem_description": "The goal is to maximize the total market value of companies by optimally allocating office spaces in various buildings, subject to constraints on the number of stories available in each building and the sales performance of each company.",
  "optimization_formulation": {
    "objective": "maximize total_market_value = \u2211(market_value_coefficient[i] * x[i])",
    "decision_variables": "x[i] represents the allocation of office space to company i in a specific building, integer",
    "constraints": [
      "\u2211(x[i]) <= Stories[b] for each building b",
      "\u2211(Sales_billion[i] * x[i]) >= minimum_sales_requirement",
      "x[i] >= 0 for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "market_value_coefficient[i]": {
        "currently_mapped_to": "Companies.Market_Value_billion",
        "mapping_adequacy": "good",
        "description": "Represents the market value contribution of company i"
      }
    },
    "constraint_bounds": {
      "Stories[b]": {
        "currently_mapped_to": "buildings.Stories",
        "mapping_adequacy": "good",
        "description": "Represents the maximum number of stories available in building b"
      },
      "minimum_sales_requirement": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Represents the minimum total sales required for the allocation"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "Office_locations.building_id, Office_locations.company_id",
        "mapping_adequacy": "partial",
        "description": "Represents the allocation of office space to company i in a specific building",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Minimum sales requirement parameter",
    "Specific mapping of decision variables to represent allocation"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping of decision variables and ensure all necessary parameters are available"
  }
}
