Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:32:33

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: employee_hire_evaluation

```sql
CREATE TABLE employee (
  Employee_ID NUMBER,
  Name TEXT,
  Age NUMBER,
  City TEXT
);
```

```sql
CREATE TABLE shop (
  Shop_ID NUMBER,
  Name TEXT,
  Location TEXT,
  District TEXT,
  Number_products NUMBER,
  Manager_name TEXT
);
```

```sql
CREATE TABLE hiring (
  Shop_ID NUMBER,
  Employee_ID NUMBER,
  Start_from TEXT,
  Is_full_time OTHERS
);
```

```sql
CREATE TABLE evaluation (
  Employee_ID TEXT,
  Year_awarded TEXT,
  Bonus 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": "employee_hire_evaluation",
  "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": "employee_hire_evaluation",
  "iteration": 0,
  "business_context": "A retail company wants to optimize the allocation of employees to shops to maximize the total bonus awarded to employees while ensuring each shop has a minimum number of employees and each employee is assigned to exactly one shop.",
  "optimization_problem_description": "The goal is to maximize the total bonus awarded to employees by optimally assigning them to shops. Each shop requires a minimum number of employees, and each employee can only be assigned to one shop. The bonus for each employee is known from past evaluations.",
  "optimization_formulation": {
    "objective": "maximize \u2211(bonus[Employee_ID] \u00d7 x[Employee_ID, Shop_ID])",
    "decision_variables": "x[Employee_ID, Shop_ID] - binary variable indicating if Employee_ID is assigned to Shop_ID",
    "constraints": [
      "\u2211(x[Employee_ID, Shop_ID]) = 1 for each Employee_ID",
      "\u2211(x[Employee_ID, Shop_ID]) \u2265 min_employees for each Shop_ID",
      "x[Employee_ID, Shop_ID] \u2208 {0, 1} for all Employee_ID, Shop_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "bonus[Employee_ID]": {
        "currently_mapped_to": "evaluation.Bonus",
        "mapping_adequacy": "good",
        "description": "Bonus awarded to each employee based on past evaluations"
      }
    },
    "constraint_bounds": {
      "min_employees[Shop_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of employees required for each shop"
      }
    },
    "decision_variables": {
      "x[Employee_ID, Shop_ID]": {
        "currently_mapped_to": "hiring.Shop_ID and hiring.Employee_ID",
        "mapping_adequacy": "partial",
        "description": "Binary variable indicating if an employee is assigned to a shop",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Minimum number of employees required for each shop (min_employees)",
    "Binary decision variable mapping for employee-shop assignment"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping of decision variables and ensure all necessary data for constraints are available"
  }
}
