Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:36:07

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 chain aims to optimize employee hiring and allocation across shops to minimize total hiring costs while ensuring each shop has sufficient staff and employees are fairly evaluated based on their bonuses.",
  "optimization_problem_description": "The objective is to minimize the total hiring costs by deciding the number of full-time and part-time employees to hire for each shop, ensuring that each shop meets its staffing requirements and that employees receive bonuses based on their evaluations.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_full_time \u00d7 x_full_time[Shop_ID] + cost_part_time \u00d7 x_part_time[Shop_ID])",
    "decision_variables": {
      "x_full_time[Shop_ID]": "Number of full-time employees to hire for each shop (integer)",
      "x_part_time[Shop_ID]": "Number of part-time employees to hire for each shop (integer)"
    },
    "constraints": [
      "x_full_time[Shop_ID] + x_part_time[Shop_ID] \u2265 min_staff[Shop_ID] for each shop",
      "x_full_time[Shop_ID] \u2264 max_full_time[Shop_ID] for each shop",
      "x_part_time[Shop_ID] \u2264 max_part_time[Shop_ID] for each shop",
      "\u2211(bonus[Employee_ID] \u00d7 y[Employee_ID]) \u2264 total_bonus_budget",
      "y[Employee_ID] \u2264 1 for each employee (binary decision to award bonus)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_full_time": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Cost of hiring a full-time employee"
      },
      "cost_part_time": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Cost of hiring a part-time employee"
      }
    },
    "constraint_bounds": {
      "min_staff[Shop_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum staff required for each shop"
      },
      "max_full_time[Shop_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum full-time employees allowed for each shop"
      },
      "max_part_time[Shop_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum part-time employees allowed for each shop"
      },
      "total_bonus_budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total budget allocated for employee bonuses"
      }
    },
    "decision_variables": {
      "x_full_time[Shop_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of full-time employees to hire for each shop",
        "variable_type": "integer"
      },
      "x_part_time[Shop_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of part-time employees to hire for each shop",
        "variable_type": "integer"
      },
      "y[Employee_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision to award bonus to an employee",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Cost of hiring full-time and part-time employees",
    "Minimum staff required for each shop",
    "Maximum full-time and part-time employees allowed for each shop",
    "Total budget allocated for employee bonuses"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map the missing coefficients and constraints to the schema or business configuration logic."
  }
}
