Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:29:24

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: machine_repair

```sql
CREATE TABLE repair (
  repair_ID NUMBER,
  name TEXT,
  Launch_Date TEXT,
  Notes TEXT
);
```

```sql
CREATE TABLE machine (
  Machine_ID NUMBER,
  Making_Year NUMBER,
  Class TEXT,
  Team TEXT,
  Machine_series TEXT,
  value_points NUMBER,
  quality_rank NUMBER
);
```

```sql
CREATE TABLE technician (
  technician_id NUMBER,
  Name TEXT,
  Team TEXT,
  Starting_Year NUMBER,
  Age NUMBER
);
```

```sql
CREATE TABLE repair_assignment (
  technician_id NUMBER,
  repair_ID NUMBER,
  Machine_ID 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": "machine_repair",
  "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": "machine_repair",
  "iteration": 0,
  "business_context": "A company wants to optimize the assignment of technicians to machine repairs to minimize the total value points of machines being repaired, ensuring that each repair is assigned to exactly one technician and each technician can handle a limited number of repairs.",
  "optimization_problem_description": "The goal is to minimize the total value points of machines assigned to technicians for repair, subject to constraints on technician availability and repair requirements.",
  "optimization_formulation": {
    "objective": "minimize sum(value_points[machine_id] * x[technician_id, repair_id])",
    "decision_variables": "x[technician_id, repair_id] - binary variable indicating if technician is assigned to repair",
    "constraints": [
      "sum(x[technician_id, repair_id] for technician_id) = 1 for each repair_id",
      "sum(x[technician_id, repair_id] for repair_id) <= max_repairs_per_technician for each technician_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "value_points[machine_id]": {
        "currently_mapped_to": "machine.value_points",
        "mapping_adequacy": "good",
        "description": "Represents the value points of the machine being repaired"
      }
    },
    "constraint_bounds": {
      "max_repairs_per_technician": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of repairs a technician can handle"
      }
    },
    "decision_variables": {
      "x[technician_id, repair_id]": {
        "currently_mapped_to": "repair_assignment.technician_id and repair_assignment.repair_ID",
        "mapping_adequacy": "partial",
        "description": "Binary variable indicating if a technician is assigned to a repair",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Maximum number of repairs a technician can handle (max_repairs_per_technician)"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Determine the maximum number of repairs each technician can handle and ensure all necessary data is available for constraints"
  }
}
