Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-28 00:09:12

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: customer_complaints

```sql
CREATE TABLE Staff (
  staff_id NUMBER,
  gender TEXT,
  first_name TEXT,
  last_name TEXT,
  email_address TEXT,
  phone_number TEXT
);
```

```sql
CREATE TABLE Customers (
  customer_id NUMBER,
  customer_type_code TEXT,
  address_line_1 TEXT,
  address_line_2 TEXT,
  town_city TEXT,
  state TEXT,
  email_address TEXT,
  phone_number TEXT
);
```

```sql
CREATE TABLE Products (
  product_id NUMBER,
  parent_product_id NUMBER,
  product_category_code TEXT,
  date_product_first_available TIME,
  date_product_discontinued TIME,
  product_name TEXT,
  product_description TEXT,
  product_price NUMBER
);
```

```sql
CREATE TABLE Complaints (
  complaint_id NUMBER,
  product_id NUMBER,
  customer_id NUMBER,
  complaint_outcome_code TEXT,
  complaint_status_code TEXT,
  complaint_type_code TEXT,
  date_complaint_raised TIME,
  date_complaint_closed TIME,
  staff_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": "customer_complaints",
  "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": "customer_complaints",
  "iteration": 0,
  "business_context": "The business aims to optimize the allocation of staff to handle customer complaints efficiently, minimizing the total time taken to resolve complaints while ensuring each complaint is addressed by a staff member.",
  "optimization_problem_description": "The goal is to minimize the total time taken to resolve all complaints by optimally assigning staff to complaints. Each staff member can handle a certain number of complaints, and each complaint has a specific resolution time. The objective is to minimize the sum of resolution times across all complaints.",
  "optimization_formulation": {
    "objective": "minimize total_resolution_time = sum(resolution_time[i] * x[i]) for all complaints i",
    "decision_variables": "x[i] = 1 if complaint i is assigned to a staff member, 0 otherwise (binary)",
    "constraints": [
      "sum(x[i] for all i assigned to staff j) <= max_complaints_per_staff[j] for all staff j",
      "sum(x[i] for all staff j) = 1 for all complaints i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "resolution_time[i]": {
        "currently_mapped_to": "Complaints.date_complaint_closed - Complaints.date_complaint_raised",
        "mapping_adequacy": "partial",
        "description": "Represents the time taken to resolve complaint i"
      }
    },
    "constraint_bounds": {
      "max_complaints_per_staff[j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of complaints staff j can handle"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "Complaints.complaint_id",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if complaint i is assigned to a staff member",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Maximum number of complaints each staff member can handle",
    "Resolution time for each complaint"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine mapping of resolution times and determine staff capacity constraints"
  }
}
