Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:31:13

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: insurance_policies

```sql
CREATE TABLE Customers (
  Customer_ID NUMBER,
  Customer_Details TEXT
);
```

```sql
CREATE TABLE Customer_Policies (
  Policy_ID NUMBER,
  Customer_ID NUMBER,
  Policy_Type_Code TEXT,
  Start_Date TIME,
  End_Date TIME
);
```

```sql
CREATE TABLE Claims (
  Claim_ID NUMBER,
  Policy_ID NUMBER,
  Date_Claim_Made TIME,
  Date_Claim_Settled TIME,
  Amount_Claimed NUMBER,
  Amount_Settled NUMBER
);
```

```sql
CREATE TABLE Settlements (
  Settlement_ID NUMBER,
  Claim_ID NUMBER,
  Date_Claim_Made TIME,
  Date_Claim_Settled TIME,
  Amount_Claimed NUMBER,
  Amount_Settled NUMBER,
  Customer_Policy_ID NUMBER
);
```

```sql
CREATE TABLE Payments (
  Payment_ID NUMBER,
  Settlement_ID NUMBER,
  Payment_Method_Code TEXT,
  Date_Payment_Made TIME,
  Amount_Payment 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": "insurance_policies",
  "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": "insurance_policies",
  "iteration": 0,
  "business_context": "The insurance company aims to minimize the total cost of settling claims while ensuring that the settlement amounts are fair and within budget constraints. The company wants to optimize the allocation of settlement amounts across claims to minimize the total payout.",
  "optimization_problem_description": "The optimization problem involves minimizing the total amount settled across all claims, subject to constraints on the maximum amount that can be settled per claim, the total budget available for settlements, and ensuring that the settlement amount is at least a minimum percentage of the claimed amount.",
  "optimization_formulation": {
    "objective": "minimize \u2211(Amount_Settled)",
    "decision_variables": "Amount_Settled (continuous)",
    "constraints": [
      "Amount_Settled \u2264 Amount_Claimed for each claim",
      "Amount_Settled \u2265 0.5 * Amount_Claimed for each claim",
      "\u2211(Amount_Settled) \u2264 Total_Budget",
      "Amount_Settled \u2264 Maximum_Settlement_Per_Claim for each claim"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Amount_Settled[Claim_ID]": {
        "currently_mapped_to": "Settlements.Amount_Settled",
        "mapping_adequacy": "good",
        "description": "The amount settled for each claim"
      }
    },
    "constraint_bounds": {
      "Amount_Claimed[Claim_ID]": {
        "currently_mapped_to": "Claims.Amount_Claimed",
        "mapping_adequacy": "good",
        "description": "The maximum amount that can be settled for each claim"
      },
      "Total_Budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The total budget available for settlements"
      },
      "Maximum_Settlement_Per_Claim[Claim_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum amount that can be settled per claim"
      }
    },
    "decision_variables": {
      "Amount_Settled[Claim_ID]": {
        "currently_mapped_to": "Settlements.Amount_Settled",
        "mapping_adequacy": "good",
        "description": "The amount settled for each claim",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total_Budget",
    "Maximum_Settlement_Per_Claim"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define the total budget and maximum settlement per claim parameters for complete optimization model"
  }
}
