# Complete Optimization Problem and Solution: insurance_policies

## 1. Problem Context and Goals

### Context  
An insurance company is focused on optimizing its resource allocation to efficiently settle claims. The primary decision involves determining the amount to be settled for each claim, denoted as Amount_Settled[i], where i represents each individual claim. The company's operational objective is to minimize the total payouts across all claims. This is achieved by ensuring that the total amount settled is as low as possible while adhering to the constraints of the maximum claimable amount and the necessity to settle claims within a specified time frame. The business configuration includes a critical parameter: the maximum allowable time period for settling a claim, which is used as a constraint to ensure timely settlements. This parameter is set at 30 days, aligning with industry standards to balance efficient processing and customer satisfaction. The data presented reflects current operational information, focusing on precise decision-making that naturally leads to a linear optimization formulation. Resource limitations are expressed through linear constraints, avoiding any scenarios that would require nonlinear relationships.

### Goals  
The primary goal of the optimization process is to minimize the total amount paid out in claim settlements. This involves strategically determining the settlement amount for each claim to ensure the total payouts are minimized. Success in this optimization is measured by the reduction in total settlement costs, aligning with the company's financial objectives. The goal is articulated in natural language, emphasizing the linear nature of the optimization task without resorting to mathematical symbols or equations.

## 2. Constraints    

The optimization process is governed by two main constraints that align with linear mathematical forms:

- The amount settled for each claim must not exceed the maximum amount claimed. This ensures that settlements are fair and within the agreed-upon limits.
- Each claim must be settled within a maximum period of 30 days from the date it was received. This constraint ensures that the company adheres to industry standards for timely claim processing, enhancing customer satisfaction and operational efficiency.

These constraints are described in business terms that naturally lead to linear mathematical expressions, avoiding any need for variable products or divisions.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Added Date_Claim_Received column to Claims table to address missing data requirement for settlement period calculation. Updated business configuration logic for max_settlement_period.

CREATE TABLE Claims (
  Amount_Settled FLOAT,
  Amount_Claimed FLOAT,
  Date_Claim_Settled DATE,
  Date_Claim_Received DATE
);


```

### Data Dictionary  
The Claims table serves as the central repository for information related to insurance claims and their settlements. Each column within the table has a specific business purpose and role in the optimization process:

- **Amount_Settled**: Represents the amount settled for each claim. It plays a crucial role in the objective function, where the goal is to minimize the total payouts.
- **Amount_Claimed**: Indicates the maximum amount that can be settled for each claim. This serves as a constraint bound, ensuring settlements do not exceed the claimed amounts.
- **Date_Claim_Settled**: The date on which the claim was settled. It is used to ensure that claims are settled within the allowed period, contributing to the timely processing constraint.
- **Date_Claim_Received**: The date on which the claim was received. This information is essential for calculating the settlement period constraint, ensuring compliance with the maximum allowable time frame.

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical insurance claim scenarios, ensuring that the amounts settled are realistic and within the claimed amounts, and that settlement periods are within the configured maximum period.

-- Realistic data for Claims
INSERT INTO Claims (Amount_Settled, Amount_Claimed, Date_Claim_Settled, Date_Claim_Received) VALUES (1000.0, 1200.0, 2023-01-15, 2023-01-01);
INSERT INTO Claims (Amount_Settled, Amount_Claimed, Date_Claim_Settled, Date_Claim_Received) VALUES (1500.0, 1600.0, 2023-02-20, 2023-02-01);
INSERT INTO Claims (Amount_Settled, Amount_Claimed, Date_Claim_Settled, Date_Claim_Received) VALUES (2000.0, 2500.0, 2023-03-10, 2023-03-01);


```