Iteration final - PROBLEM_DESCRIPTION
Sequence: 9
Timestamp: 2025-07-25 22:30:52

Prompt:
You are a business analyst creating structured optimization problem documentation.

DATA SOURCES EXPLANATION:
- FINAL OR ANALYSIS: Final converged optimization problem from alternating process (iteration 3), contains business context and schema mapping evaluation
- DATABASE SCHEMA: Current database structure after iterative adjustments  
- DATA DICTIONARY: Business meanings and optimization roles of tables and columns
- CURRENT STORED VALUES: Realistic business data generated by triple expert (business + data + optimization)
- BUSINESS CONFIGURATION: Scalar parameters and business logic formulas separated from table data

CRITICAL REQUIREMENTS: 
- Ensure problem description naturally leads to LINEAR or MIXED-INTEGER optimization formulation
- Make business context consistent with the intended decision variables and objectives
- Align constraint descriptions with expected mathematical constraints
- Ensure data descriptions map clearly to expected coefficient sources
- Maintain business authenticity while fixing mathematical consistency issues
- Avoid business scenarios that would naturally require nonlinear relationships (variable products, divisions, etc.)

AUTO-EXTRACTED CONTEXT REQUIREMENTS:
- Business decisions match expected decision variables: resources_allocated[i] (continuous)
- Operational parameters align with expected linear objective: minimize ∑(killed[i] + injured[i])
- Business configuration includes: Total number of resources available (used for Constraint bound for total resources), Maximum allowed casualties per location (used for Constraint bound for casualties per location)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate

FINAL OR ANALYSIS:
{
  "database_id": "perpetrator",
  "iteration": 3,
  "business_context": "A security agency aims to minimize the total number of casualties (killed and injured) by optimally allocating resources to monitor and prevent incidents in different locations. The agency has a limited number of resources and must ensure that the allocation does not exceed the maximum allowed casualties per location.",
  "optimization_problem_description": "The agency wants to minimize the total casualties (sum of killed and injured) by deciding how many resources to allocate to each location. The resources are limited, and each location has a different impact on reducing casualties based on historical data. The problem is formulated as a linear optimization problem with constraints on total resources and maximum allowed casualties per location.",
  "optimization_formulation": {
    "objective": "minimize \u2211(killed[i] + injured[i])",
    "decision_variables": "resources_allocated[i] (continuous)",
    "constraints": "\u2211resources_allocated[i] \u2264 total_resources, killed[i] + injured[i] \u2264 max_casualties[i]"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "killed[i]": {
        "currently_mapped_to": "Casualties.killed",
        "mapping_adequacy": "good",
        "description": "Number of killed in the location"
      },
      "injured[i]": {
        "currently_mapped_to": "Casualties.injured",
        "mapping_adequacy": "good",
        "description": "Number of injured in the location"
      }
    },
    "constraint_bounds": {
      "total_resources": {
        "currently_mapped_to": "business_configuration_logic.total_resources",
        "mapping_adequacy": "good",
        "description": "Total number of resources available"
      },
      "max_casualties[i]": {
        "currently_mapped_to": "business_configuration_logic.max_casualties",
        "mapping_adequacy": "good",
        "description": "Maximum allowed casualties per location"
      }
    },
    "decision_variables": {
      "resources_allocated[i]": {
        "currently_mapped_to": "ResourceAllocation.resources_allocated",
        "mapping_adequacy": "good",
        "description": "Number of resources allocated to the location",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 3 Database Schema
-- Objective: Added missing scalar parameters to business configuration logic, ensured schema follows normalization principles, and updated data dictionary to reflect changes.

CREATE TABLE ResourceAllocation (
  location_id INTEGER,
  resources_allocated FLOAT
);

CREATE TABLE Casualties (
  location_id INTEGER,
  killed INTEGER,
  injured INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on historical data and realistic scenarios for a security agency, ensuring that the optimization problem remains meaningful and solvable.

-- Realistic data for ResourceAllocation
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (1, 20.0);
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (2, 15.0);
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (3, 10.0);

-- Realistic data for Casualties
INSERT INTO Casualties (location_id, killed, injured) VALUES (1, 5, 25);
INSERT INTO Casualties (location_id, killed, injured) VALUES (2, 3, 15);
INSERT INTO Casualties (location_id, killed, injured) VALUES (3, 1, 10);


```

DATA DICTIONARY:
{
  "tables": {
    "ResourceAllocation": {
      "business_purpose": "Number of resources allocated to each location",
      "optimization_role": "decision_variables",
      "columns": {
        "location_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each location",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "resources_allocated": {
          "data_type": "FLOAT",
          "business_meaning": "Number of resources allocated to the location",
          "optimization_purpose": "Decision variable x[i]",
          "sample_values": "5.0, 10.0, 15.0"
        }
      }
    },
    "Casualties": {
      "business_purpose": "Number of killed and injured per location",
      "optimization_role": "objective_coefficients",
      "columns": {
        "location_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each location",
          "optimization_purpose": "Index for objective coefficients",
          "sample_values": "1, 2, 3"
        },
        "killed": {
          "data_type": "INTEGER",
          "business_meaning": "Number of killed in the location",
          "optimization_purpose": "Objective coefficient for killed",
          "sample_values": "2, 5, 8"
        },
        "injured": {
          "data_type": "INTEGER",
          "business_meaning": "Number of injured in the location",
          "optimization_purpose": "Objective coefficient for injured",
          "sample_values": "10, 15, 20"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "total_resources": {
    "data_type": "INTEGER",
    "business_meaning": "Total number of resources available",
    "optimization_role": "Constraint bound for total resources",
    "configuration_type": "scalar_parameter",
    "value": 45,
    "business_justification": "Total resources are limited to ensure optimal allocation across locations"
  },
  "max_casualties": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum allowed casualties per location",
    "optimization_role": "Constraint bound for casualties per location",
    "configuration_type": "scalar_parameter",
    "value": 30,
    "business_justification": "Maximum allowed casualties per location to ensure safety and minimize risk"
  }
}

Business Configuration Design: 
Our system separates business logic design from value determination:
- Configuration Logic (business_configuration_logic.json): Templates designed by data engineers with sample_value for scalars and actual formulas for business logic
- Configuration Values (business_configuration.json): Realistic values determined by domain experts for scalar parameters only
- Design Rationale: Ensures business logic consistency while allowing flexible parameter tuning


TASK: Create structured markdown documentation for SECTIONS 1-3 ONLY (Problem Description).

EXACT MARKDOWN STRUCTURE TO FOLLOW:

# Complete Optimization Problem and Solution: perpetrator

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: resources_allocated[i] (continuous)
- Operational parameters align with expected linear objective: minimize ∑(killed[i] + injured[i])
- Business configuration includes: Total number of resources available (used for Constraint bound for total resources), Maximum allowed casualties per location (used for Constraint bound for casualties per location)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate
- CRITICAL: Include ALL business configuration information (scalar parameters AND business logic formulas) in natural business language

### Goals  
[Regenerate goals that clearly lead to LINEAR mathematical objective:]
- Optimization goal: minimize
- Metric to optimize: minimize ∑(killed[i] + injured[i])
- Success measurement aligned with expected coefficient sources
- Use natural language to precisely describe linear optimization goal
- NO mathematical formulas, equations, or symbolic notation

## 2. Constraints    

[Regenerate constraints that directly match expected LINEAR mathematical constraints:]
- Expected constraint: ∑resources_allocated[i] ≤ total_resources, killed[i] + injured[i] ≤ max_casualties[i] (Form: Standard constraint form based on business requirements)

[Each constraint should be described in business terms that naturally lead to LINEAR mathematical forms (no variable products or divisions)]

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 3 Database Schema
-- Objective: Added missing scalar parameters to business configuration logic, ensured schema follows normalization principles, and updated data dictionary to reflect changes.

CREATE TABLE ResourceAllocation (
  location_id INTEGER,
  resources_allocated FLOAT
);

CREATE TABLE Casualties (
  location_id INTEGER,
  killed INTEGER,
  injured INTEGER
);


```

### Data Dictionary  
[Create comprehensive business-oriented data dictionary mapping tables and columns to their business purposes and optimization roles - NOT technical database terms. Base this on the data_dictionary provided but rewrite in business language that clearly connects to the expected linear mathematical formulation]

### Current Stored Values  
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on historical data and realistic scenarios for a security agency, ensuring that the optimization problem remains meaningful and solvable.

-- Realistic data for ResourceAllocation
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (1, 20.0);
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (2, 15.0);
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (3, 10.0);

-- Realistic data for Casualties
INSERT INTO Casualties (location_id, killed, injured) VALUES (1, 5, 25);
INSERT INTO Casualties (location_id, killed, injured) VALUES (2, 3, 15);
INSERT INTO Casualties (location_id, killed, injured) VALUES (3, 1, 10);


```

STOP HERE - Do not include section 4 (Mathematical Optimization Formulation).

Response:
# Complete Optimization Problem and Solution: perpetrator

## 1. Problem Context and Goals

### Context  
A security agency is tasked with minimizing the total number of casualties (both killed and injured) across various locations by strategically allocating its limited resources. The agency must decide how many resources to assign to each location to effectively monitor and prevent incidents. Historical data indicates that the allocation of resources directly impacts the reduction of casualties in each location. The agency operates under two critical operational constraints:  
1. The total number of resources available for allocation is fixed and cannot be exceeded.  
2. Each location has a maximum allowable number of casualties, which must not be surpassed.  

The agency’s decision-making process focuses on determining the optimal number of resources to allocate to each location, ensuring that the total resources used do not exceed the available capacity and that the casualties in each location remain within the predefined safety limits. This problem is inherently linear, as the relationships between resource allocation, casualties, and constraints are proportional and additive, without any nonlinear interactions such as variable products or divisions.

### Goals  
The primary goal of the agency is to minimize the total number of casualties across all locations. This is achieved by optimizing the allocation of resources to each location, ensuring that the sum of killed and injured individuals is as low as possible. Success is measured by the reduction in casualties, which is directly influenced by the effective distribution of resources. The agency aims to achieve this goal while adhering to the operational constraints of total resource availability and maximum allowable casualties per location.

## 2. Constraints  

The agency’s optimization problem is subject to the following constraints:  
1. **Total Resource Constraint**: The sum of resources allocated to all locations must not exceed the total number of resources available. This ensures that the agency does not overcommit its limited resources.  
2. **Maximum Casualties Constraint**: For each location, the sum of killed and injured individuals must not exceed the maximum allowed casualties. This ensures that safety thresholds are maintained in every location.  

These constraints are linear and proportional, ensuring that the optimization problem remains straightforward and solvable using linear methods.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 3 Database Schema
-- Objective: Added missing scalar parameters to business configuration logic, ensured schema follows normalization principles, and updated data dictionary to reflect changes.

CREATE TABLE ResourceAllocation (
  location_id INTEGER,
  resources_allocated FLOAT
);

CREATE TABLE Casualties (
  location_id INTEGER,
  killed INTEGER,
  injured INTEGER
);
```

### Data Dictionary  
- **ResourceAllocation Table**:  
  - **location_id**: A unique identifier for each location where resources are allocated.  
  - **resources_allocated**: The number of resources assigned to a specific location. This is the decision variable in the optimization problem.  

- **Casualties Table**:  
  - **location_id**: A unique identifier for each location where casualties are recorded.  
  - **killed**: The number of individuals killed in a specific location. This is a coefficient in the optimization objective.  
  - **injured**: The number of individuals injured in a specific location. This is a coefficient in the optimization objective.  

### Current Stored Values  
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on historical data and realistic scenarios for a security agency, ensuring that the optimization problem remains meaningful and solvable.

-- Realistic data for ResourceAllocation
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (1, 20.0);
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (2, 15.0);
INSERT INTO ResourceAllocation (location_id, resources_allocated) VALUES (3, 10.0);

-- Realistic data for Casualties
INSERT INTO Casualties (location_id, killed, injured) VALUES (1, 5, 25);
INSERT INTO Casualties (location_id, killed, injured) VALUES (2, 3, 15);
INSERT INTO Casualties (location_id, killed, injured) VALUES (3, 1, 10);
```
