Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-27 22:15:01

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 2), 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: {'students_assigned[i]': 'integer', 'pet_weight_assigned[i]': 'continuous'}
- Operational parameters align with expected linear objective: minimize max_workload = max(sum(students_assigned[i] + pet_weight_assigned[i] for each advisor i))
- Business configuration includes: Coefficient for the workload of advisor in the objective function (used for Used in the objective function to calculate workload)
- 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": "pets_1",
  "iteration": 2,
  "business_context": "A university is optimizing the allocation of student advisors to students with pets, ensuring balanced workloads in terms of student numbers and total pet weight. The goal is to minimize the maximum workload across all advisors.",
  "optimization_problem_description": "Minimize the maximum workload of any advisor, where workload is a linear combination of the number of students and total pet weight assigned to each advisor. Each student is assigned to exactly one advisor, and each advisor has limits on the number of students and total pet weight they can handle.",
  "optimization_formulation": {
    "objective": "minimize max_workload = max(sum(students_assigned[i] + pet_weight_assigned[i] for each advisor i))",
    "decision_variables": {
      "students_assigned[i]": "integer",
      "pet_weight_assigned[i]": "continuous"
    },
    "constraints": {
      "sum(students_assigned[i]) <= MaxStudents[i]": "for each advisor i",
      "sum(pet_weight_assigned[i]) <= MaxWeight[i]": "for each advisor i",
      "sum(students_assigned[i]) = 1": "for each student"
    }
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "workload_coefficient": {
        "currently_mapped_to": "business_configuration_logic.workload_coefficient",
        "mapping_adequacy": "good",
        "description": "Coefficient for the workload of advisor in the objective function"
      }
    },
    "constraint_bounds": {
      "MaxStudents[i]": {
        "currently_mapped_to": "AdvisorConstraints.MaxStudents",
        "mapping_adequacy": "good",
        "description": "Maximum number of students an advisor can handle"
      },
      "MaxWeight[i]": {
        "currently_mapped_to": "AdvisorConstraints.MaxWeight",
        "mapping_adequacy": "good",
        "description": "Maximum total pet weight an advisor can handle"
      }
    },
    "decision_variables": {
      "students_assigned[i]": {
        "currently_mapped_to": "Has_Pet.StuID",
        "mapping_adequacy": "good",
        "description": "Number of students assigned to advisor i",
        "variable_type": "integer"
      },
      "pet_weight_assigned[i]": {
        "currently_mapped_to": "PetWeightAssignment.TotalPetWeight",
        "mapping_adequacy": "good",
        "description": "Total pet weight assigned to advisor i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Has_Pet (
  StuID INTEGER,
  PetID INTEGER,
  AdvisorID INTEGER
);

CREATE TABLE AdvisorConstraints (
  AdvisorID INTEGER,
  MaxStudents INTEGER,
  MaxWeight FLOAT
);

CREATE TABLE PetWeightAssignment (
  AdvisorID INTEGER,
  TotalPetWeight FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical university advisor workloads and average pet weights, ensuring that constraints are neither too tight nor too loose, allowing for a balanced distribution of students and pets.

-- Realistic data for Has_Pet
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (1, 101, 201);
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (2, 102, 202);
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (3, 103, 203);

-- Realistic data for AdvisorConstraints
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (201, 5, 100.0);
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (202, 6, 120.0);
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (203, 7, 150.0);

-- Realistic data for PetWeightAssignment
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (201, 50.0);
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (202, 60.0);
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (203, 70.0);


```

DATA DICTIONARY:
{
  "tables": {
    "Has_Pet": {
      "business_purpose": "Maps students to their pets and advisors",
      "optimization_role": "decision_variables",
      "columns": {
        "StuID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each student",
          "optimization_purpose": "Used to assign students to advisors",
          "sample_values": "1, 2, 3"
        },
        "PetID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each pet",
          "optimization_purpose": "Links pets to students",
          "sample_values": "101, 102, 103"
        },
        "AdvisorID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each advisor",
          "optimization_purpose": "Used to assign students to advisors",
          "sample_values": "201, 202, 203"
        }
      }
    },
    "AdvisorConstraints": {
      "business_purpose": "Stores constraints for advisors",
      "optimization_role": "constraint_bounds",
      "columns": {
        "AdvisorID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each advisor",
          "optimization_purpose": "Links constraints to advisors",
          "sample_values": "201, 202, 203"
        },
        "MaxStudents": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of students an advisor can handle",
          "optimization_purpose": "Constraint for optimization",
          "sample_values": "5, 6, 7"
        },
        "MaxWeight": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum total pet weight an advisor can handle",
          "optimization_purpose": "Constraint for optimization",
          "sample_values": "100.0, 120.0, 150.0"
        }
      }
    },
    "PetWeightAssignment": {
      "business_purpose": "Stores the total weight of pets assigned to each advisor",
      "optimization_role": "decision_variables",
      "columns": {
        "AdvisorID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each advisor",
          "optimization_purpose": "Links pet weight to advisors",
          "sample_values": "201, 202, 203"
        },
        "TotalPetWeight": {
          "data_type": "FLOAT",
          "business_meaning": "Total weight of pets assigned to an advisor",
          "optimization_purpose": "Used to calculate advisor workload",
          "sample_values": "50.0, 60.0, 70.0"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "workload_coefficient": {
    "data_type": "FLOAT",
    "business_meaning": "Coefficient for the workload of advisor in the objective function",
    "optimization_role": "Used in the objective function to calculate workload",
    "configuration_type": "scalar_parameter",
    "value": 1.0,
    "business_justification": "A coefficient of 1.0 ensures that both student numbers and pet weights are equally considered in workload calculations."
  }
}

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: pets_1

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: {'students_assigned[i]': 'integer', 'pet_weight_assigned[i]': 'continuous'}
- Operational parameters align with expected linear objective: minimize max_workload = max(sum(students_assigned[i] + pet_weight_assigned[i] for each advisor i))
- Business configuration includes: Coefficient for the workload of advisor in the objective function (used for Used in the objective function to calculate workload)
- 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 max_workload = max(sum(students_assigned[i] + pet_weight_assigned[i] for each advisor 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: {'sum(students_assigned[i]) <= MaxStudents[i]': 'for each advisor i', 'sum(pet_weight_assigned[i]) <= MaxWeight[i]': 'for each advisor i', 'sum(students_assigned[i]) = 1': 'for each student'} (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 2 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Has_Pet (
  StuID INTEGER,
  PetID INTEGER,
  AdvisorID INTEGER
);

CREATE TABLE AdvisorConstraints (
  AdvisorID INTEGER,
  MaxStudents INTEGER,
  MaxWeight FLOAT
);

CREATE TABLE PetWeightAssignment (
  AdvisorID INTEGER,
  TotalPetWeight FLOAT
);


```

### 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 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical university advisor workloads and average pet weights, ensuring that constraints are neither too tight nor too loose, allowing for a balanced distribution of students and pets.

-- Realistic data for Has_Pet
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (1, 101, 201);
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (2, 102, 202);
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (3, 103, 203);

-- Realistic data for AdvisorConstraints
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (201, 5, 100.0);
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (202, 6, 120.0);
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (203, 7, 150.0);

-- Realistic data for PetWeightAssignment
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (201, 50.0);
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (202, 60.0);
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (203, 70.0);


```

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

Response:
# Complete Optimization Problem and Solution: pets_1

## 1. Problem Context and Goals

### Context  
The university is focused on optimizing the allocation of student advisors to students who own pets. The primary aim is to ensure that each advisor's workload is balanced, considering both the number of students and the total weight of pets assigned to them. The decision-making process involves assigning students to advisors, where the number of students assigned is an integer value, and the total pet weight assigned is a continuous value. The operational goal is to minimize the maximum workload of any advisor, which is determined by the sum of the number of students and the total pet weight assigned to each advisor. The business configuration includes a workload coefficient, set at 1.0, which ensures that both student numbers and pet weights are equally considered in workload calculations. This setup allows for precise operational decision-making that aligns with linear optimization formulations, avoiding any nonlinear relationships such as variable products or divisions. The constraints are based on the maximum number of students and total pet weight each advisor can handle, ensuring resource limitations are respected.

### Goals  
The optimization goal is to minimize the maximum workload of any advisor. This involves reducing the highest sum of students and pet weight assigned to any single advisor. Success in this optimization is measured by achieving a balanced distribution of workloads across all advisors, ensuring no advisor is overburdened. The linear optimization goal is clearly defined by focusing on minimizing the maximum workload, which is a straightforward linear objective.

## 2. Constraints    

The constraints for this optimization problem are designed to ensure that each advisor's workload remains within manageable limits. Specifically, the constraints include:

- Each advisor can handle a maximum number of students, which is defined by the advisor's capacity.
- Each advisor can also handle a maximum total pet weight, ensuring that the pet weight assigned does not exceed this limit.
- Each student must be assigned to exactly one advisor, ensuring that all students are accounted for in the allocation process.

These constraints are expressed in business terms that naturally lead to linear mathematical forms, ensuring that the optimization problem remains linear and manageable.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data, modifying existing tables to improve mapping adequacy, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Has_Pet (
  StuID INTEGER,
  PetID INTEGER,
  AdvisorID INTEGER
);

CREATE TABLE AdvisorConstraints (
  AdvisorID INTEGER,
  MaxStudents INTEGER,
  MaxWeight FLOAT
);

CREATE TABLE PetWeightAssignment (
  AdvisorID INTEGER,
  TotalPetWeight FLOAT
);
```

### Data Dictionary  
The data dictionary provides a comprehensive mapping of tables and columns to their business purposes and optimization roles:

- **Has_Pet**: This table maps students to their pets and advisors. It plays a crucial role in decision variables, where each student (StuID) is uniquely identified and linked to their respective pet (PetID) and advisor (AdvisorID).

- **AdvisorConstraints**: This table stores the constraints for each advisor, detailing the maximum number of students (MaxStudents) and the maximum total pet weight (MaxWeight) that each advisor can handle. These constraints are critical for ensuring that the optimization respects the resource limitations of each advisor.

- **PetWeightAssignment**: This table records the total weight of pets assigned to each advisor. It is used to calculate the advisor's workload, ensuring that the total pet weight assigned does not exceed the advisor's capacity.

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical university advisor workloads and average pet weights, ensuring that constraints are neither too tight nor too loose, allowing for a balanced distribution of students and pets.

-- Realistic data for Has_Pet
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (1, 101, 201);
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (2, 102, 202);
INSERT INTO Has_Pet (StuID, PetID, AdvisorID) VALUES (3, 103, 203);

-- Realistic data for AdvisorConstraints
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (201, 5, 100.0);
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (202, 6, 120.0);
INSERT INTO AdvisorConstraints (AdvisorID, MaxStudents, MaxWeight) VALUES (203, 7, 150.0);

-- Realistic data for PetWeightAssignment
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (201, 50.0);
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (202, 60.0);
INSERT INTO PetWeightAssignment (AdvisorID, TotalPetWeight) VALUES (203, 70.0);
```
