Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-25 22:31:11

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: resource_allocation[PetID] (continuous)
- Operational parameters align with expected linear objective: minimize ∑(cost_per_pet_type[PetType] × resource_allocation[PetID])
- Business configuration includes: Minimum resource allocation per pet (used for Lower bound for decision variables), Maximum resource allocation per pet (used for Upper bound for decision variables)
- 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 aims to optimize the allocation of pet care resources to students based on their pets' needs and the students' demographics. The goal is to minimize the total cost of pet care while ensuring that each pet receives adequate care based on its type, age, and weight, and that the total resources do not exceed the available budget and weight capacity.",
  "optimization_problem_description": "The optimization problem aims to minimize the total cost of pet care by allocating resources efficiently. The decision variables represent the amount of resources allocated to each pet. Constraints ensure that each pet receives a minimum level of care based on its type, age, and weight, and that the total resources do not exceed the available budget and weight capacity.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_per_pet_type[PetType] \u00d7 resource_allocation[PetID])",
    "decision_variables": "resource_allocation[PetID] (continuous)",
    "constraints": [
      "resource_allocation[PetID] \u2265 min_care[PetType]",
      "resource_allocation[PetID] \u2264 max_care[PetType]",
      "\u2211(resource_allocation[PetID]) \u2264 max_resource_allocation",
      "resource_allocation[PetID] \u2265 min_resource_allocation"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_pet_type[PetType]": {
        "currently_mapped_to": "pet_type_costs.cost",
        "mapping_adequacy": "good",
        "description": "Cost associated with caring for each pet type"
      }
    },
    "constraint_bounds": {
      "min_care[PetType]": {
        "currently_mapped_to": "pet_care_requirements.min_care",
        "mapping_adequacy": "good",
        "description": "Minimum care requirement for each pet type"
      },
      "max_care[PetType]": {
        "currently_mapped_to": "pet_care_requirements.max_care",
        "mapping_adequacy": "good",
        "description": "Maximum care requirement for each pet type"
      },
      "max_resource_allocation": {
        "currently_mapped_to": "business_configuration_logic.max_resource_allocation",
        "mapping_adequacy": "good",
        "description": "Maximum total resource allocation"
      },
      "min_resource_allocation": {
        "currently_mapped_to": "business_configuration_logic.min_resource_allocation",
        "mapping_adequacy": "good",
        "description": "Minimum resource allocation per pet"
      }
    },
    "decision_variables": {
      "resource_allocation[PetID]": {
        "currently_mapped_to": "resource_allocation.amount",
        "mapping_adequacy": "good",
        "description": "Amount of resources allocated to each pet",
        "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: Added resource_allocation table to map decision variables, updated business configuration logic with new scalar parameters, and ensured all mappings align with OR expert's requirements.

CREATE TABLE pet_type_costs (
  pet_type STRING,
  cost FLOAT
);

CREATE TABLE pet_care_requirements (
  pet_type STRING,
  min_care FLOAT,
  max_care FLOAT
);

CREATE TABLE resource_allocation (
  pet_id STRING,
  amount FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic pet care costs, care requirements, and resource allocation limits, ensuring that the optimization problem remains meaningful and solvable.

-- Realistic data for pet_type_costs
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('dog', 50.0);
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('cat', 30.0);
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('bird', 20.0);

-- Realistic data for pet_care_requirements
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('dog', 10.0, 100.0);
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('cat', 5.0, 50.0);
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('bird', 3.0, 30.0);

-- Realistic data for resource_allocation
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet1', 50.0);
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet2', 30.0);
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet3', 20.0);


```

DATA DICTIONARY:
{
  "tables": {
    "pet_type_costs": {
      "business_purpose": "Cost associated with caring for each pet type",
      "optimization_role": "objective_coefficients",
      "columns": {
        "pet_type": {
          "data_type": "STRING",
          "business_meaning": "Type of pet",
          "optimization_purpose": "Index for cost coefficient",
          "sample_values": [
            "dog",
            "cat",
            "bird"
          ]
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost per pet type",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": [
            50.0,
            30.0,
            20.0
          ]
        }
      }
    },
    "pet_care_requirements": {
      "business_purpose": "Minimum and maximum care requirements for each pet type",
      "optimization_role": "constraint_bounds",
      "columns": {
        "pet_type": {
          "data_type": "STRING",
          "business_meaning": "Type of pet",
          "optimization_purpose": "Index for care requirements",
          "sample_values": [
            "dog",
            "cat",
            "bird"
          ]
        },
        "min_care": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum care requirement",
          "optimization_purpose": "Lower bound in constraints",
          "sample_values": [
            10.0,
            5.0,
            3.0
          ]
        },
        "max_care": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum care requirement",
          "optimization_purpose": "Upper bound in constraints",
          "sample_values": [
            100.0,
            50.0,
            30.0
          ]
        }
      }
    },
    "resource_allocation": {
      "business_purpose": "Amount of resources allocated to each pet",
      "optimization_role": "decision_variables",
      "columns": {
        "pet_id": {
          "data_type": "STRING",
          "business_meaning": "Unique identifier for each pet",
          "optimization_purpose": "Index for decision variables",
          "sample_values": [
            "pet1",
            "pet2",
            "pet3"
          ]
        },
        "amount": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of resources allocated",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": [
            50.0,
            30.0,
            20.0
          ]
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "min_resource_allocation": {
    "data_type": "FLOAT",
    "business_meaning": "Minimum resource allocation per pet",
    "optimization_role": "Lower bound for decision variables",
    "configuration_type": "scalar_parameter",
    "value": 0.0,
    "business_justification": "Ensures that no pet is allocated negative resources, which is not feasible."
  },
  "max_resource_allocation": {
    "data_type": "FLOAT",
    "business_meaning": "Maximum resource allocation per pet",
    "optimization_role": "Upper bound for decision variables",
    "configuration_type": "scalar_parameter",
    "value": 500.0,
    "business_justification": "Reflects the university's budget constraints and ensures that resource allocation does not exceed available funds."
  }
}

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: resource_allocation[PetID] (continuous)
- Operational parameters align with expected linear objective: minimize ∑(cost_per_pet_type[PetType] × resource_allocation[PetID])
- Business configuration includes: Minimum resource allocation per pet (used for Lower bound for decision variables), Maximum resource allocation per pet (used for Upper bound for decision variables)
- 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 ∑(cost_per_pet_type[PetType] × resource_allocation[PetID])
- 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: ['resource_allocation[PetID] ≥ min_care[PetType]', 'resource_allocation[PetID] ≤ max_care[PetType]', '∑(resource_allocation[PetID]) ≤ max_resource_allocation', 'resource_allocation[PetID] ≥ min_resource_allocation'] (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: Added resource_allocation table to map decision variables, updated business configuration logic with new scalar parameters, and ensured all mappings align with OR expert's requirements.

CREATE TABLE pet_type_costs (
  pet_type STRING,
  cost FLOAT
);

CREATE TABLE pet_care_requirements (
  pet_type STRING,
  min_care FLOAT,
  max_care FLOAT
);

CREATE TABLE resource_allocation (
  pet_id STRING,
  amount 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 realistic pet care costs, care requirements, and resource allocation limits, ensuring that the optimization problem remains meaningful and solvable.

-- Realistic data for pet_type_costs
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('dog', 50.0);
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('cat', 30.0);
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('bird', 20.0);

-- Realistic data for pet_care_requirements
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('dog', 10.0, 100.0);
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('cat', 5.0, 50.0);
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('bird', 3.0, 30.0);

-- Realistic data for resource_allocation
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet1', 50.0);
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet2', 30.0);
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet3', 20.0);


```

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 tasked with efficiently allocating pet care resources to students based on their pets' needs and the students' demographics. The primary business decision involves determining the amount of resources to allocate to each pet, represented as a continuous variable. The operational parameters are designed to minimize the total cost of pet care, which is calculated by multiplying the cost associated with each pet type by the resources allocated to each pet. 

The business configuration includes two critical scalar parameters: the minimum resource allocation per pet, ensuring that no pet receives negative resources, and the maximum resource allocation per pet, which reflects the university's budget constraints. These parameters serve as lower and upper bounds for the decision variables, respectively. The optimization problem is designed to ensure that each pet receives adequate care based on its type, age, and weight, while the total resources allocated do not exceed the available budget and weight capacity.

### Goals  
The optimization goal is to minimize the total cost of pet care. This is achieved by efficiently allocating resources to each pet, ensuring that the sum of the costs associated with each pet type multiplied by the resources allocated to each pet is as low as possible. Success is measured by achieving the lowest possible total cost while adhering to the constraints on resource allocation and care requirements.

## 2. Constraints    

The optimization problem is subject to several constraints that ensure the allocation of resources is both feasible and adequate. Each pet must receive a minimum level of care based on its type, ensuring that no pet is neglected. Additionally, the resources allocated to each pet must not exceed the maximum care requirement for its type, preventing over-allocation. 

The total resources allocated across all pets must not exceed the university's maximum resource allocation limit, ensuring that the budget is not exceeded. Finally, each pet must receive at least the minimum resource allocation, ensuring that no pet is allocated negative resources. These constraints are designed to maintain a balance between adequate care and budget limitations.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Added resource_allocation table to map decision variables, updated business configuration logic with new scalar parameters, and ensured all mappings align with OR expert's requirements.

CREATE TABLE pet_type_costs (
  pet_type STRING,
  cost FLOAT
);

CREATE TABLE pet_care_requirements (
  pet_type STRING,
  min_care FLOAT,
  max_care FLOAT
);

CREATE TABLE resource_allocation (
  pet_id STRING,
  amount FLOAT
);


```

### Data Dictionary  
- **pet_type_costs**: This table contains the cost associated with caring for each pet type. The `pet_type` column identifies the type of pet, and the `cost` column represents the cost per pet type, which is used as a coefficient in the objective function.
  
- **pet_care_requirements**: This table defines the minimum and maximum care requirements for each pet type. The `pet_type` column identifies the type of pet, while the `min_care` and `max_care` columns represent the lower and upper bounds for resource allocation, respectively.
  
- **resource_allocation**: This table tracks the amount of resources allocated to each pet. The `pet_id` column uniquely identifies each pet, and the `amount` column represents the decision variable in the optimization problem, indicating the resources allocated to each pet.

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic pet care costs, care requirements, and resource allocation limits, ensuring that the optimization problem remains meaningful and solvable.

-- Realistic data for pet_type_costs
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('dog', 50.0);
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('cat', 30.0);
INSERT INTO pet_type_costs (pet_type, cost) VALUES ('bird', 20.0);

-- Realistic data for pet_care_requirements
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('dog', 10.0, 100.0);
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('cat', 5.0, 50.0);
INSERT INTO pet_care_requirements (pet_type, min_care, max_care) VALUES ('bird', 3.0, 30.0);

-- Realistic data for resource_allocation
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet1', 50.0);
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet2', 30.0);
INSERT INTO resource_allocation (pet_id, amount) VALUES ('pet3', 20.0);


```
