Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-27 23:59:07

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 1), 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: units_produced[i] for each phone model i, where i is an integer
- Operational parameters align with expected linear objective: maximize total_profit = sum(profit_per_unit[i] * units_produced[i]) for all i
- Business configuration includes: Total available RAM for production (used for Constraint bound for RAM usage), Total available ROM for production (used for Constraint bound for ROM usage), Total available screen resources for production (used for Constraint bound for screen usage)
- 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": "phone_1",
  "iteration": 1,
  "business_context": "A mobile phone company aims to optimize the production of different phone models to maximize profit while considering constraints such as available RAM, ROM, and screen resources.",
  "optimization_problem_description": "The company needs to decide how many units of each phone model to produce in order to maximize profit. Each phone model requires specific amounts of RAM, ROM, and screen resources, and there are limits on the total available resources. The objective is to maximize the total profit from selling the phones.",
  "optimization_formulation": {
    "objective": "maximize total_profit = sum(profit_per_unit[i] * units_produced[i]) for all i",
    "decision_variables": "units_produced[i] for each phone model i, where i is an integer",
    "constraints": [
      "sum(RAM_required[i] * units_produced[i]) <= total_RAM_available",
      "sum(ROM_required[i] * units_produced[i]) <= total_ROM_available",
      "sum(screen_required[i] * units_produced[i]) <= total_screen_available"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "profit_per_unit[i]": {
        "currently_mapped_to": "ObjectiveCoefficients.profit_per_unit",
        "mapping_adequacy": "good",
        "description": "Profit earned per unit of phone model i"
      }
    },
    "constraint_bounds": {
      "total_RAM_available": {
        "currently_mapped_to": "business_configuration_logic.total_RAM_available",
        "mapping_adequacy": "good",
        "description": "Total available RAM for production"
      },
      "total_ROM_available": {
        "currently_mapped_to": "business_configuration_logic.total_ROM_available",
        "mapping_adequacy": "good",
        "description": "Total available ROM for production"
      },
      "total_screen_available": {
        "currently_mapped_to": "business_configuration_logic.total_screen_available",
        "mapping_adequacy": "good",
        "description": "Total available screen resources for production"
      }
    },
    "decision_variables": {
      "units_produced[i]": {
        "currently_mapped_to": "DecisionVariables.units_produced",
        "mapping_adequacy": "good",
        "description": "Number of units produced for phone model i",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables, objective coefficients, and constraint bounds, and moving scalar parameters to configuration logic. This addresses the OR expert's mapping gaps and missing data requirements.

CREATE TABLE PhoneModels (
  model_id INTEGER,
  RAM_required INTEGER,
  ROM_required INTEGER,
  screen_required INTEGER
);

CREATE TABLE ObjectiveCoefficients (
  model_id INTEGER,
  profit_per_unit FLOAT
);

CREATE TABLE DecisionVariables (
  model_id INTEGER,
  units_produced INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical resource requirements and profit margins for different phone models, ensuring that the total available resources are sufficient to produce a meaningful number of units for each model.

-- Realistic data for PhoneModels
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (1, 4, 16, 1);
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (2, 8, 32, 2);
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (3, 16, 64, 3);

-- Realistic data for ObjectiveCoefficients
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (1, 50.0);
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (2, 75.0);
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (3, 100.0);

-- Realistic data for DecisionVariables
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (1, 2000);
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (2, 1000);
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (3, 500);


```

DATA DICTIONARY:
{
  "tables": {
    "PhoneModels": {
      "business_purpose": "Details of each phone model including resource requirements and profit",
      "optimization_role": "business_data",
      "columns": {
        "model_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each phone model",
          "optimization_purpose": "Reference for decision variables and coefficients",
          "sample_values": "1, 2, 3"
        },
        "RAM_required": {
          "data_type": "INTEGER",
          "business_meaning": "RAM required per unit of phone model",
          "optimization_purpose": "Used in RAM constraint calculation",
          "sample_values": "4, 8, 16"
        },
        "ROM_required": {
          "data_type": "INTEGER",
          "business_meaning": "ROM required per unit of phone model",
          "optimization_purpose": "Used in ROM constraint calculation",
          "sample_values": "16, 32, 64"
        },
        "screen_required": {
          "data_type": "INTEGER",
          "business_meaning": "Screen resources required per unit of phone model",
          "optimization_purpose": "Used in screen constraint calculation",
          "sample_values": "1, 2, 3"
        }
      }
    },
    "ObjectiveCoefficients": {
      "business_purpose": "Profit per unit for each phone model",
      "optimization_role": "objective_coefficients",
      "columns": {
        "model_id": {
          "data_type": "INTEGER",
          "business_meaning": "Reference to phone model",
          "optimization_purpose": "Links profit to specific phone model",
          "sample_values": "1, 2, 3"
        },
        "profit_per_unit": {
          "data_type": "FLOAT",
          "business_meaning": "Profit earned per unit of phone model",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "50.0, 75.0, 100.0"
        }
      }
    },
    "DecisionVariables": {
      "business_purpose": "Number of units produced for each phone model",
      "optimization_role": "decision_variables",
      "columns": {
        "model_id": {
          "data_type": "INTEGER",
          "business_meaning": "Reference to phone model",
          "optimization_purpose": "Links production units to specific phone model",
          "sample_values": "1, 2, 3"
        },
        "units_produced": {
          "data_type": "INTEGER",
          "business_meaning": "Number of units produced for phone model",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "100, 200, 300"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "total_RAM_available": {
    "data_type": "INTEGER",
    "business_meaning": "Total available RAM for production",
    "optimization_role": "Constraint bound for RAM usage",
    "configuration_type": "scalar_parameter",
    "value": 16000,
    "business_justification": "Reflects the total RAM capacity available for production, allowing for a balanced production of all models."
  },
  "total_ROM_available": {
    "data_type": "INTEGER",
    "business_meaning": "Total available ROM for production",
    "optimization_role": "Constraint bound for ROM usage",
    "configuration_type": "scalar_parameter",
    "value": 32000,
    "business_justification": "Reflects the total ROM capacity available for production, ensuring sufficient resources for all models."
  },
  "total_screen_available": {
    "data_type": "INTEGER",
    "business_meaning": "Total available screen resources for production",
    "optimization_role": "Constraint bound for screen usage",
    "configuration_type": "scalar_parameter",
    "value": 10000,
    "business_justification": "Reflects the total screen resources available, allowing for a feasible production plan."
  }
}

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: phone_1

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: units_produced[i] for each phone model i, where i is an integer
- Operational parameters align with expected linear objective: maximize total_profit = sum(profit_per_unit[i] * units_produced[i]) for all i
- Business configuration includes: Total available RAM for production (used for Constraint bound for RAM usage), Total available ROM for production (used for Constraint bound for ROM usage), Total available screen resources for production (used for Constraint bound for screen usage)
- 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: maximize
- Metric to optimize: maximize total_profit = sum(profit_per_unit[i] * units_produced[i]) for all 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(RAM_required[i] * units_produced[i]) <= total_RAM_available', 'sum(ROM_required[i] * units_produced[i]) <= total_ROM_available', 'sum(screen_required[i] * units_produced[i]) <= total_screen_available'] (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 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables, objective coefficients, and constraint bounds, and moving scalar parameters to configuration logic. This addresses the OR expert's mapping gaps and missing data requirements.

CREATE TABLE PhoneModels (
  model_id INTEGER,
  RAM_required INTEGER,
  ROM_required INTEGER,
  screen_required INTEGER
);

CREATE TABLE ObjectiveCoefficients (
  model_id INTEGER,
  profit_per_unit FLOAT
);

CREATE TABLE DecisionVariables (
  model_id INTEGER,
  units_produced 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 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical resource requirements and profit margins for different phone models, ensuring that the total available resources are sufficient to produce a meaningful number of units for each model.

-- Realistic data for PhoneModels
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (1, 4, 16, 1);
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (2, 8, 32, 2);
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (3, 16, 64, 3);

-- Realistic data for ObjectiveCoefficients
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (1, 50.0);
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (2, 75.0);
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (3, 100.0);

-- Realistic data for DecisionVariables
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (1, 2000);
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (2, 1000);
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (3, 500);


```

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

Response:
# Complete Optimization Problem and Solution: phone_1

## 1. Problem Context and Goals

### Context  
A mobile phone company is focused on optimizing the production of its various phone models to achieve maximum profitability. The decision at hand involves determining the number of units to produce for each phone model, denoted as `units_produced[i]`, where `i` represents each distinct phone model. The primary objective is to maximize the total profit, which is calculated as the sum of the profit per unit for each model multiplied by the number of units produced for that model.

The company operates under specific resource constraints, which include the total available RAM, ROM, and screen resources. These constraints are critical as they define the maximum capacity for production. The total available RAM, ROM, and screen resources are scalar parameters that guide the production limits. The business configuration includes:

- Total available RAM for production, which serves as the constraint bound for RAM usage.
- Total available ROM for production, which serves as the constraint bound for ROM usage.
- Total available screen resources for production, which serves as the constraint bound for screen usage.

The operational parameters are aligned with a linear objective, ensuring that the decision-making process is straightforward and adheres to linear relationships. The focus is on precise operational decision-making that leads to linear formulations, avoiding any scenarios that would require nonlinear relationships such as variable products or divisions. The business configuration parameters are referenced appropriately to ensure a consistent and realistic production plan.

### Goals  
The primary goal of the optimization process is to maximize the total profit from the production of mobile phone models. This involves determining the optimal number of units to produce for each model to achieve the highest possible profit. The metric to optimize is the total profit, which is calculated as the sum of the profit per unit for each phone model multiplied by the number of units produced for that model. Success is measured by the alignment of production decisions with the expected profit coefficients, ensuring that the optimization goal is clearly defined and achievable within the given resource constraints.

## 2. Constraints    

The production process is subject to several constraints that ensure the efficient use of available resources. These constraints are described in business terms that naturally lead to linear mathematical forms:

- The total RAM required for the production of all phone models must not exceed the total available RAM. This constraint ensures that the production plan is feasible given the RAM resources.
- The total ROM required for the production of all phone models must not exceed the total available ROM. This constraint ensures that the production plan is feasible given the ROM resources.
- The total screen resources required for the production of all phone models must not exceed the total available screen resources. This constraint ensures that the production plan is feasible given the screen resources.

These constraints are critical in guiding the production decisions and ensuring that the optimization process remains within the bounds of available resources.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables, objective coefficients, and constraint bounds, and moving scalar parameters to configuration logic. This addresses the OR expert's mapping gaps and missing data requirements.

CREATE TABLE PhoneModels (
  model_id INTEGER,
  RAM_required INTEGER,
  ROM_required INTEGER,
  screen_required INTEGER
);

CREATE TABLE ObjectiveCoefficients (
  model_id INTEGER,
  profit_per_unit FLOAT
);

CREATE TABLE DecisionVariables (
  model_id INTEGER,
  units_produced INTEGER
);
```

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

- **PhoneModels**: This table contains details of each phone model, including the resource requirements for RAM, ROM, and screen resources. It plays a crucial role in the optimization process by providing the necessary data for constraint calculations.
  - **model_id**: A unique identifier for each phone model, used to reference decision variables and coefficients.
  - **RAM_required**: The amount of RAM required per unit of the phone model, used in the RAM constraint calculation.
  - **ROM_required**: The amount of ROM required per unit of the phone model, used in the ROM constraint calculation.
  - **screen_required**: The screen resources required per unit of the phone model, used in the screen constraint calculation.

- **ObjectiveCoefficients**: This table contains the profit per unit for each phone model, serving as the objective coefficients in the optimization process.
  - **model_id**: A reference to the phone model, linking profit to the specific model.
  - **profit_per_unit**: The profit earned per unit of the phone model, used as a coefficient in the objective function.

- **DecisionVariables**: This table records the number of units produced for each phone model, representing the decision variables in the optimization model.
  - **model_id**: A reference to the phone model, linking production units to the specific model.
  - **units_produced**: The number of units produced for the phone model, serving as the decision variable in the optimization model.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical resource requirements and profit margins for different phone models, ensuring that the total available resources are sufficient to produce a meaningful number of units for each model.

-- Realistic data for PhoneModels
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (1, 4, 16, 1);
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (2, 8, 32, 2);
INSERT INTO PhoneModels (model_id, RAM_required, ROM_required, screen_required) VALUES (3, 16, 64, 3);

-- Realistic data for ObjectiveCoefficients
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (1, 50.0);
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (2, 75.0);
INSERT INTO ObjectiveCoefficients (model_id, profit_per_unit) VALUES (3, 100.0);

-- Realistic data for DecisionVariables
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (1, 2000);
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (2, 1000);
INSERT INTO DecisionVariables (model_id, units_produced) VALUES (3, 500);
```
