Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-25 22:45:02

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: x[i,j] = number of phones produced with chip model i and screen mode j (integer)
- Operational parameters align with expected linear objective: minimize ∑(cost_of_chip_model[i] + cost_of_screen_mode[j]) * x[i,j]
- Business configuration includes: minimum total RAM required for all phones (used for constraint bound), minimum total ROM required for all phones (used for constraint bound), minimum accreditation level required for all phones (used for constraint bound)
- 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 phone manufacturer aims to optimize the production of phones by minimizing the total cost while meeting specific hardware and accreditation requirements. The manufacturer needs to decide how many phones of each model to produce, considering the cost of chip models and screen modes, while ensuring that the phones meet certain RAM, ROM, and accreditation level constraints.",
  "optimization_problem_description": "Minimize the total cost of producing phones by selecting the optimal quantity of each phone model, subject to constraints on total RAM, ROM, and accreditation level requirements.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_of_chip_model[i] + cost_of_screen_mode[j]) * x[i,j]",
    "decision_variables": "x[i,j] = number of phones produced with chip model i and screen mode j (integer)",
    "constraints": [
      "\u2211(RAM_MiB[i] * x[i,j]) \u2265 total_RAM_required",
      "\u2211(ROM_MiB[i] * x[i,j]) \u2265 total_ROM_required",
      "\u2211(Accreditation_level[j] * x[i,j]) \u2265 total_accreditation_required"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_of_chip_model[i]": {
        "currently_mapped_to": "chip_models.cost",
        "mapping_adequacy": "good",
        "description": "cost associated with chip model i"
      },
      "cost_of_screen_mode[j]": {
        "currently_mapped_to": "screen_modes.cost",
        "mapping_adequacy": "good",
        "description": "cost associated with screen mode j"
      }
    },
    "constraint_bounds": {
      "total_RAM_required": {
        "currently_mapped_to": "business_configuration_logic.total_RAM_required",
        "mapping_adequacy": "good",
        "description": "minimum total RAM required for all phones"
      },
      "total_ROM_required": {
        "currently_mapped_to": "business_configuration_logic.total_ROM_required",
        "mapping_adequacy": "good",
        "description": "minimum total ROM required for all phones"
      },
      "total_accreditation_required": {
        "currently_mapped_to": "business_configuration_logic.total_accreditation_required",
        "mapping_adequacy": "good",
        "description": "minimum accreditation level required for all phones"
      }
    },
    "decision_variables": {
      "x[i,j]": {
        "currently_mapped_to": "phone_production.quantity",
        "mapping_adequacy": "good",
        "description": "number of phones produced with chip model i and screen mode j",
        "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 and configuration logic updates implemented to address missing optimization data requirements and mapping gaps identified by the OR expert.

CREATE TABLE chip_models (
  chip_model_id INTEGER,
  cost FLOAT,
  RAM_MiB INTEGER,
  ROM_MiB INTEGER
);

CREATE TABLE screen_modes (
  screen_mode_id INTEGER,
  cost FLOAT,
  Accreditation_level INTEGER
);

CREATE TABLE phone_production (
  chip_model_id INTEGER,
  screen_mode_id INTEGER,
  quantity INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards for phone manufacturing, ensuring realistic costs, capacities, and accreditation levels. The data was designed to create a meaningful optimization problem by balancing costs and constraints.

-- Realistic data for chip_models
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (1, 50.0, 2048, 32768);
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (2, 75.0, 4096, 65536);
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (3, 100.0, 8192, 131072);

-- Realistic data for screen_modes
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (1, 30.0, 3);
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (2, 45.0, 4);
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (3, 60.0, 5);

-- Realistic data for phone_production
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (1, 1, 10);
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (2, 2, 20);
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (3, 3, 30);


```

DATA DICTIONARY:
{
  "tables": {
    "chip_models": {
      "business_purpose": "cost and specifications of chip models used in phone production",
      "optimization_role": "objective_coefficients",
      "columns": {
        "chip_model_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for chip model",
          "optimization_purpose": "index i in optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "cost associated with the chip model",
          "optimization_purpose": "coefficient in objective function",
          "sample_values": [
            50.0,
            75.0,
            100.0
          ]
        },
        "RAM_MiB": {
          "data_type": "INTEGER",
          "business_meaning": "RAM capacity of the chip model in MiB",
          "optimization_purpose": "used in RAM constraint",
          "sample_values": [
            2048,
            4096,
            8192
          ]
        },
        "ROM_MiB": {
          "data_type": "INTEGER",
          "business_meaning": "ROM capacity of the chip model in MiB",
          "optimization_purpose": "used in ROM constraint",
          "sample_values": [
            32768,
            65536,
            131072
          ]
        }
      }
    },
    "screen_modes": {
      "business_purpose": "cost and specifications of screen modes used in phone production",
      "optimization_role": "objective_coefficients",
      "columns": {
        "screen_mode_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for screen mode",
          "optimization_purpose": "index j in optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "cost associated with the screen mode",
          "optimization_purpose": "coefficient in objective function",
          "sample_values": [
            30.0,
            45.0,
            60.0
          ]
        },
        "Accreditation_level": {
          "data_type": "INTEGER",
          "business_meaning": "accreditation level of the screen mode",
          "optimization_purpose": "used in accreditation constraint",
          "sample_values": [
            3,
            4,
            5
          ]
        }
      }
    },
    "phone_production": {
      "business_purpose": "number of phones produced with specific chip models and screen modes",
      "optimization_role": "decision_variables",
      "columns": {
        "chip_model_id": {
          "data_type": "INTEGER",
          "business_meaning": "chip model used in phone production",
          "optimization_purpose": "index i in optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "screen_mode_id": {
          "data_type": "INTEGER",
          "business_meaning": "screen mode used in phone production",
          "optimization_purpose": "index j in optimization model",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "quantity": {
          "data_type": "INTEGER",
          "business_meaning": "number of phones produced",
          "optimization_purpose": "decision variable x[i,j]",
          "sample_values": [
            10,
            20,
            30
          ]
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "total_RAM_required": {
    "data_type": "INTEGER",
    "business_meaning": "minimum total RAM required for all phones",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter",
    "value": 8000,
    "business_justification": "Minimum total RAM required to meet production targets for all phone models."
  },
  "total_ROM_required": {
    "data_type": "INTEGER",
    "business_meaning": "minimum total ROM required for all phones",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter",
    "value": 128000,
    "business_justification": "Minimum total ROM required to meet production targets for all phone models."
  },
  "total_accreditation_required": {
    "data_type": "INTEGER",
    "business_meaning": "minimum accreditation level required for all phones",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter",
    "value": 5,
    "business_justification": "Minimum accreditation level required to ensure all phones meet quality standards."
  }
}

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: x[i,j] = number of phones produced with chip model i and screen mode j (integer)
- Operational parameters align with expected linear objective: minimize ∑(cost_of_chip_model[i] + cost_of_screen_mode[j]) * x[i,j]
- Business configuration includes: minimum total RAM required for all phones (used for constraint bound), minimum total ROM required for all phones (used for constraint bound), minimum accreditation level required for all phones (used for constraint bound)
- 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_of_chip_model[i] + cost_of_screen_mode[j]) * x[i,j]
- 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: ['∑(RAM_MiB[i] * x[i,j]) ≥ total_RAM_required', '∑(ROM_MiB[i] * x[i,j]) ≥ total_ROM_required', '∑(Accreditation_level[j] * x[i,j]) ≥ total_accreditation_required'] (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 and configuration logic updates implemented to address missing optimization data requirements and mapping gaps identified by the OR expert.

CREATE TABLE chip_models (
  chip_model_id INTEGER,
  cost FLOAT,
  RAM_MiB INTEGER,
  ROM_MiB INTEGER
);

CREATE TABLE screen_modes (
  screen_mode_id INTEGER,
  cost FLOAT,
  Accreditation_level INTEGER
);

CREATE TABLE phone_production (
  chip_model_id INTEGER,
  screen_mode_id INTEGER,
  quantity 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 industry standards for phone manufacturing, ensuring realistic costs, capacities, and accreditation levels. The data was designed to create a meaningful optimization problem by balancing costs and constraints.

-- Realistic data for chip_models
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (1, 50.0, 2048, 32768);
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (2, 75.0, 4096, 65536);
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (3, 100.0, 8192, 131072);

-- Realistic data for screen_modes
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (1, 30.0, 3);
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (2, 45.0, 4);
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (3, 60.0, 5);

-- Realistic data for phone_production
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (1, 1, 10);
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (2, 2, 20);
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (3, 3, 30);


```

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 phone manufacturer is tasked with optimizing the production of phones to minimize total costs while meeting specific hardware and accreditation requirements. The manufacturer must decide how many phones to produce for each combination of chip model and screen mode. Each chip model has an associated cost, RAM capacity, and ROM capacity, while each screen mode has an associated cost and accreditation level. The goal is to determine the optimal number of phones to produce for each chip model and screen mode combination, ensuring that the total RAM, ROM, and accreditation levels across all produced phones meet or exceed the minimum requirements set by the business.  

The business has established the following minimum requirements for all phones produced:  
- **Total RAM Required**: 8,000 MiB  
- **Total ROM Required**: 128,000 MiB  
- **Total Accreditation Level Required**: 5  

These requirements ensure that the phones meet production targets and quality standards. The manufacturer must balance the costs of chip models and screen modes while adhering to these constraints.  

### Goals  
The primary goal of this optimization problem is to minimize the total cost of producing phones. This cost is determined by the sum of the costs of the chip models and screen modes used in each phone, multiplied by the number of phones produced for each combination. Success is measured by achieving the lowest possible total cost while ensuring that the minimum RAM, ROM, and accreditation level requirements are met.  

## 2. Constraints  

The optimization problem must adhere to the following constraints:  
1. **Total RAM Constraint**: The combined RAM capacity of all phones produced must meet or exceed the minimum total RAM requirement of 8,000 MiB. This is calculated by summing the RAM capacity of each chip model multiplied by the number of phones produced with that chip model.  
2. **Total ROM Constraint**: The combined ROM capacity of all phones produced must meet or exceed the minimum total ROM requirement of 128,000 MiB. This is calculated by summing the ROM capacity of each chip model multiplied by the number of phones produced with that chip model.  
3. **Total Accreditation Level Constraint**: The combined accreditation level of all phones produced must meet or exceed the minimum total accreditation level requirement of 5. This is calculated by summing the accreditation level of each screen mode multiplied by the number of phones produced with that screen mode.  

These constraints ensure that the phones produced meet the necessary hardware and quality standards while minimizing production costs.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes and configuration logic updates implemented to address missing optimization data requirements and mapping gaps identified by the OR expert.

CREATE TABLE chip_models (
  chip_model_id INTEGER,
  cost FLOAT,
  RAM_MiB INTEGER,
  ROM_MiB INTEGER
);

CREATE TABLE screen_modes (
  screen_mode_id INTEGER,
  cost FLOAT,
  Accreditation_level INTEGER
);

CREATE TABLE phone_production (
  chip_model_id INTEGER,
  screen_mode_id INTEGER,
  quantity INTEGER
);
```

### Data Dictionary  
- **chip_models**:  
  - **chip_model_id**: Unique identifier for each chip model.  
  - **cost**: The cost associated with using the chip model in phone production.  
  - **RAM_MiB**: The RAM capacity of the chip model, measured in MiB.  
  - **ROM_MiB**: The ROM capacity of the chip model, measured in MiB.  

- **screen_modes**:  
  - **screen_mode_id**: Unique identifier for each screen mode.  
  - **cost**: The cost associated with using the screen mode in phone production.  
  - **Accreditation_level**: The accreditation level of the screen mode, indicating its quality standard.  

- **phone_production**:  
  - **chip_model_id**: The chip model used in the production of a specific phone.  
  - **screen_mode_id**: The screen mode used in the production of a specific phone.  
  - **quantity**: The number of phones produced with the specified chip model and screen mode combination.  

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on industry standards for phone manufacturing, ensuring realistic costs, capacities, and accreditation levels. The data was designed to create a meaningful optimization problem by balancing costs and constraints.

-- Realistic data for chip_models
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (1, 50.0, 2048, 32768);
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (2, 75.0, 4096, 65536);
INSERT INTO chip_models (chip_model_id, cost, RAM_MiB, ROM_MiB) VALUES (3, 100.0, 8192, 131072);

-- Realistic data for screen_modes
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (1, 30.0, 3);
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (2, 45.0, 4);
INSERT INTO screen_modes (screen_mode_id, cost, Accreditation_level) VALUES (3, 60.0, 5);

-- Realistic data for phone_production
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (1, 1, 10);
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (2, 2, 20);
INSERT INTO phone_production (chip_model_id, screen_mode_id, quantity) VALUES (3, 3, 30);
```
