Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-27 22:07:19

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: Num_of_stock[Market_ID, Phone_ID] - integer
- Operational parameters align with expected linear objective: maximize sum(Price[Phone_ID] * Num_of_stock[Market_ID, Phone_ID])
- Business configuration includes: Maximum stock that can be allocated to each shop (used for Used as a constraint in optimization model)
- 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_market",
  "iteration": 2,
  "business_context": "A phone retailer aims to optimize the distribution of phone stock across different markets to maximize revenue, considering market ranking and stock availability, while adhering to stock constraints per market.",
  "optimization_problem_description": "The objective is to maximize total revenue from phone sales by optimally distributing available phone stock to various markets, considering market ranking and stock constraints.",
  "optimization_formulation": {
    "objective": "maximize sum(Price[Phone_ID] * Num_of_stock[Market_ID, Phone_ID])",
    "decision_variables": "Num_of_stock[Market_ID, Phone_ID] - integer",
    "constraints": [
      "sum(Num_of_stock[Market_ID, Phone_ID]) <= available_stock[Phone_ID] for all Phone_ID",
      "Num_of_stock[Market_ID, Phone_ID] <= max_stock_per_shop for all Market_ID, Phone_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Price[Phone_ID]": {
        "currently_mapped_to": "phone_prices.Price",
        "mapping_adequacy": "good",
        "description": "Price of each phone model used as a coefficient for revenue calculation"
      }
    },
    "constraint_bounds": {
      "available_stock[Phone_ID]": {
        "currently_mapped_to": "phone_market.available_stock",
        "mapping_adequacy": "good",
        "description": "Total available stock for each phone model"
      },
      "max_stock_per_shop": {
        "currently_mapped_to": "business_configuration_logic.max_stock_per_shop",
        "mapping_adequacy": "good",
        "description": "Maximum stock that can be allocated to each shop"
      }
    },
    "decision_variables": {
      "Num_of_stock[Market_ID, Phone_ID]": {
        "currently_mapped_to": "phone_market.Num_of_stock",
        "mapping_adequacy": "good",
        "description": "Number of phones allocated to a market",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Added a new table for phone prices to address missing objective coefficients. Updated existing tables to ensure all optimization requirements are met. Moved scalar parameters to configuration logic.

CREATE TABLE phone_market (
  Market_ID INTEGER,
  Phone_ID INTEGER,
  Num_of_stock INTEGER,
  available_stock INTEGER
);

CREATE TABLE phone_prices (
  Phone_ID INTEGER,
  Price FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical market sizes, phone pricing strategies, and stock management practices in the retail phone industry.

-- Realistic data for phone_market
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (1, 101, 30, 150);
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (2, 102, 50, 200);
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (3, 103, 20, 100);

-- Realistic data for phone_prices
INSERT INTO phone_prices (Phone_ID, Price) VALUES (101, 299.99);
INSERT INTO phone_prices (Phone_ID, Price) VALUES (102, 399.99);
INSERT INTO phone_prices (Phone_ID, Price) VALUES (103, 499.99);


```

DATA DICTIONARY:
{
  "tables": {
    "phone_market": {
      "business_purpose": "Links phone models to markets with stock allocation",
      "optimization_role": "decision_variables",
      "columns": {
        "Market_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each market",
          "optimization_purpose": "Used to allocate stock to specific markets",
          "sample_values": "1, 2, 3"
        },
        "Phone_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each phone model",
          "optimization_purpose": "Used to allocate specific phone models",
          "sample_values": "101, 102, 103"
        },
        "Num_of_stock": {
          "data_type": "INTEGER",
          "business_meaning": "Number of phones allocated to a market",
          "optimization_purpose": "Decision variable for stock allocation",
          "sample_values": "10, 20, 30"
        },
        "available_stock": {
          "data_type": "INTEGER",
          "business_meaning": "Total available stock for each phone model",
          "optimization_purpose": "Constraint bound for stock allocation",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "phone_prices": {
      "business_purpose": "Stores the price of each phone model",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Phone_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each phone model",
          "optimization_purpose": "Links price to specific phone models",
          "sample_values": "101, 102, 103"
        },
        "Price": {
          "data_type": "FLOAT",
          "business_meaning": "Price of each phone model",
          "optimization_purpose": "Coefficient for revenue calculation",
          "sample_values": "299.99, 399.99, 499.99"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "max_stock_per_shop": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum stock that can be allocated to each shop",
    "optimization_role": "Used as a constraint in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 100,
    "business_justification": "This value reflects typical inventory constraints in retail stores, ensuring that stock levels are manageable and do not exceed storage capacity."
  }
}

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_market

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: Num_of_stock[Market_ID, Phone_ID] - integer
- Operational parameters align with expected linear objective: maximize sum(Price[Phone_ID] * Num_of_stock[Market_ID, Phone_ID])
- Business configuration includes: Maximum stock that can be allocated to each shop (used for Used as a constraint in optimization model)
- 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 sum(Price[Phone_ID] * Num_of_stock[Market_ID, Phone_ID])
- 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(Num_of_stock[Market_ID, Phone_ID]) <= available_stock[Phone_ID] for all Phone_ID', 'Num_of_stock[Market_ID, Phone_ID] <= max_stock_per_shop for all Market_ID, Phone_ID'] (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 a new table for phone prices to address missing objective coefficients. Updated existing tables to ensure all optimization requirements are met. Moved scalar parameters to configuration logic.

CREATE TABLE phone_market (
  Market_ID INTEGER,
  Phone_ID INTEGER,
  Num_of_stock INTEGER,
  available_stock INTEGER
);

CREATE TABLE phone_prices (
  Phone_ID INTEGER,
  Price 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 market sizes, phone pricing strategies, and stock management practices in the retail phone industry.

-- Realistic data for phone_market
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (1, 101, 30, 150);
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (2, 102, 50, 200);
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (3, 103, 20, 100);

-- Realistic data for phone_prices
INSERT INTO phone_prices (Phone_ID, Price) VALUES (101, 299.99);
INSERT INTO phone_prices (Phone_ID, Price) VALUES (102, 399.99);
INSERT INTO phone_prices (Phone_ID, Price) VALUES (103, 499.99);


```

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

Response:
# Complete Optimization Problem and Solution: phone_market

## 1. Problem Context and Goals

### Context  
A phone retailer is focused on optimizing the distribution of its phone stock across various markets to maximize revenue. The decision-making process involves determining the number of phones to allocate to each market, represented by the decision variable Num_of_stock[Market_ID, Phone_ID], which is an integer. The retailer aims to maximize revenue by considering the price of each phone model and the number of units allocated to each market. The operational parameters include a maximum stock limit that can be allocated to each shop, ensuring that stock levels remain manageable and do not exceed storage capacity. This constraint is crucial for maintaining efficient inventory management and is reflected in the business configuration as a scalar parameter. The retailer's strategy is to align stock distribution with market demand while adhering to these constraints, ensuring that the optimization process remains linear and straightforward.

### Goals  
The primary goal of the optimization process is to maximize the total revenue generated from phone sales. This is achieved by strategically distributing the available phone stock to various markets, taking into account the price of each phone model and the number of units allocated. The success of this optimization is measured by the total revenue, which is calculated as the sum of the product of the price of each phone model and the number of units allocated to each market. The optimization goal is clearly defined as maximizing this revenue metric, ensuring that the process remains linear and focused on achieving the highest possible financial return.

## 2. Constraints    

The optimization process is subject to several constraints that ensure the feasibility and efficiency of the stock distribution strategy. The first constraint ensures that the total number of phones allocated to all markets does not exceed the available stock for each phone model. This constraint is critical for maintaining inventory balance and preventing over-allocation. The second constraint limits the number of phones that can be allocated to each shop, ensuring that stock levels remain within manageable limits and do not exceed the maximum stock capacity defined in the business configuration. These constraints are expressed in linear terms, aligning with the retailer's operational requirements and ensuring that the optimization process remains straightforward and effective.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Added a new table for phone prices to address missing objective coefficients. Updated existing tables to ensure all optimization requirements are met. Moved scalar parameters to configuration logic.

CREATE TABLE phone_market (
  Market_ID INTEGER,
  Phone_ID INTEGER,
  Num_of_stock INTEGER,
  available_stock INTEGER
);

CREATE TABLE phone_prices (
  Phone_ID INTEGER,
  Price FLOAT
);
```

### Data Dictionary  
The data dictionary provides a comprehensive overview of the tables and columns used in the optimization process, highlighting their business purposes and roles in the optimization model:

- **phone_market**: This table links phone models to markets, detailing the stock allocation for each market. It plays a crucial role in defining the decision variables for the optimization process.
  - **Market_ID**: An integer identifier for each market, used to allocate stock to specific markets.
  - **Phone_ID**: An integer identifier for each phone model, used to allocate specific phone models.
  - **Num_of_stock**: An integer representing the number of phones allocated to a market, serving as the decision variable for stock allocation.
  - **available_stock**: An integer indicating the total available stock for each phone model, serving as a constraint bound for stock allocation.

- **phone_prices**: This table stores the price of each phone model, providing the coefficients for the revenue calculation in the optimization model.
  - **Phone_ID**: An integer identifier for each phone model, linking the price to specific phone models.
  - **Price**: A float representing the price of each phone model, used as a coefficient for revenue calculation.

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical market sizes, phone pricing strategies, and stock management practices in the retail phone industry.

-- Realistic data for phone_market
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (1, 101, 30, 150);
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (2, 102, 50, 200);
INSERT INTO phone_market (Market_ID, Phone_ID, Num_of_stock, available_stock) VALUES (3, 103, 20, 100);

-- Realistic data for phone_prices
INSERT INTO phone_prices (Phone_ID, Price) VALUES (101, 299.99);
INSERT INTO phone_prices (Phone_ID, Price) VALUES (102, 399.99);
INSERT INTO phone_prices (Phone_ID, Price) VALUES (103, 499.99);
```
