Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-27 23:02:51

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] represents the allocation of office space to company i in a building, where x[i] is a binary variable indicating whether the company is allocated space in the building (1) or not (0)
- Operational parameters align with expected linear objective: maximize total_market_value = ∑(Market_Value_billion[i] * x[i])
- Business configuration includes: Represents the minimum total sales required for the allocation (used for Used as a constraint in the 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": "company_office",
  "iteration": 1,
  "business_context": "The company aims to optimize the allocation of office spaces across different buildings to maximize its market value, considering constraints like available stories in buildings and the company's sales performance.",
  "optimization_problem_description": "Maximize the total market value of companies by optimally allocating office spaces in various buildings, subject to constraints on the number of stories available in each building and the minimum sales performance required for allocation.",
  "optimization_formulation": {
    "objective": "maximize total_market_value = \u2211(Market_Value_billion[i] * x[i])",
    "decision_variables": "x[i] represents the allocation of office space to company i in a building, where x[i] is a binary variable indicating whether the company is allocated space in the building (1) or not (0)",
    "constraints": [
      "\u2211(x[i]) <= Stories[j] for each building j",
      "\u2211(Sales_billion[i] * x[i]) >= minimum_sales_requirement"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Market_Value_billion[i]": {
        "currently_mapped_to": "Companies.Market_Value_billion",
        "mapping_adequacy": "good",
        "description": "Represents the market value contribution of each company"
      }
    },
    "constraint_bounds": {
      "Stories[j]": {
        "currently_mapped_to": "buildings.Stories",
        "mapping_adequacy": "good",
        "description": "Represents the maximum number of stories available in each building"
      },
      "minimum_sales_requirement": {
        "currently_mapped_to": "business_configuration_logic.minimum_sales_requirement",
        "mapping_adequacy": "good",
        "description": "Represents the minimum total sales required for the allocation"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "Office_Allocations.building_id, Office_Allocations.company_id",
        "mapping_adequacy": "good",
        "description": "Represents the allocation of office space to a company in a building",
        "variable_type": "binary"
      }
    }
  },
  "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 a new table for decision variables, modifying existing tables to fill mapping gaps, and moving scalar parameters to configuration logic. Business configuration logic updated to include minimum sales requirement as a scalar parameter.

CREATE TABLE Companies (
  Market_Value_billion FLOAT,
  Sales_billion FLOAT
);

CREATE TABLE buildings (
  Stories INTEGER
);

CREATE TABLE Office_Allocations (
  building_id INTEGER,
  company_id INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical market values and sales figures for mid-sized companies and realistic building capacities in urban areas.

-- Realistic data for Companies
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (12.0, 6.5);
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (18.0, 8.0);
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (14.5, 7.0);

-- Realistic data for buildings
INSERT INTO buildings (Stories) VALUES (12);
INSERT INTO buildings (Stories) VALUES (18);
INSERT INTO buildings (Stories) VALUES (15);

-- Realistic data for Office_Allocations
INSERT INTO Office_Allocations (building_id, company_id) VALUES (1, 101);
INSERT INTO Office_Allocations (building_id, company_id) VALUES (2, 102);
INSERT INTO Office_Allocations (building_id, company_id) VALUES (3, 103);


```

DATA DICTIONARY:
{
  "tables": {
    "Companies": {
      "business_purpose": "Stores information about companies including market value and sales",
      "optimization_role": "objective_coefficients/business_data",
      "columns": {
        "Market_Value_billion": {
          "data_type": "FLOAT",
          "business_meaning": "Market value contribution of the company",
          "optimization_purpose": "Used in objective function",
          "sample_values": "10.5, 20.0, 15.3"
        },
        "Sales_billion": {
          "data_type": "FLOAT",
          "business_meaning": "Sales performance of the company",
          "optimization_purpose": "Used in sales-based constraints",
          "sample_values": "5.0, 7.5, 6.0"
        }
      }
    },
    "buildings": {
      "business_purpose": "Stores information about buildings including available stories",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Stories": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of stories available in the building",
          "optimization_purpose": "Used in story-based constraints",
          "sample_values": "10, 15, 20"
        }
      }
    },
    "Office_Allocations": {
      "business_purpose": "Represents allocation of office spaces to companies in buildings",
      "optimization_role": "decision_variables",
      "columns": {
        "building_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the building",
          "optimization_purpose": "Part of decision variable mapping",
          "sample_values": "1, 2, 3"
        },
        "company_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the company",
          "optimization_purpose": "Part of decision variable mapping",
          "sample_values": "101, 102, 103"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "minimum_sales_requirement": {
    "data_type": "FLOAT",
    "business_meaning": "Represents the minimum total sales required for the allocation",
    "optimization_role": "Used as a constraint in the optimization model",
    "configuration_type": "scalar_parameter",
    "value": 20.0,
    "business_justification": "This value ensures that only companies with significant sales performance are considered, aligning with business goals."
  }
}

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: company_office

## 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] represents the allocation of office space to company i in a building, where x[i] is a binary variable indicating whether the company is allocated space in the building (1) or not (0)
- Operational parameters align with expected linear objective: maximize total_market_value = ∑(Market_Value_billion[i] * x[i])
- Business configuration includes: Represents the minimum total sales required for the allocation (used for Used as a constraint in the 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 total_market_value = ∑(Market_Value_billion[i] * x[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: ['∑(x[i]) <= Stories[j] for each building j', '∑(Sales_billion[i] * x[i]) >= minimum_sales_requirement'] (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 a new table for decision variables, modifying existing tables to fill mapping gaps, and moving scalar parameters to configuration logic. Business configuration logic updated to include minimum sales requirement as a scalar parameter.

CREATE TABLE Companies (
  Market_Value_billion FLOAT,
  Sales_billion FLOAT
);

CREATE TABLE buildings (
  Stories INTEGER
);

CREATE TABLE Office_Allocations (
  building_id INTEGER,
  company_id 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 market values and sales figures for mid-sized companies and realistic building capacities in urban areas.

-- Realistic data for Companies
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (12.0, 6.5);
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (18.0, 8.0);
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (14.5, 7.0);

-- Realistic data for buildings
INSERT INTO buildings (Stories) VALUES (12);
INSERT INTO buildings (Stories) VALUES (18);
INSERT INTO buildings (Stories) VALUES (15);

-- Realistic data for Office_Allocations
INSERT INTO Office_Allocations (building_id, company_id) VALUES (1, 101);
INSERT INTO Office_Allocations (building_id, company_id) VALUES (2, 102);
INSERT INTO Office_Allocations (building_id, company_id) VALUES (3, 103);


```

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

Response:
# Complete Optimization Problem and Solution: company_office

## 1. Problem Context and Goals

### Context  
The company is focused on optimizing the allocation of office spaces across various buildings to enhance its market value. The decision-making process involves determining whether a company should be allocated space in a building, represented by a binary decision variable. The primary objective is to maximize the total market value by strategically assigning office spaces to companies. This decision is influenced by the market value contribution of each company and is subject to constraints such as the number of available stories in each building and a minimum sales performance threshold. The business configuration includes a minimum sales requirement, ensuring that only companies with significant sales performance are considered for allocation. This approach ensures that the allocation process is both efficient and aligned with the company's strategic goals.

### Goals  
The primary goal of this optimization problem is to maximize the total market value of the companies by effectively allocating office spaces in various buildings. The metric for optimization is the total market value, which is calculated based on the market value contribution of each company that is allocated space. Success in this context is measured by the ability to maximize this total market value while adhering to the constraints related to building capacities and sales performance. The optimization process is linear, focusing on maximizing the sum of market values associated with the allocated companies.

## 2. Constraints    

The allocation of office spaces is subject to several constraints that ensure the feasibility and strategic alignment of the decision-making process:

- The total number of companies allocated to a building must not exceed the number of available stories in that building. This constraint ensures that the physical capacity of each building is respected.
- The total sales performance of the companies allocated to office spaces must meet or exceed a predefined minimum sales requirement. This constraint ensures that only companies with a significant sales performance are considered, aligning with the company's strategic objectives.

These constraints are designed to naturally lead to linear mathematical formulations, ensuring that the optimization process remains efficient and effective.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating a new table for decision variables, modifying existing tables to fill mapping gaps, and moving scalar parameters to configuration logic. Business configuration logic updated to include minimum sales requirement as a scalar parameter.

CREATE TABLE Companies (
  Market_Value_billion FLOAT,
  Sales_billion FLOAT
);

CREATE TABLE buildings (
  Stories INTEGER
);

CREATE TABLE Office_Allocations (
  building_id INTEGER,
  company_id INTEGER
);
```

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

- **Companies Table**: This table stores information about each company, including their market value and sales performance. The market value is used as a coefficient in the objective function, while sales performance is used in sales-based constraints.
  - **Market_Value_billion**: Represents the market value contribution of each company, crucial for calculating the total market value.
  - **Sales_billion**: Indicates the sales performance of each company, used to ensure that only companies meeting the minimum sales requirement are considered.

- **Buildings Table**: This table contains information about the buildings, specifically the number of available stories. This data is used to ensure that the allocation does not exceed the building's capacity.
  - **Stories**: Represents the maximum number of stories available in each building, serving as a constraint in the allocation process.

- **Office_Allocations Table**: This table represents the allocation of office spaces to companies within buildings. It is central to the decision-making process, mapping the allocation decisions.
  - **building_id**: Identifies the building where the office space is allocated.
  - **company_id**: Identifies the company that is allocated office space.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical market values and sales figures for mid-sized companies and realistic building capacities in urban areas.

-- Realistic data for Companies
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (12.0, 6.5);
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (18.0, 8.0);
INSERT INTO Companies (Market_Value_billion, Sales_billion) VALUES (14.5, 7.0);

-- Realistic data for buildings
INSERT INTO buildings (Stories) VALUES (12);
INSERT INTO buildings (Stories) VALUES (18);
INSERT INTO buildings (Stories) VALUES (15);

-- Realistic data for Office_Allocations
INSERT INTO Office_Allocations (building_id, company_id) VALUES (1, 101);
INSERT INTO Office_Allocations (building_id, company_id) VALUES (2, 102);
INSERT INTO Office_Allocations (building_id, company_id) VALUES (3, 103);
```
