# Complete Optimization Problem and Solution: cre_Doc_Template_Mgt

## 1. Problem Context and Goals

### Context  
The company is focused on optimizing the assignment of templates to documents to minimize the total number of templates used, thereby reducing maintenance costs and ensuring document consistency. The decision-making process involves determining whether a template is used, represented by a binary variable for each template. Additionally, each document must be assigned to exactly one template, which is also represented by a binary variable indicating the assignment. The operational parameters are aligned with the objective of minimizing the total cost associated with using templates. This cost is a critical factor in refining the objective function, as it reflects the financial implications of template usage. The business configuration includes the cost associated with each template, which is used to refine the objective function by incorporating these costs. The data presented reflects current operational information, focusing on precise decision-making that leads to linear formulations. Resource limitations are considered to ensure that constraints are linear, avoiding scenarios that require nonlinear relationships. The business configuration parameters, including scalar parameters and business logic formulas, are integral to this process, ensuring consistency and flexibility in parameter tuning.

### Goals  
The primary goal of this optimization problem is to minimize the total cost of templates used across all documents. The metric to optimize is the sum of the costs associated with each template that is used. Success is measured by the ability to minimize this sum, aligning with the expected coefficient sources. The optimization goal is clearly defined in natural language, focusing on minimizing the total cost without using mathematical formulas or symbolic notation.

## 2. Constraints    

The constraints for this optimization problem are designed to ensure that each document is assigned exactly one template and that template usage is linked to document assignment. The first constraint ensures that each document is assigned to exactly one template, reflecting the business requirement that every document must have a template. The second constraint links template usage to document assignment, ensuring that a template is only considered used if it is assigned to at least one document. These constraints are described in business terms that naturally lead to linear mathematical forms, avoiding variable products or divisions.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a new table for template costs, modifying existing tables to include necessary fields, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE Templates (
  Template_ID INTEGER,
  Cost FLOAT
);

CREATE TABLE Documents (
  Document_ID INTEGER
);

CREATE TABLE Template_Costs (
  Template_ID INTEGER,
  Cost FLOAT
);
```

### Data Dictionary  
The data dictionary provides a comprehensive mapping of tables and columns to their business purposes and optimization roles. The "Templates" table stores information about document templates, with each template having a unique identifier and an associated cost. This cost is used to refine the objective function in the optimization problem. The "Documents" table contains information about documents, with each document having a unique identifier. This table plays a crucial role in ensuring that each document is assigned a template. The "Template_Costs" table stores cost data for each template, linking the cost to the templates and playing a role in the objective function. This business-oriented data dictionary 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 business scenarios where template costs vary to reflect complexity and usage frequency. Document IDs were assigned sequentially to ensure unique identification.

-- Realistic data for Templates
INSERT INTO Templates (Template_ID, Cost) VALUES (1, 50.0);
INSERT INTO Templates (Template_ID, Cost) VALUES (2, 75.0);
INSERT INTO Templates (Template_ID, Cost) VALUES (3, 100.0);

-- Realistic data for Documents
INSERT INTO Documents (Document_ID) VALUES (101);
INSERT INTO Documents (Document_ID) VALUES (102);
INSERT INTO Documents (Document_ID) VALUES (103);

-- Realistic data for Template_Costs
INSERT INTO Template_Costs (Template_ID, Cost) VALUES (1, 50.0);
INSERT INTO Template_Costs (Template_ID, Cost) VALUES (2, 75.0);
INSERT INTO Template_Costs (Template_ID, Cost) VALUES (3, 100.0);
```