Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-27 22:27:58

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: medicine_enzyme_interaction.selected[i] for all interactions i, where selected is a binary variable indicating if the interaction is chosen for research
- Operational parameters align with expected linear objective: maximize sum(impact_coefficients.coefficient[i] * medicine_enzyme_interaction.selected[i]) for all interactions i
- Business configuration includes: Total budget available for research (used for Constraint bound for total cost), Total research resources available (used for Constraint bound for total resource 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": "medicine_enzyme_interaction",
  "iteration": 1,
  "business_context": "A pharmaceutical company is optimizing the allocation of research resources to study interactions between medicines and enzymes. The objective is to maximize the potential impact of research by prioritizing interactions that are most likely to lead to significant medical advancements, within budget and resource constraints.",
  "optimization_problem_description": "The company needs to decide which medicine-enzyme interactions to prioritize for research, given a limited budget and resource constraints. The objective is to maximize the expected impact of the research, which is estimated based on historical data and expert opinions.",
  "optimization_formulation": {
    "objective": "maximize sum(impact_coefficients.coefficient[i] * medicine_enzyme_interaction.selected[i]) for all interactions i",
    "decision_variables": "medicine_enzyme_interaction.selected[i] for all interactions i, where selected is a binary variable indicating if the interaction is chosen for research",
    "constraints": [
      "sum(interaction_costs.cost[i] * medicine_enzyme_interaction.selected[i]) <= business_configuration_logic.budget",
      "sum(resource_usage.resources[i] * medicine_enzyme_interaction.selected[i]) <= business_configuration_logic.total_resources"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "impact_coefficient[i]": {
        "currently_mapped_to": "impact_coefficients.coefficient",
        "mapping_adequacy": "good",
        "description": "Estimated impact of researching each interaction"
      }
    },
    "constraint_bounds": {
      "budget_constraint": {
        "currently_mapped_to": "business_configuration_logic.budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for research"
      },
      "resource_constraint": {
        "currently_mapped_to": "business_configuration_logic.total_resources",
        "mapping_adequacy": "good",
        "description": "Total research resources available"
      }
    },
    "decision_variables": {
      "selected[i]": {
        "currently_mapped_to": "medicine_enzyme_interaction.selected",
        "mapping_adequacy": "good",
        "description": "Indicates if the interaction is selected for research",
        "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 new tables for impact coefficients, costs, and resource usage, and updating business configuration logic for budget and total resources.

CREATE TABLE impact_coefficients (
  interaction_id INTEGER,
  coefficient FLOAT
);

CREATE TABLE interaction_costs (
  interaction_id INTEGER,
  cost FLOAT
);

CREATE TABLE resource_usage (
  interaction_id INTEGER,
  resources FLOAT
);

CREATE TABLE medicine_enzyme_interaction (
  interaction_id INTEGER,
  selected BOOLEAN
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical research costs, resource usage, and expected impacts in pharmaceutical research, ensuring a balance between high-impact and low-cost interactions.

-- Realistic data for impact_coefficients
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (1, 1.5);
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (2, 0.9);
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (3, 1.2);

-- Realistic data for interaction_costs
INSERT INTO interaction_costs (interaction_id, cost) VALUES (1, 1500);
INSERT INTO interaction_costs (interaction_id, cost) VALUES (2, 800);
INSERT INTO interaction_costs (interaction_id, cost) VALUES (3, 1200);

-- Realistic data for resource_usage
INSERT INTO resource_usage (interaction_id, resources) VALUES (1, 25);
INSERT INTO resource_usage (interaction_id, resources) VALUES (2, 10);
INSERT INTO resource_usage (interaction_id, resources) VALUES (3, 18);

-- Realistic data for medicine_enzyme_interaction
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (1, False);
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (2, True);
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (3, True);


```

DATA DICTIONARY:
{
  "tables": {
    "impact_coefficients": {
      "business_purpose": "Stores estimated impact of researching each interaction",
      "optimization_role": "objective_coefficients",
      "columns": {
        "interaction_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each interaction",
          "optimization_purpose": "Links to decision variables",
          "sample_values": "1, 2, 3"
        },
        "coefficient": {
          "data_type": "FLOAT",
          "business_meaning": "Estimated impact coefficient",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.5, 1.2, 0.8"
        }
      }
    },
    "interaction_costs": {
      "business_purpose": "Stores cost associated with researching each interaction",
      "optimization_role": "constraint_bounds",
      "columns": {
        "interaction_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each interaction",
          "optimization_purpose": "Links to decision variables",
          "sample_values": "1, 2, 3"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost of researching the interaction",
          "optimization_purpose": "Used in cost constraint",
          "sample_values": "1000, 2000, 1500"
        }
      }
    },
    "resource_usage": {
      "business_purpose": "Stores resource usage for each interaction",
      "optimization_role": "constraint_bounds",
      "columns": {
        "interaction_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each interaction",
          "optimization_purpose": "Links to decision variables",
          "sample_values": "1, 2, 3"
        },
        "resources": {
          "data_type": "FLOAT",
          "business_meaning": "Resources required for researching the interaction",
          "optimization_purpose": "Used in resource constraint",
          "sample_values": "10, 20, 15"
        }
      }
    },
    "medicine_enzyme_interaction": {
      "business_purpose": "Stores information about medicine-enzyme interactions",
      "optimization_role": "decision_variables",
      "columns": {
        "interaction_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each interaction",
          "optimization_purpose": "Primary key",
          "sample_values": "1, 2, 3"
        },
        "selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the interaction is selected for research",
          "optimization_purpose": "Decision variable",
          "sample_values": "true, false"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "budget": {
    "data_type": "INTEGER",
    "business_meaning": "Total budget available for research",
    "optimization_role": "Constraint bound for total cost",
    "configuration_type": "scalar_parameter",
    "value": 3000,
    "business_justification": "Reflects a realistic budget for a small-scale research project, allowing for strategic selection of interactions."
  },
  "total_resources": {
    "data_type": "INTEGER",
    "business_meaning": "Total research resources available",
    "optimization_role": "Constraint bound for total resource usage",
    "configuration_type": "scalar_parameter",
    "value": 50,
    "business_justification": "Represents the total available resources, ensuring feasibility of selected interactions within constraints."
  }
}

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: medicine_enzyme_interaction

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: medicine_enzyme_interaction.selected[i] for all interactions i, where selected is a binary variable indicating if the interaction is chosen for research
- Operational parameters align with expected linear objective: maximize sum(impact_coefficients.coefficient[i] * medicine_enzyme_interaction.selected[i]) for all interactions i
- Business configuration includes: Total budget available for research (used for Constraint bound for total cost), Total research resources available (used for Constraint bound for total resource 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 sum(impact_coefficients.coefficient[i] * medicine_enzyme_interaction.selected[i]) for all interactions 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(interaction_costs.cost[i] * medicine_enzyme_interaction.selected[i]) <= business_configuration_logic.budget', 'sum(resource_usage.resources[i] * medicine_enzyme_interaction.selected[i]) <= business_configuration_logic.total_resources'] (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 impact coefficients, costs, and resource usage, and updating business configuration logic for budget and total resources.

CREATE TABLE impact_coefficients (
  interaction_id INTEGER,
  coefficient FLOAT
);

CREATE TABLE interaction_costs (
  interaction_id INTEGER,
  cost FLOAT
);

CREATE TABLE resource_usage (
  interaction_id INTEGER,
  resources FLOAT
);

CREATE TABLE medicine_enzyme_interaction (
  interaction_id INTEGER,
  selected BOOLEAN
);


```

### 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 research costs, resource usage, and expected impacts in pharmaceutical research, ensuring a balance between high-impact and low-cost interactions.

-- Realistic data for impact_coefficients
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (1, 1.5);
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (2, 0.9);
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (3, 1.2);

-- Realistic data for interaction_costs
INSERT INTO interaction_costs (interaction_id, cost) VALUES (1, 1500);
INSERT INTO interaction_costs (interaction_id, cost) VALUES (2, 800);
INSERT INTO interaction_costs (interaction_id, cost) VALUES (3, 1200);

-- Realistic data for resource_usage
INSERT INTO resource_usage (interaction_id, resources) VALUES (1, 25);
INSERT INTO resource_usage (interaction_id, resources) VALUES (2, 10);
INSERT INTO resource_usage (interaction_id, resources) VALUES (3, 18);

-- Realistic data for medicine_enzyme_interaction
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (1, False);
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (2, True);
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (3, True);


```

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

Response:
# Complete Optimization Problem and Solution: medicine_enzyme_interaction

## 1. Problem Context and Goals

### Context  
A pharmaceutical company is focused on optimizing its research efforts to study interactions between medicines and enzymes. The primary decision involves selecting which interactions to prioritize for research. Each interaction is represented by a binary decision variable, indicating whether it is chosen for research. The company aims to maximize the potential impact of its research efforts by selecting interactions that are most likely to lead to significant medical advancements. This decision-making process is constrained by a limited budget and available research resources.

The operational parameters are aligned with a linear objective, where the goal is to maximize the sum of the estimated impact coefficients for the selected interactions. The business configuration includes a total budget available for research, which serves as a constraint on the total cost, and total research resources available, which limits the total resource usage. These constraints ensure that the selection of interactions remains within the company's financial and operational capabilities.

The data used in this process reflects current operational information, focusing on precise decision-making that leads to a linear formulation. The constraints are designed to match expected linear relationships, avoiding any scenarios that would require nonlinear relationships such as variable products or divisions. The specific operational parameters are mapped to expected coefficient sources, and business configuration parameters are referenced where appropriate.

### Goals  
The optimization goal is to maximize the potential impact of the research efforts. This is achieved by selecting interactions that have the highest estimated impact coefficients. The metric to optimize is the sum of the impact coefficients for all selected interactions. Success is measured by the alignment of the selected interactions with the expected coefficient sources, ensuring that the research efforts are focused on the most promising opportunities. The optimization goal is described in natural language, emphasizing the linear nature of the objective without using mathematical formulas or symbolic notation.

## 2. Constraints    

The constraints for this optimization problem are directly aligned with expected linear mathematical forms. The first constraint ensures that the total cost of the selected interactions does not exceed the available budget. This is achieved by summing the costs associated with each selected interaction and ensuring that this total remains within the budgetary limits. The second constraint ensures that the total resource usage for the selected interactions does not exceed the available research resources. This involves summing the resource requirements for each selected interaction and ensuring that this total remains within the resource constraints. Both constraints are described in business terms that naturally lead to linear mathematical forms, avoiding any variable products or divisions.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for impact coefficients, costs, and resource usage, and updating business configuration logic for budget and total resources.

CREATE TABLE impact_coefficients (
  interaction_id INTEGER,
  coefficient FLOAT
);

CREATE TABLE interaction_costs (
  interaction_id INTEGER,
  cost FLOAT
);

CREATE TABLE resource_usage (
  interaction_id INTEGER,
  resources FLOAT
);

CREATE TABLE medicine_enzyme_interaction (
  interaction_id INTEGER,
  selected BOOLEAN
);
```

### Data Dictionary  
The data dictionary provides a comprehensive mapping of tables and columns to their business purposes and optimization roles. Each table serves a specific function in the optimization process:

- **Impact Coefficients Table**: This table stores the estimated impact of researching each interaction. The interaction ID uniquely identifies each interaction, while the coefficient represents the estimated impact. This table plays a critical role in the objective function, as the coefficients are used to determine the potential impact of the selected interactions.

- **Interaction Costs Table**: This table contains the costs associated with researching each interaction. The interaction ID links each cost to a specific interaction, and the cost column represents the financial expenditure required for research. This table is essential for the cost constraint, ensuring that the total cost of selected interactions remains within the budget.

- **Resource Usage Table**: This table records the resource usage for each interaction. The interaction ID connects each resource requirement to a specific interaction, and the resources column indicates the amount of resources needed. This table is crucial for the resource constraint, ensuring that the total resource usage of selected interactions stays within the available resources.

- **Medicine-Enzyme Interaction Table**: This table stores information about the interactions between medicines and enzymes. The interaction ID serves as the primary key, and the selected column is a binary variable indicating whether the interaction is chosen for research. This table represents the decision variables in the optimization problem.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical research costs, resource usage, and expected impacts in pharmaceutical research, ensuring a balance between high-impact and low-cost interactions.

-- Realistic data for impact_coefficients
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (1, 1.5);
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (2, 0.9);
INSERT INTO impact_coefficients (interaction_id, coefficient) VALUES (3, 1.2);

-- Realistic data for interaction_costs
INSERT INTO interaction_costs (interaction_id, cost) VALUES (1, 1500);
INSERT INTO interaction_costs (interaction_id, cost) VALUES (2, 800);
INSERT INTO interaction_costs (interaction_id, cost) VALUES (3, 1200);

-- Realistic data for resource_usage
INSERT INTO resource_usage (interaction_id, resources) VALUES (1, 25);
INSERT INTO resource_usage (interaction_id, resources) VALUES (2, 10);
INSERT INTO resource_usage (interaction_id, resources) VALUES (3, 18);

-- Realistic data for medicine_enzyme_interaction
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (1, False);
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (2, True);
INSERT INTO medicine_enzyme_interaction (interaction_id, selected) VALUES (3, True);
```
