Iteration final - PROBLEM_DESCRIPTION
Sequence: 9
Timestamp: 2025-07-25 22:33:39

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 3), 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[medicine_id] ∈ {0, 1} (binary decision variable indicating whether medicine_id is selected)
- Operational parameters align with expected linear objective: maximize ∑(effectiveness_score[medicine_id] × x[medicine_id])
- Business configuration includes: Maximum allowed total adverse interaction score (used for Upper bound for the adverse interaction constraint), Maximum number of medicines that can be selected (used for Upper bound for the selection count constraint)
- 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": 3,
  "business_context": "A pharmaceutical company aims to optimize the selection of medicines for a clinical trial by maximizing the overall effectiveness score while ensuring the total adverse interaction score does not exceed a specified limit and the number of selected medicines does not exceed a predefined maximum.",
  "optimization_problem_description": "Select a combination of medicines that maximizes the total effectiveness score while ensuring the total adverse interaction score is within the allowed limit and the number of selected medicines does not exceed the maximum allowed.",
  "optimization_formulation": {
    "objective": "maximize \u2211(effectiveness_score[medicine_id] \u00d7 x[medicine_id])",
    "decision_variables": "x[medicine_id] \u2208 {0, 1} (binary decision variable indicating whether medicine_id is selected)",
    "constraints": [
      "\u2211(adverse_interaction_score[medicine_id] \u00d7 x[medicine_id]) \u2264 max_adverse_interaction_score",
      "\u2211(x[medicine_id]) \u2264 max_selected_medicines",
      "x[medicine_id] \u2264 FDA_approved[medicine_id] for all medicine_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "effectiveness_score[medicine_id]": {
        "currently_mapped_to": "medicine_effectiveness.effectiveness_score",
        "mapping_adequacy": "good",
        "description": "Effectiveness score of each medicine in the objective function"
      }
    },
    "constraint_bounds": {
      "max_adverse_interaction_score": {
        "currently_mapped_to": "business_configuration_logic.max_adverse_interaction_score",
        "mapping_adequacy": "good",
        "description": "Maximum allowed total adverse interaction score"
      },
      "max_selected_medicines": {
        "currently_mapped_to": "business_configuration_logic.max_selected_medicines",
        "mapping_adequacy": "good",
        "description": "Maximum number of medicines that can be selected"
      },
      "FDA_approved[medicine_id]": {
        "currently_mapped_to": "medicine.FDA_approved",
        "mapping_adequacy": "good",
        "description": "Constraint ensuring only FDA-approved medicines are selected"
      }
    },
    "decision_variables": {
      "x[medicine_id]": {
        "currently_mapped_to": "medicine_selection.is_selected",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether a medicine is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 3 Database Schema
-- Objective: Schema changes include adding missing scalar parameters to business configuration logic and ensuring all optimization mappings are complete. No table modifications or deletions were necessary.

CREATE TABLE medicine_effectiveness (
  medicine_id INTEGER,
  effectiveness_score FLOAT
);

CREATE TABLE medicine_adverse_interaction (
  medicine_id INTEGER,
  adverse_interaction_score FLOAT
);

CREATE TABLE medicine (
  medicine_id INTEGER,
  FDA_approved BOOLEAN
);

CREATE TABLE medicine_selection (
  medicine_id INTEGER,
  is_selected BOOLEAN
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic pharmaceutical data, ensuring effectiveness scores and adverse interaction scores are within plausible ranges. The number of medicines and their FDA approval statuses were chosen to reflect a typical clinical trial scenario.

-- Realistic data for medicine_effectiveness
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (1, 0.85);
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (2, 0.75);
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (3, 0.9);

-- Realistic data for medicine_adverse_interaction
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (1, 0.15);
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (2, 0.25);
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (3, 0.1);

-- Realistic data for medicine
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (1, True);
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (2, False);
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (3, True);

-- Realistic data for medicine_selection
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (1, False);
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (2, False);
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (3, False);


```

DATA DICTIONARY:
{
  "tables": {
    "medicine_effectiveness": {
      "business_purpose": "Effectiveness scores of medicines based on enzyme interactions",
      "optimization_role": "objective_coefficients",
      "columns": {
        "medicine_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each medicine",
          "optimization_purpose": "Links to decision variable x[medicine_id]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "effectiveness_score": {
          "data_type": "FLOAT",
          "business_meaning": "Effectiveness score of the medicine",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": [
            0.8,
            0.9,
            0.7
          ]
        }
      }
    },
    "medicine_adverse_interaction": {
      "business_purpose": "Adverse interaction scores of medicines based on enzyme interactions",
      "optimization_role": "constraint_bounds",
      "columns": {
        "medicine_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each medicine",
          "optimization_purpose": "Links to decision variable x[medicine_id]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "adverse_interaction_score": {
          "data_type": "FLOAT",
          "business_meaning": "Adverse interaction score of the medicine",
          "optimization_purpose": "Coefficient in the constraint",
          "sample_values": [
            0.2,
            0.3,
            0.1
          ]
        }
      }
    },
    "medicine": {
      "business_purpose": "List of medicines with FDA approval status",
      "optimization_role": "constraint_bounds",
      "columns": {
        "medicine_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each medicine",
          "optimization_purpose": "Links to decision variable x[medicine_id]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "FDA_approved": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the medicine is FDA approved",
          "optimization_purpose": "Constraint on decision variable x[medicine_id]",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    },
    "medicine_selection": {
      "business_purpose": "Binary decision variable indicating whether a medicine is selected for the clinical trial",
      "optimization_role": "decision_variables",
      "columns": {
        "medicine_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each medicine",
          "optimization_purpose": "Links to decision variable x[medicine_id]",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "is_selected": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates whether the medicine is selected",
          "optimization_purpose": "Binary decision variable x[medicine_id]",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "max_adverse_interaction_score": {
    "data_type": "FLOAT",
    "business_meaning": "Maximum allowed total adverse interaction score",
    "optimization_role": "Upper bound for the adverse interaction constraint",
    "configuration_type": "scalar_parameter",
    "value": 0.5,
    "business_justification": "A realistic upper limit for total adverse interactions, ensuring patient safety."
  },
  "max_selected_medicines": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of medicines that can be selected",
    "optimization_role": "Upper bound for the selection count constraint",
    "configuration_type": "scalar_parameter",
    "value": 3,
    "business_justification": "A practical limit on the number of medicines to manage trial complexity."
  }
}

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: x[medicine_id] ∈ {0, 1} (binary decision variable indicating whether medicine_id is selected)
- Operational parameters align with expected linear objective: maximize ∑(effectiveness_score[medicine_id] × x[medicine_id])
- Business configuration includes: Maximum allowed total adverse interaction score (used for Upper bound for the adverse interaction constraint), Maximum number of medicines that can be selected (used for Upper bound for the selection count constraint)
- 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 ∑(effectiveness_score[medicine_id] × x[medicine_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: ['∑(adverse_interaction_score[medicine_id] × x[medicine_id]) ≤ max_adverse_interaction_score', '∑(x[medicine_id]) ≤ max_selected_medicines', 'x[medicine_id] ≤ FDA_approved[medicine_id] for all medicine_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 3 Database Schema
-- Objective: Schema changes include adding missing scalar parameters to business configuration logic and ensuring all optimization mappings are complete. No table modifications or deletions were necessary.

CREATE TABLE medicine_effectiveness (
  medicine_id INTEGER,
  effectiveness_score FLOAT
);

CREATE TABLE medicine_adverse_interaction (
  medicine_id INTEGER,
  adverse_interaction_score FLOAT
);

CREATE TABLE medicine (
  medicine_id INTEGER,
  FDA_approved BOOLEAN
);

CREATE TABLE medicine_selection (
  medicine_id INTEGER,
  is_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 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic pharmaceutical data, ensuring effectiveness scores and adverse interaction scores are within plausible ranges. The number of medicines and their FDA approval statuses were chosen to reflect a typical clinical trial scenario.

-- Realistic data for medicine_effectiveness
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (1, 0.85);
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (2, 0.75);
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (3, 0.9);

-- Realistic data for medicine_adverse_interaction
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (1, 0.15);
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (2, 0.25);
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (3, 0.1);

-- Realistic data for medicine
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (1, True);
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (2, False);
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (3, True);

-- Realistic data for medicine_selection
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (1, False);
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (2, False);
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (3, False);


```

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 preparing for a clinical trial and needs to select a combination of medicines that maximizes the overall effectiveness of the treatment while ensuring patient safety and managing trial complexity. Each medicine has a known effectiveness score, which quantifies its potential benefit, and an adverse interaction score, which measures its potential risks when combined with other medicines. The company must decide which medicines to include in the trial, with the decision for each medicine being binary—either it is selected or it is not.

The selection process is guided by two critical operational parameters:  
1. **Maximum Allowed Total Adverse Interaction Score**: The total adverse interaction score of all selected medicines must not exceed 0.5, ensuring patient safety.  
2. **Maximum Number of Medicines That Can Be Selected**: No more than 3 medicines can be included in the trial to manage complexity and resource allocation.  

Additionally, only medicines that are FDA-approved are eligible for selection. The company aims to make these decisions in a way that maximizes the total effectiveness score of the selected medicines while adhering to these constraints.

### Goals  
The primary goal of this optimization problem is to maximize the total effectiveness score of the medicines selected for the clinical trial. This is achieved by carefully choosing which medicines to include, ensuring that their combined effectiveness is as high as possible. Success is measured by the sum of the effectiveness scores of the selected medicines, with higher values indicating a more effective treatment combination. The optimization process ensures that this goal is achieved while respecting the constraints on adverse interactions, the number of medicines, and FDA approval status.

## 2. Constraints  

The selection of medicines for the clinical trial is subject to the following constraints:  
1. **Adverse Interaction Limit**: The total adverse interaction score of all selected medicines must not exceed the maximum allowed value of 0.5. This ensures that the combined risk of the selected medicines remains within safe limits.  
2. **Medicine Count Limit**: The total number of medicines selected for the trial must not exceed the maximum allowed value of 3. This constraint helps manage the complexity and resource requirements of the trial.  
3. **FDA Approval Requirement**: Only medicines that are FDA-approved can be selected for the trial. This ensures that all included medicines meet regulatory standards for safety and efficacy.  

These constraints ensure that the selected combination of medicines is both effective and safe, while also being practical to implement in a clinical trial setting.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 3 Database Schema
-- Objective: Schema changes include adding missing scalar parameters to business configuration logic and ensuring all optimization mappings are complete. No table modifications or deletions were necessary.

CREATE TABLE medicine_effectiveness (
  medicine_id INTEGER,
  effectiveness_score FLOAT
);

CREATE TABLE medicine_adverse_interaction (
  medicine_id INTEGER,
  adverse_interaction_score FLOAT
);

CREATE TABLE medicine (
  medicine_id INTEGER,
  FDA_approved BOOLEAN
);

CREATE TABLE medicine_selection (
  medicine_id INTEGER,
  is_selected BOOLEAN
);
```

### Data Dictionary  
- **medicine_effectiveness**:  
  - **Purpose**: Stores the effectiveness scores of medicines based on enzyme interactions.  
  - **Columns**:  
    - `medicine_id`: Unique identifier for each medicine.  
    - `effectiveness_score`: Quantifies the potential benefit of the medicine.  

- **medicine_adverse_interaction**:  
  - **Purpose**: Stores the adverse interaction scores of medicines based on enzyme interactions.  
  - **Columns**:  
    - `medicine_id`: Unique identifier for each medicine.  
    - `adverse_interaction_score`: Measures the potential risk of the medicine when combined with others.  

- **medicine**:  
  - **Purpose**: Lists all medicines along with their FDA approval status.  
  - **Columns**:  
    - `medicine_id`: Unique identifier for each medicine.  
    - `FDA_approved`: Indicates whether the medicine is approved by the FDA.  

- **medicine_selection**:  
  - **Purpose**: Tracks the selection status of each medicine for the clinical trial.  
  - **Columns**:  
    - `medicine_id`: Unique identifier for each medicine.  
    - `is_selected`: Indicates whether the medicine has been selected for the trial.  

### Current Stored Values  
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic pharmaceutical data, ensuring effectiveness scores and adverse interaction scores are within plausible ranges. The number of medicines and their FDA approval statuses were chosen to reflect a typical clinical trial scenario.

-- Realistic data for medicine_effectiveness
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (1, 0.85);
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (2, 0.75);
INSERT INTO medicine_effectiveness (medicine_id, effectiveness_score) VALUES (3, 0.9);

-- Realistic data for medicine_adverse_interaction
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (1, 0.15);
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (2, 0.25);
INSERT INTO medicine_adverse_interaction (medicine_id, adverse_interaction_score) VALUES (3, 0.1);

-- Realistic data for medicine
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (1, True);
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (2, False);
INSERT INTO medicine (medicine_id, FDA_approved) VALUES (3, True);

-- Realistic data for medicine_selection
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (1, False);
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (2, False);
INSERT INTO medicine_selection (medicine_id, is_selected) VALUES (3, False);
```
