Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-27 22:41:29

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: assignment[member_id, event_id] are binary variables indicating if a member is assigned to an event
- Operational parameters align with expected linear objective: maximize total_effectiveness = sum(efficiency_score[member_id, event_id] * assignment[member_id, event_id])
- Business configuration includes: Maximum number of members that can be assigned to a single event (used for Used as a constraint bound 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": "party_people",
  "iteration": 2,
  "business_context": "A political organization is optimizing the allocation of its members to various party events to maximize the overall effectiveness of the events. Each member has a certain effectiveness score for each event, and the goal is to assign members to events in a way that maximizes the total effectiveness while respecting constraints such as the number of members per event and availability.",
  "optimization_problem_description": "The problem is to maximize the total effectiveness of party events by optimally assigning members to events. Each member has a specific effectiveness score for each event, and the assignment must respect constraints such as the maximum number of members per event and the availability of members.",
  "optimization_formulation": {
    "objective": "maximize total_effectiveness = sum(efficiency_score[member_id, event_id] * assignment[member_id, event_id])",
    "decision_variables": "assignment[member_id, event_id] are binary variables indicating if a member is assigned to an event",
    "constraints": [
      "sum(assignment[member_id, event_id]) <= max_members_per_event for each event_id",
      "assignment[member_id, event_id] <= is_available[member_id, event_id] for each member_id, event_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "efficiency_score[member_id, event_id]": {
        "currently_mapped_to": "effectiveness_scores.efficiency_score",
        "mapping_adequacy": "good",
        "description": "Effectiveness score of a member for a specific event"
      }
    },
    "constraint_bounds": {
      "max_members_per_event[event_id]": {
        "currently_mapped_to": "party_events.max_members_per_event",
        "mapping_adequacy": "good",
        "description": "Maximum number of members that can be assigned to the event"
      },
      "is_available[member_id, event_id]": {
        "currently_mapped_to": "member_availability.is_available",
        "mapping_adequacy": "good",
        "description": "Indicates if a member is available for an event"
      }
    },
    "decision_variables": {
      "assignment[member_id, event_id]": {
        "currently_mapped_to": "member_event_assignments.assignment",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if a member is assigned to an event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for decision variables, modifying existing tables to better map decision variables, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE effectiveness_scores (
  member_id INTEGER,
  event_id INTEGER,
  efficiency_score FLOAT
);

CREATE TABLE member_availability (
  member_id INTEGER,
  event_id INTEGER,
  is_available BOOLEAN
);

CREATE TABLE party_events (
  event_id INTEGER,
  Member_in_charge_ID INTEGER,
  max_members_per_event INTEGER
);

CREATE TABLE member_event_assignments (
  member_id INTEGER,
  event_id INTEGER,
  assignment BOOLEAN
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical event sizes and member availability patterns in political organizations, ensuring a balance between event capacity and member effectiveness.

-- Realistic data for effectiveness_scores
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (1, 101, 0.85);
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (2, 102, 0.95);
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (3, 103, 0.75);

-- Realistic data for member_availability
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (1, 101, True);
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (2, 102, False);
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (3, 103, True);

-- Realistic data for party_events
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (101, 1, 50);
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (102, 2, 100);
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (103, 3, 150);

-- Realistic data for member_event_assignments
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (1, 101, True);
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (2, 102, False);
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (3, 103, True);


```

DATA DICTIONARY:
{
  "tables": {
    "effectiveness_scores": {
      "business_purpose": "Stores effectiveness scores of members for each event",
      "optimization_role": "objective_coefficients",
      "columns": {
        "member_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member",
          "optimization_purpose": "Index for effectiveness scores",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for an event",
          "optimization_purpose": "Index for effectiveness scores",
          "sample_values": "101, 102, 103"
        },
        "efficiency_score": {
          "data_type": "FLOAT",
          "business_meaning": "Effectiveness score of a member for a specific event",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "0.8, 0.9, 1.0"
        }
      }
    },
    "member_availability": {
      "business_purpose": "Indicates availability of members for events",
      "optimization_role": "constraint_bounds",
      "columns": {
        "member_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member",
          "optimization_purpose": "Index for availability",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for an event",
          "optimization_purpose": "Index for availability",
          "sample_values": "101, 102, 103"
        },
        "is_available": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a member is available for an event",
          "optimization_purpose": "Constraint in optimization model",
          "sample_values": "true, false"
        }
      }
    },
    "party_events": {
      "business_purpose": "Stores information about party events",
      "optimization_role": "business_data",
      "columns": {
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for an event",
          "optimization_purpose": "Index for event data",
          "sample_values": "101, 102, 103"
        },
        "Member_in_charge_ID": {
          "data_type": "INTEGER",
          "business_meaning": "ID of the member in charge of the event",
          "optimization_purpose": "Decision variable mapping",
          "sample_values": "1, 2, 3"
        },
        "max_members_per_event": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of members that can be assigned to the event",
          "optimization_purpose": "Constraint bound",
          "sample_values": "50, 100, 150"
        }
      }
    },
    "member_event_assignments": {
      "business_purpose": "Stores binary decision variables indicating member assignments to events",
      "optimization_role": "decision_variables",
      "columns": {
        "member_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for an event",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "101, 102, 103"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Binary variable indicating if a member is assigned to an event",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "max_members_per_event": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of members that can be assigned to a single event",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 100,
    "business_justification": "A value of 100 is realistic for large events, allowing for significant participation while maintaining manageability."
  }
}

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: party_people

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: assignment[member_id, event_id] are binary variables indicating if a member is assigned to an event
- Operational parameters align with expected linear objective: maximize total_effectiveness = sum(efficiency_score[member_id, event_id] * assignment[member_id, event_id])
- Business configuration includes: Maximum number of members that can be assigned to a single event (used for Used as a constraint bound 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 total_effectiveness = sum(efficiency_score[member_id, event_id] * assignment[member_id, event_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(assignment[member_id, event_id]) <= max_members_per_event for each event_id', 'assignment[member_id, event_id] <= is_available[member_id, event_id] for each member_id, event_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: Schema changes include creating a new table for decision variables, modifying existing tables to better map decision variables, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE effectiveness_scores (
  member_id INTEGER,
  event_id INTEGER,
  efficiency_score FLOAT
);

CREATE TABLE member_availability (
  member_id INTEGER,
  event_id INTEGER,
  is_available BOOLEAN
);

CREATE TABLE party_events (
  event_id INTEGER,
  Member_in_charge_ID INTEGER,
  max_members_per_event INTEGER
);

CREATE TABLE member_event_assignments (
  member_id INTEGER,
  event_id INTEGER,
  assignment 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 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical event sizes and member availability patterns in political organizations, ensuring a balance between event capacity and member effectiveness.

-- Realistic data for effectiveness_scores
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (1, 101, 0.85);
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (2, 102, 0.95);
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (3, 103, 0.75);

-- Realistic data for member_availability
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (1, 101, True);
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (2, 102, False);
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (3, 103, True);

-- Realistic data for party_events
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (101, 1, 50);
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (102, 2, 100);
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (103, 3, 150);

-- Realistic data for member_event_assignments
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (1, 101, True);
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (2, 102, False);
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (3, 103, True);


```

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

Response:
# Complete Optimization Problem and Solution: party_people

## 1. Problem Context and Goals

### Context  
A political organization is focused on enhancing the effectiveness of its events by strategically assigning its members to various party events. Each member has a unique effectiveness score for each event, reflecting their potential contribution to the event's success. The organization aims to assign members to events in a manner that maximizes the overall effectiveness of these events. This involves making decisions about which members to assign to which events, represented by binary decision variables indicating whether a member is assigned to an event. The operational parameters include maximizing the total effectiveness, which is the sum of the effectiveness scores of assigned members. The business configuration includes a constraint on the maximum number of members that can be assigned to a single event, ensuring that no event is overstaffed. This constraint is crucial for maintaining the quality and manageability of the events. The organization must also consider the availability of members, ensuring that assignments are only made if a member is available for a particular event. These decisions and constraints are framed in a linear optimization model, focusing on precise operational decision-making without involving nonlinear relationships.

### Goals  
The primary goal of the optimization is to maximize the total effectiveness of the party events. This is achieved by optimally assigning members to events based on their effectiveness scores. The success of this optimization is measured by the total effectiveness, which is the sum of the effectiveness scores of all assigned members. The objective is to ensure that the assignments lead to the highest possible total effectiveness, aligning with the expected coefficient sources. This goal is articulated in natural language, focusing on the linear optimization objective without using mathematical formulas or symbolic notation.

## 2. Constraints    

The optimization problem is subject to several constraints that ensure the feasibility and practicality of the assignments:

- Each event has a maximum number of members that can be assigned, which is determined by the event's capacity. This constraint ensures that no event is overstaffed, maintaining the quality and manageability of the event.
- Members can only be assigned to events if they are available. This constraint respects the availability of members, ensuring that assignments are feasible and realistic.

These constraints are described in business terms that naturally lead to linear mathematical forms, avoiding any nonlinear relationships.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for decision variables, modifying existing tables to better map decision variables, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE effectiveness_scores (
  member_id INTEGER,
  event_id INTEGER,
  efficiency_score FLOAT
);

CREATE TABLE member_availability (
  member_id INTEGER,
  event_id INTEGER,
  is_available BOOLEAN
);

CREATE TABLE party_events (
  event_id INTEGER,
  Member_in_charge_ID INTEGER,
  max_members_per_event INTEGER
);

CREATE TABLE member_event_assignments (
  member_id INTEGER,
  event_id INTEGER,
  assignment BOOLEAN
);
```

### Data Dictionary  
The data dictionary provides a comprehensive mapping of tables and columns to their business purposes and optimization roles:

- **Effectiveness Scores**: This table stores the effectiveness scores of members for each event. These scores are used as coefficients in the objective function to determine the total effectiveness of the assignments.
  - **Member ID**: A unique identifier for each member, used as an index for effectiveness scores.
  - **Event ID**: A unique identifier for each event, used as an index for effectiveness scores.
  - **Efficiency Score**: The effectiveness score of a member for a specific event, serving as a coefficient in the objective function.

- **Member Availability**: This table indicates the availability of members for events, serving as a constraint in the optimization model.
  - **Member ID**: A unique identifier for each member, used as an index for availability.
  - **Event ID**: A unique identifier for each event, used as an index for availability.
  - **Is Available**: A boolean indicating if a member is available for an event, used as a constraint in the optimization model.

- **Party Events**: This table stores information about party events, including the maximum number of members that can be assigned to each event.
  - **Event ID**: A unique identifier for each event, used as an index for event data.
  - **Member in Charge ID**: The ID of the member in charge of the event, used for decision variable mapping.
  - **Max Members per Event**: The maximum number of members that can be assigned to the event, serving as a constraint bound.

- **Member Event Assignments**: This table stores binary decision variables indicating member assignments to events.
  - **Member ID**: A unique identifier for each member, used as an index for decision variables.
  - **Event ID**: A unique identifier for each event, used as an index for decision variables.
  - **Assignment**: A binary variable indicating if a member is assigned to an event, serving as a decision variable in the optimization model.

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical event sizes and member availability patterns in political organizations, ensuring a balance between event capacity and member effectiveness.

-- Realistic data for effectiveness_scores
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (1, 101, 0.85);
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (2, 102, 0.95);
INSERT INTO effectiveness_scores (member_id, event_id, efficiency_score) VALUES (3, 103, 0.75);

-- Realistic data for member_availability
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (1, 101, True);
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (2, 102, False);
INSERT INTO member_availability (member_id, event_id, is_available) VALUES (3, 103, True);

-- Realistic data for party_events
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (101, 1, 50);
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (102, 2, 100);
INSERT INTO party_events (event_id, Member_in_charge_ID, max_members_per_event) VALUES (103, 3, 150);

-- Realistic data for member_event_assignments
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (1, 101, True);
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (2, 102, False);
INSERT INTO member_event_assignments (member_id, event_id, assignment) VALUES (3, 103, True);
```
