Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-27 21:40:57

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: x[swimmer_id, event_id] are binary variables indicating if swimmer_id is assigned to event_id
- Operational parameters align with expected linear objective: maximize total_performance_score = ∑(performance_score[swimmer_id, event_id] × x[swimmer_id, event_id])
- Business configuration includes: Maximum number of events a swimmer can participate in (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": "swimming",
  "iteration": 2,
  "business_context": "Optimize the allocation of swimmers to events to maximize the overall performance score, considering stadium capacity and swimmer participation limits.",
  "optimization_problem_description": "Maximize the total performance score of swimmers across events while ensuring each event does not exceed stadium capacity and each swimmer participates in a limited number of events.",
  "optimization_formulation": {
    "objective": "maximize total_performance_score = \u2211(performance_score[swimmer_id, event_id] \u00d7 x[swimmer_id, event_id])",
    "decision_variables": "x[swimmer_id, event_id] are binary variables indicating if swimmer_id is assigned to event_id",
    "constraints": [
      "\u2211(x[swimmer_id, event_id]) <= max_events_per_swimmer for each swimmer_id",
      "\u2211(x[swimmer_id, event_id]) <= capacity[event_id] for each event_id"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "performance_score[swimmer_id, event_id]": {
        "currently_mapped_to": "PerformanceScores.performance_score",
        "mapping_adequacy": "good",
        "description": "Performance score of a swimmer in an event"
      }
    },
    "constraint_bounds": {
      "max_events_per_swimmer": {
        "currently_mapped_to": "business_configuration_logic.max_events_per_swimmer",
        "mapping_adequacy": "good",
        "description": "Maximum number of events a swimmer can participate in"
      },
      "capacity[event_id]": {
        "currently_mapped_to": "StadiumCapacities.capacity",
        "mapping_adequacy": "good",
        "description": "Capacity of the stadium for the event"
      }
    },
    "decision_variables": {
      "x[swimmer_id, event_id]": {
        "currently_mapped_to": "SwimmerEventAssignments.assignment",
        "mapping_adequacy": "good",
        "description": "Indicates if a swimmer 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: Added StadiumCapacities table to address missing stadium capacity data requirement and updated business configuration logic for scalar parameters.

CREATE TABLE PerformanceScores (
  swimmer_id INTEGER,
  event_id INTEGER,
  performance_score FLOAT
);

CREATE TABLE SwimmerEventAssignments (
  swimmer_id INTEGER,
  event_id INTEGER,
  assignment BOOLEAN
);

CREATE TABLE StadiumCapacities (
  event_id INTEGER,
  capacity INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical swimming event sizes, swimmer capabilities, and stadium capacities to ensure a balanced and realistic optimization scenario.

-- Realistic data for PerformanceScores
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (1, 101, 9.5);
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (2, 102, 8.7);
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (3, 103, 9.0);

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

-- Realistic data for StadiumCapacities
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (101, 500);
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (102, 1000);
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (103, 1500);


```

DATA DICTIONARY:
{
  "tables": {
    "PerformanceScores": {
      "business_purpose": "Stores performance scores for each swimmer in each event",
      "optimization_role": "objective_coefficients",
      "columns": {
        "swimmer_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each swimmer",
          "optimization_purpose": "Index for performance scores",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each event",
          "optimization_purpose": "Index for performance scores",
          "sample_values": "101, 102, 103"
        },
        "performance_score": {
          "data_type": "FLOAT",
          "business_meaning": "Performance score of a swimmer in an event",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "9.5, 8.7, 9.0"
        }
      }
    },
    "SwimmerEventAssignments": {
      "business_purpose": "Tracks which swimmers are assigned to which events",
      "optimization_role": "decision_variables",
      "columns": {
        "swimmer_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each swimmer",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each event",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "101, 102, 103"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a swimmer is assigned to an event",
          "optimization_purpose": "Binary decision variable",
          "sample_values": "true, false"
        }
      }
    },
    "StadiumCapacities": {
      "business_purpose": "Stores the capacity of each event's stadium",
      "optimization_role": "constraint_bounds",
      "columns": {
        "event_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each event",
          "optimization_purpose": "Index for stadium capacities",
          "sample_values": "101, 102, 103"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Capacity of the stadium for the event",
          "optimization_purpose": "Constraint bound for event capacity",
          "sample_values": "500, 1000, 1500"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "max_events_per_swimmer": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of events a swimmer can participate in",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 3,
    "business_justification": "Allowing each swimmer to participate in up to 3 events ensures a balance between maximizing participation and maintaining performance quality."
  }
}

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: swimming

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: x[swimmer_id, event_id] are binary variables indicating if swimmer_id is assigned to event_id
- Operational parameters align with expected linear objective: maximize total_performance_score = ∑(performance_score[swimmer_id, event_id] × x[swimmer_id, event_id])
- Business configuration includes: Maximum number of events a swimmer can participate in (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_performance_score = ∑(performance_score[swimmer_id, event_id] × x[swimmer_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: ['∑(x[swimmer_id, event_id]) <= max_events_per_swimmer for each swimmer_id', '∑(x[swimmer_id, event_id]) <= capacity[event_id] for each 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: Added StadiumCapacities table to address missing stadium capacity data requirement and updated business configuration logic for scalar parameters.

CREATE TABLE PerformanceScores (
  swimmer_id INTEGER,
  event_id INTEGER,
  performance_score FLOAT
);

CREATE TABLE SwimmerEventAssignments (
  swimmer_id INTEGER,
  event_id INTEGER,
  assignment BOOLEAN
);

CREATE TABLE StadiumCapacities (
  event_id INTEGER,
  capacity 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 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical swimming event sizes, swimmer capabilities, and stadium capacities to ensure a balanced and realistic optimization scenario.

-- Realistic data for PerformanceScores
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (1, 101, 9.5);
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (2, 102, 8.7);
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (3, 103, 9.0);

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

-- Realistic data for StadiumCapacities
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (101, 500);
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (102, 1000);
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (103, 1500);


```

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

Response:
# Complete Optimization Problem and Solution: Swimming

## 1. Problem Context and Goals

### Context  
In the competitive swimming domain, the primary objective is to optimize the allocation of swimmers to various events to maximize the overall performance score. This involves making strategic decisions about which swimmers participate in which events. Each decision is represented by a binary choice, indicating whether a swimmer is assigned to a specific event. The operational goal is to maximize the total performance score, which is calculated by summing the performance scores of swimmers across all events they participate in. 

The business configuration includes a critical parameter: the maximum number of events a swimmer can participate in. This parameter ensures that swimmers are not over-committed, allowing them to maintain high performance levels. Additionally, each event is subject to stadium capacity constraints, ensuring that the number of participants does not exceed the venue's limits. These constraints are linear in nature, aligning with the overall linear optimization framework.

### Goals  
The primary goal of this optimization problem is to maximize the total performance score of swimmers across all events. This involves selecting the optimal set of swimmer-event assignments that yield the highest cumulative performance score. Success is measured by the total performance score achieved, which is directly influenced by the performance scores of individual swimmers in their respective events. The optimization process is linear, focusing on maximizing this score without involving complex mathematical operations.

## 2. Constraints    

The optimization problem is subject to two main constraints:

- Each swimmer can participate in a limited number of events, as defined by the maximum events per swimmer parameter. This ensures that no swimmer is over-committed, maintaining their ability to perform optimally.
  
- Each event has a stadium capacity limit, which restricts the number of swimmers that can participate in that event. This constraint ensures that the number of participants does not exceed the venue's capacity, maintaining safety and logistical feasibility.

These constraints are expressed in a linear form, ensuring that the optimization problem remains within the realm of linear programming.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Added StadiumCapacities table to address missing stadium capacity data requirement and updated business configuration logic for scalar parameters.

CREATE TABLE PerformanceScores (
  swimmer_id INTEGER,
  event_id INTEGER,
  performance_score FLOAT
);

CREATE TABLE SwimmerEventAssignments (
  swimmer_id INTEGER,
  event_id INTEGER,
  assignment BOOLEAN
);

CREATE TABLE StadiumCapacities (
  event_id INTEGER,
  capacity INTEGER
);
```

### Data Dictionary  
The data used in this optimization problem is structured into three main tables, each serving a specific business purpose:

- **PerformanceScores**: This table records the performance scores of swimmers in various events. Each entry includes a swimmer identifier, an event identifier, and the corresponding performance score. These scores serve as the coefficients in the objective function, representing the potential contribution of each swimmer-event assignment to the total performance score.

- **SwimmerEventAssignments**: This table tracks the assignments of swimmers to events. Each entry indicates whether a swimmer is assigned to a particular event. The assignment is a binary decision variable, reflecting the choice of whether a swimmer participates in an event.

- **StadiumCapacities**: This table contains the capacity limits for each event's venue. Each entry specifies the maximum number of participants allowed in an event, serving as a constraint bound 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 swimming event sizes, swimmer capabilities, and stadium capacities to ensure a balanced and realistic optimization scenario.

-- Realistic data for PerformanceScores
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (1, 101, 9.5);
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (2, 102, 8.7);
INSERT INTO PerformanceScores (swimmer_id, event_id, performance_score) VALUES (3, 103, 9.0);

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

-- Realistic data for StadiumCapacities
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (101, 500);
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (102, 1000);
INSERT INTO StadiumCapacities (event_id, capacity) VALUES (103, 1500);
```
