Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-28 00:21:27

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: x[journalist_ID, Event_ID] are binary variables indicating if journalist covers the event
- Operational parameters align with expected linear objective: maximize ∑(Event_Attendance[Event_ID] × x[journalist_ID, Event_ID])
- Business configuration includes: Maximum number of events a journalist can cover (used for Constraint bound in optimization model), Total number of journalists available (used for 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": "news_report",
  "iteration": 1,
  "business_context": "A news agency wants to optimize the allocation of journalists to events to maximize the total event attendance covered by journalists, considering constraints on the number of events a journalist can cover and the total number of journalists available.",
  "optimization_problem_description": "Maximize the total event attendance covered by journalists, subject to constraints on the number of events each journalist can cover and the total number of journalists available.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Event_Attendance[Event_ID] \u00d7 x[journalist_ID, Event_ID])",
    "decision_variables": "x[journalist_ID, Event_ID] are binary variables indicating if journalist covers the event",
    "constraints": [
      "\u2211(x[journalist_ID, Event_ID]) <= max_events_per_journalist for each journalist_ID",
      "\u2211(x[journalist_ID, Event_ID]) <= total_journalists for each Event_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Event_Attendance[Event_ID]": {
        "currently_mapped_to": "event.Event_Attendance",
        "mapping_adequacy": "good",
        "description": "Number of attendees expected at the event"
      }
    },
    "constraint_bounds": {
      "max_events_per_journalist": {
        "currently_mapped_to": "business_configuration_logic.max_events_per_journalist",
        "mapping_adequacy": "good",
        "description": "Maximum number of events a journalist can cover"
      },
      "total_journalists": {
        "currently_mapped_to": "business_configuration_logic.total_journalists",
        "mapping_adequacy": "good",
        "description": "Total number of journalists available"
      }
    },
    "decision_variables": {
      "x[journalist_ID, Event_ID]": {
        "currently_mapped_to": "journalist_event_assignment.journalist_ID, journalist_event_assignment.Event_ID",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if a journalist 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 1 Database Schema
-- Objective: Schema changes include creating new tables for missing constraint bounds and modifying existing tables to better map decision variables. Configuration logic updates include moving scalar parameters to JSON for better management.

CREATE TABLE event (
  Event_ID INTEGER,
  Event_Attendance INTEGER
);

CREATE TABLE journalist_event_assignment (
  journalist_ID INTEGER,
  Event_ID INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were chosen to reflect a realistic scenario where journalists cover events with varying attendance, ensuring constraints are met and the optimization problem is solvable.

-- Realistic data for event
INSERT INTO event (Event_ID, Event_Attendance) VALUES (1, 150);
INSERT INTO event (Event_ID, Event_Attendance) VALUES (2, 250);
INSERT INTO event (Event_ID, Event_Attendance) VALUES (3, 100);

-- Realistic data for journalist_event_assignment
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (1, 1);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (1, 2);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (2, 2);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (2, 3);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (3, 1);


```

DATA DICTIONARY:
{
  "tables": {
    "event": {
      "business_purpose": "Stores information about events including attendance",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Event_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each event",
          "optimization_purpose": "Index for objective coefficients",
          "sample_values": "1, 2, 3"
        },
        "Event_Attendance": {
          "data_type": "INTEGER",
          "business_meaning": "Number of attendees expected at the event",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "journalist_event_assignment": {
      "business_purpose": "Tracks assignments of journalists to events",
      "optimization_role": "decision_variables",
      "columns": {
        "journalist_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each journalist",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "Event_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each event",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "max_events_per_journalist": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of events a journalist can cover",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 3,
    "business_justification": "Allows journalists to cover multiple events without overburdening them, reflecting typical workload capacity."
  },
  "total_journalists": {
    "data_type": "INTEGER",
    "business_meaning": "Total number of journalists available",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 5,
    "business_justification": "Reflects a small to medium-sized news agency with a limited number of journalists available for event coverage."
  }
}

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: news_report

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: x[journalist_ID, Event_ID] are binary variables indicating if journalist covers the event
- Operational parameters align with expected linear objective: maximize ∑(Event_Attendance[Event_ID] × x[journalist_ID, Event_ID])
- Business configuration includes: Maximum number of events a journalist can cover (used for Constraint bound in optimization model), Total number of journalists available (used for 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 ∑(Event_Attendance[Event_ID] × x[journalist_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[journalist_ID, Event_ID]) <= max_events_per_journalist for each journalist_ID', '∑(x[journalist_ID, Event_ID]) <= total_journalists 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 1 Database Schema
-- Objective: Schema changes include creating new tables for missing constraint bounds and modifying existing tables to better map decision variables. Configuration logic updates include moving scalar parameters to JSON for better management.

CREATE TABLE event (
  Event_ID INTEGER,
  Event_Attendance INTEGER
);

CREATE TABLE journalist_event_assignment (
  journalist_ID INTEGER,
  Event_ID 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 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were chosen to reflect a realistic scenario where journalists cover events with varying attendance, ensuring constraints are met and the optimization problem is solvable.

-- Realistic data for event
INSERT INTO event (Event_ID, Event_Attendance) VALUES (1, 150);
INSERT INTO event (Event_ID, Event_Attendance) VALUES (2, 250);
INSERT INTO event (Event_ID, Event_Attendance) VALUES (3, 100);

-- Realistic data for journalist_event_assignment
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (1, 1);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (1, 2);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (2, 2);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (2, 3);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (3, 1);


```

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

Response:
# Complete Optimization Problem and Solution: news_report

## 1. Problem Context and Goals

### Context  
The news agency is focused on optimizing the allocation of its journalists to various events. The primary decision involves determining whether a journalist should cover a specific event, represented by binary decisions for each journalist-event pair. The agency aims to maximize the total attendance at events covered by journalists, which is a linear objective. The operational parameters include the maximum number of events a journalist can cover and the total number of journalists available. These parameters are crucial for setting the constraints in the optimization model. The business configuration specifies that each journalist can cover up to a certain number of events, ensuring they are not overburdened, and reflects the total number of journalists available for assignments. This setup ensures that the problem remains linear, avoiding any nonlinear relationships such as variable products or divisions.

### Goals  
The primary goal of the optimization is to maximize the total attendance at events covered by journalists. This involves maximizing the sum of the expected attendance at each event that a journalist covers. The success of this optimization is measured by the total attendance achieved, aligning with the expected coefficients derived from event attendance data. The objective is clearly defined in linear terms, focusing on maximizing the sum of attendance figures for events covered by journalists.

## 2. Constraints    

The constraints for this optimization problem are straightforward and linear. Each journalist can cover a limited number of events, ensuring they are not overworked. This is represented by a constraint that limits the sum of events assigned to each journalist to the maximum number of events they can cover. Additionally, the total number of journalists available imposes a constraint on the number of journalists that can be assigned to each event. These constraints are expressed in business terms that naturally lead to linear mathematical forms, ensuring the problem remains within the realm of linear optimization.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing constraint bounds and modifying existing tables to better map decision variables. Configuration logic updates include moving scalar parameters to JSON for better management.

CREATE TABLE event (
  Event_ID INTEGER,
  Event_Attendance INTEGER
);

CREATE TABLE journalist_event_assignment (
  journalist_ID INTEGER,
  Event_ID INTEGER
);
```

### Data Dictionary  
The data dictionary provides a business-oriented view of the tables and columns, mapping them to their purposes and roles in the optimization process. 

- **Event Table**: This table stores information about each event, including the expected number of attendees. The Event_ID serves as a unique identifier for each event, while the Event_Attendance column provides the attendance figures used as coefficients in the optimization objective.

- **Journalist Event Assignment Table**: This table tracks which journalists are assigned to which events. The journalist_ID and Event_ID columns serve as indices for the decision variables, indicating the assignment of journalists to events.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were chosen to reflect a realistic scenario where journalists cover events with varying attendance, ensuring constraints are met and the optimization problem is solvable.

-- Realistic data for event
INSERT INTO event (Event_ID, Event_Attendance) VALUES (1, 150);
INSERT INTO event (Event_ID, Event_Attendance) VALUES (2, 250);
INSERT INTO event (Event_ID, Event_Attendance) VALUES (3, 100);

-- Realistic data for journalist_event_assignment
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (1, 1);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (1, 2);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (2, 2);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (2, 3);
INSERT INTO journalist_event_assignment (journalist_ID, Event_ID) VALUES (3, 1);
```
