Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-25 22:38:12

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_ij: binary variable indicating whether ship i is assigned to mission j
- Operational parameters align with expected linear objective: minimize ∑(c_tonnage * Tonnage_i + c_speed * Speed_knots_i) * x_ij
- 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": "ship_mission",
  "iteration": 2,
  "business_context": "A shipping company aims to minimize the total operational cost of its fleet while ensuring that each ship meets specific mission requirements. The company needs to allocate ships to missions based on their tonnage, speed, and nationality constraints.",
  "optimization_problem_description": "The objective is to minimize the total operational cost of the fleet, which is a linear combination of the cost associated with each ship's tonnage and speed. The constraints ensure that each mission is assigned to exactly one ship, each ship is assigned to at most one mission, and the ship's tonnage and speed meet the mission requirements.",
  "optimization_formulation": {
    "objective": "minimize \u2211(c_tonnage * Tonnage_i + c_speed * Speed_knots_i) * x_ij",
    "decision_variables": "x_ij: binary variable indicating whether ship i is assigned to mission j",
    "constraints": [
      "\u2211 x_ij = 1 for all missions j (each mission is assigned to exactly one ship)",
      "\u2211 x_ij \u2264 1 for all ships i (each ship is assigned to at most one mission)",
      "Tonnage_i \u2265 min_tonnage_j * x_ij for all ships i and missions j (ship tonnage meets mission requirement)",
      "Speed_knots_i \u2265 min_speed_j * x_ij for all ships i and missions j (ship speed meets mission requirement)",
      "nationality_i = required_nationality_j * x_ij for all ships i and missions j (ship nationality meets mission requirement)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "c_tonnage": {
        "currently_mapped_to": "business_configuration_logic.key",
        "mapping_adequacy": "good",
        "description": "Cost coefficient associated with ship tonnage"
      },
      "c_speed": {
        "currently_mapped_to": "business_configuration_logic.key",
        "mapping_adequacy": "good",
        "description": "Cost coefficient associated with ship speed"
      }
    },
    "constraint_bounds": {
      "min_tonnage_j": {
        "currently_mapped_to": "missions.min_tonnage",
        "mapping_adequacy": "good",
        "description": "Minimum tonnage required for mission j"
      },
      "min_speed_j": {
        "currently_mapped_to": "missions.min_speed",
        "mapping_adequacy": "good",
        "description": "Minimum speed required for mission j"
      },
      "required_nationality_j": {
        "currently_mapped_to": "missions.required_nationality",
        "mapping_adequacy": "good",
        "description": "Required nationality for mission j"
      }
    },
    "decision_variables": {
      "x_ij": {
        "currently_mapped_to": "ship_mission_assignments.is_assigned",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating whether ship i is assigned to mission j",
        "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 a new table for ship-to-mission assignments to address the missing decision variable x_ij. Updated the data dictionary and business configuration logic to reflect these changes.

CREATE TABLE missions (
  mission_id INTEGER,
  min_tonnage INTEGER,
  min_speed INTEGER,
  required_nationality STRING
);

CREATE TABLE ships (
  ship_id INTEGER,
  tonnage INTEGER,
  speed_knots INTEGER,
  nationality STRING
);

CREATE TABLE ship_mission_assignments (
  ship_id INTEGER,
  mission_id INTEGER,
  is_assigned BOOLEAN
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic shipping industry standards, ensuring that ships meet mission requirements and that the optimization problem remains solvable. Parameters were set to reflect typical operational costs and constraints.

-- Realistic data for missions
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (1, 5000, 20, 'USA');
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (2, 6000, 25, 'UK');
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (3, 7000, 30, 'Canada');

-- Realistic data for ships
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (1, 5500, 22, 'USA');
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (2, 6500, 27, 'UK');
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (3, 7500, 32, 'Canada');

-- Realistic data for ship_mission_assignments
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (1, 1, True);
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (2, 2, True);
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (3, 3, True);


```

DATA DICTIONARY:
{
  "tables": {
    "missions": {
      "business_purpose": "Details of each mission including minimum tonnage, speed, and nationality requirements.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "mission_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each mission",
          "optimization_purpose": "Used to link missions to ships",
          "sample_values": "1, 2, 3"
        },
        "min_tonnage": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum tonnage required for the mission",
          "optimization_purpose": "Used in the tonnage constraint",
          "sample_values": "5000, 6000, 7000"
        },
        "min_speed": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum speed required for the mission",
          "optimization_purpose": "Used in the speed constraint",
          "sample_values": "20, 25, 30"
        },
        "required_nationality": {
          "data_type": "STRING",
          "business_meaning": "Required nationality for the mission",
          "optimization_purpose": "Used in the nationality constraint",
          "sample_values": "USA, UK, Canada"
        }
      }
    },
    "ships": {
      "business_purpose": "Details of each ship including tonnage, speed, and nationality.",
      "optimization_role": "business_data",
      "columns": {
        "ship_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each ship",
          "optimization_purpose": "Used to link ships to missions",
          "sample_values": "1, 2, 3"
        },
        "tonnage": {
          "data_type": "INTEGER",
          "business_meaning": "Tonnage of the ship",
          "optimization_purpose": "Used in the tonnage constraint",
          "sample_values": "5000, 6000, 7000"
        },
        "speed_knots": {
          "data_type": "INTEGER",
          "business_meaning": "Speed of the ship in knots",
          "optimization_purpose": "Used in the speed constraint",
          "sample_values": "20, 25, 30"
        },
        "nationality": {
          "data_type": "STRING",
          "business_meaning": "Nationality of the ship",
          "optimization_purpose": "Used in the nationality constraint",
          "sample_values": "USA, UK, Canada"
        }
      }
    },
    "ship_mission_assignments": {
      "business_purpose": "Assigns ships to missions based on optimization constraints.",
      "optimization_role": "decision_variables",
      "columns": {
        "ship_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each ship",
          "optimization_purpose": "Used to link ships to missions",
          "sample_values": "1, 2, 3"
        },
        "mission_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each mission",
          "optimization_purpose": "Used to link missions to ships",
          "sample_values": "1, 2, 3"
        },
        "is_assigned": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates whether the ship is assigned to the mission",
          "optimization_purpose": "Used as the decision variable x_ij",
          "sample_values": "true, false"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:


TASK: Create structured markdown documentation for SECTIONS 1-3 ONLY (Problem Description).

EXACT MARKDOWN STRUCTURE TO FOLLOW:

# Complete Optimization Problem and Solution: ship_mission

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: x_ij: binary variable indicating whether ship i is assigned to mission j
- Operational parameters align with expected linear objective: minimize ∑(c_tonnage * Tonnage_i + c_speed * Speed_knots_i) * x_ij
- 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: minimize
- Metric to optimize: minimize ∑(c_tonnage * Tonnage_i + c_speed * Speed_knots_i) * x_ij
- 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_ij = 1 for all missions j (each mission is assigned to exactly one ship)', '∑ x_ij ≤ 1 for all ships i (each ship is assigned to at most one mission)', 'Tonnage_i ≥ min_tonnage_j * x_ij for all ships i and missions j (ship tonnage meets mission requirement)', 'Speed_knots_i ≥ min_speed_j * x_ij for all ships i and missions j (ship speed meets mission requirement)', 'nationality_i = required_nationality_j * x_ij for all ships i and missions j (ship nationality meets mission requirement)'] (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 a new table for ship-to-mission assignments to address the missing decision variable x_ij. Updated the data dictionary and business configuration logic to reflect these changes.

CREATE TABLE missions (
  mission_id INTEGER,
  min_tonnage INTEGER,
  min_speed INTEGER,
  required_nationality STRING
);

CREATE TABLE ships (
  ship_id INTEGER,
  tonnage INTEGER,
  speed_knots INTEGER,
  nationality STRING
);

CREATE TABLE ship_mission_assignments (
  ship_id INTEGER,
  mission_id INTEGER,
  is_assigned 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 realistic shipping industry standards, ensuring that ships meet mission requirements and that the optimization problem remains solvable. Parameters were set to reflect typical operational costs and constraints.

-- Realistic data for missions
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (1, 5000, 20, 'USA');
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (2, 6000, 25, 'UK');
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (3, 7000, 30, 'Canada');

-- Realistic data for ships
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (1, 5500, 22, 'USA');
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (2, 6500, 27, 'UK');
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (3, 7500, 32, 'Canada');

-- Realistic data for ship_mission_assignments
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (1, 1, True);
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (2, 2, True);
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (3, 3, True);


```

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

Response:
# Complete Optimization Problem and Solution: ship_mission

## 1. Problem Context and Goals

### Context  
A shipping company operates a fleet of ships and needs to assign them to various missions efficiently. Each mission has specific requirements, including minimum tonnage, minimum speed, and a required nationality for the ship. The company aims to minimize the total operational cost of the fleet, which is influenced by the tonnage and speed of the ships assigned to missions. The cost is calculated as a weighted sum of the ship's tonnage and speed, where the weights are predefined cost coefficients. The company must ensure that each mission is assigned to exactly one ship and that each ship is assigned to at most one mission. Additionally, the assigned ship must meet the mission's tonnage, speed, and nationality requirements. The decision to assign a ship to a mission is represented by a binary indicator, which is the core decision variable in this problem.

### Goals  
The primary goal of this optimization problem is to minimize the total operational cost of the fleet. This cost is determined by the sum of the costs associated with the tonnage and speed of the ships assigned to missions. The cost coefficients for tonnage and speed are predefined and reflect the company's operational priorities. Success is measured by achieving the lowest possible total cost while ensuring that all mission requirements are met and that the assignment constraints are satisfied.

## 2. Constraints  

1. **Mission Assignment Constraint**: Each mission must be assigned to exactly one ship. This ensures that all missions are fulfilled without overlap or omission.  
2. **Ship Assignment Constraint**: Each ship can be assigned to at most one mission. This prevents overcommitment of ships and ensures efficient resource utilization.  
3. **Tonnage Requirement Constraint**: The tonnage of the ship assigned to a mission must meet or exceed the minimum tonnage required by the mission. This ensures that the ship has the necessary capacity to handle the mission.  
4. **Speed Requirement Constraint**: The speed of the ship assigned to a mission must meet or exceed the minimum speed required by the mission. This ensures that the ship can complete the mission within the required timeframe.  
5. **Nationality Requirement Constraint**: The nationality of the ship assigned to a mission must match the required nationality specified by the mission. This ensures compliance with regulatory or contractual obligations.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Added a new table for ship-to-mission assignments to address the missing decision variable x_ij. Updated the data dictionary and business configuration logic to reflect these changes.

CREATE TABLE missions (
  mission_id INTEGER,
  min_tonnage INTEGER,
  min_speed INTEGER,
  required_nationality STRING
);

CREATE TABLE ships (
  ship_id INTEGER,
  tonnage INTEGER,
  speed_knots INTEGER,
  nationality STRING
);

CREATE TABLE ship_mission_assignments (
  ship_id INTEGER,
  mission_id INTEGER,
  is_assigned BOOLEAN
);
```

### Data Dictionary  
- **Missions**: Contains details of each mission, including the minimum tonnage, minimum speed, and required nationality.  
  - `mission_id`: Unique identifier for each mission.  
  - `min_tonnage`: Minimum tonnage required for the mission.  
  - `min_speed`: Minimum speed required for the mission.  
  - `required_nationality`: Required nationality for the mission.  

- **Ships**: Contains details of each ship, including tonnage, speed, and nationality.  
  - `ship_id`: Unique identifier for each ship.  
  - `tonnage`: Tonnage of the ship.  
  - `speed_knots`: Speed of the ship in knots.  
  - `nationality`: Nationality of the ship.  

- **Ship Mission Assignments**: Tracks the assignment of ships to missions.  
  - `ship_id`: Unique identifier for each ship.  
  - `mission_id`: Unique identifier for each mission.  
  - `is_assigned`: Indicates whether the ship is assigned to the mission.  

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic shipping industry standards, ensuring that ships meet mission requirements and that the optimization problem remains solvable. Parameters were set to reflect typical operational costs and constraints.

-- Realistic data for missions
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (1, 5000, 20, 'USA');
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (2, 6000, 25, 'UK');
INSERT INTO missions (mission_id, min_tonnage, min_speed, required_nationality) VALUES (3, 7000, 30, 'Canada');

-- Realistic data for ships
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (1, 5500, 22, 'USA');
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (2, 6500, 27, 'UK');
INSERT INTO ships (ship_id, tonnage, speed_knots, nationality) VALUES (3, 7500, 32, 'Canada');

-- Realistic data for ship_mission_assignments
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (1, 1, True);
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (2, 2, True);
INSERT INTO ship_mission_assignments (ship_id, mission_id, is_assigned) VALUES (3, 3, True);
```
