Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:46:12

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: ship_1

```sql
CREATE TABLE captain (
  Captain_ID NUMBER,
  Name TEXT,
  Ship_ID NUMBER,
  age TEXT,
  Class TEXT,
  Rank TEXT
);
```

```sql
CREATE TABLE Ship (
  Ship_ID NUMBER,
  Name TEXT,
  Type TEXT,
  Built_Year NUMBER,
  Class TEXT,
  Flag TEXT
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "ship_1",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing", 
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "ship_1",
  "iteration": 0,
  "business_context": "A shipping company aims to minimize the total operational cost of its fleet by optimally assigning captains to ships, considering factors such as captain rank, ship type, and ship age.",
  "optimization_problem_description": "The company wants to minimize the total cost of assigning captains to ships, where the cost depends on the captain's rank and the ship's type and age. The assignment must respect constraints such as each ship being assigned exactly one captain and each captain being assigned to at most one ship.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_coefficient[c][s] \u00d7 assign[c][s]) where cost_coefficient[c][s] is the cost of assigning captain c to ship s, and assign[c][s] is a binary decision variable indicating whether captain c is assigned to ship s.",
    "decision_variables": "assign[c][s]: binary variable indicating if captain c is assigned to ship s.",
    "constraints": [
      "\u2211(assign[c][s] for all c) = 1 for each ship s (each ship must have exactly one captain)",
      "\u2211(assign[c][s] for all s) \u2264 1 for each captain c (each captain can be assigned to at most one ship)",
      "assign[c][s] = 0 if captain c's rank is incompatible with ship s's type (predefined compatibility rules)",
      "assign[c][s] = 0 if ship s's age exceeds a certain threshold for captain c's rank (predefined age rules)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_coefficient[c][s]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Cost of assigning captain c to ship s, based on rank, type, and age."
      }
    },
    "constraint_bounds": {
      "ship_assignment[s]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Each ship must have exactly one captain."
      },
      "captain_assignment[c]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Each captain can be assigned to at most one ship."
      },
      "compatibility[c][s]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Predefined compatibility rules between captain rank and ship type."
      },
      "age_limit[c][s]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Predefined age rules for ship age and captain rank."
      }
    },
    "decision_variables": {
      "assign[c][s]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if captain c is assigned to ship s.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Cost coefficients for assigning captains to ships based on rank, type, and age.",
    "Compatibility rules between captain rank and ship type.",
    "Age rules for ship age and captain rank."
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define cost coefficients, compatibility rules, and age rules to complete the optimization model."
  }
}
