Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:00:42

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_mission

```sql
CREATE TABLE mission (
  Mission_ID NUMBER,
  Ship_ID NUMBER,
  Code TEXT,
  Launched_Year NUMBER,
  Location TEXT,
  Speed_knots NUMBER,
  Fate TEXT
);
```

```sql
CREATE TABLE ship (
  Ship_ID NUMBER,
  Name TEXT,
  Type TEXT,
  Nationality TEXT,
  Tonnage NUMBER
);
```



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_mission",
  "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_mission",
  "iteration": 0,
  "business_context": "Optimize the allocation of ships to missions to minimize total operational costs while ensuring all missions are covered and ship capacities are not exceeded.",
  "optimization_problem_description": "The goal is to assign ships to missions in a way that minimizes the total cost of operations, considering factors such as ship speed and tonnage. Each mission must be covered by exactly one ship, and each ship can be assigned to at most one mission at a time. The operational cost is influenced by the speed of the ship and its tonnage.",
  "optimization_formulation": {
    "objective": "minimize total_operational_cost = \u2211(cost_per_knot[i] * Speed_knots[i] + cost_per_ton[i] * Tonnage[i])",
    "decision_variables": "x[i][j] = 1 if ship i is assigned to mission j, 0 otherwise (binary)",
    "constraints": [
      "\u2211(x[i][j] for i) = 1 for all j (each mission is covered by exactly one ship)",
      "\u2211(x[i][j] for j) \u2264 1 for all i (each ship is assigned to at most one mission)",
      "x[i][j] \u2208 {0, 1} for all i, j (binary decision variables)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_knot[i]": {
        "currently_mapped_to": "mission.Speed_knots",
        "mapping_adequacy": "partial",
        "description": "Cost associated with the speed of the ship"
      },
      "cost_per_ton[i]": {
        "currently_mapped_to": "ship.Tonnage",
        "mapping_adequacy": "partial",
        "description": "Cost associated with the tonnage of the ship"
      }
    },
    "constraint_bounds": {
      "mission_coverage[j]": {
        "currently_mapped_to": "mission.Mission_ID",
        "mapping_adequacy": "good",
        "description": "Ensures each mission is covered by exactly one ship"
      },
      "ship_assignment[i]": {
        "currently_mapped_to": "ship.Ship_ID",
        "mapping_adequacy": "good",
        "description": "Ensures each ship is assigned to at most one mission"
      }
    },
    "decision_variables": {
      "x[i][j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if ship i is assigned to mission j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Cost parameters for speed and tonnage (cost_per_knot, cost_per_ton)",
    "Binary decision variable mapping for ship-mission assignments"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine cost parameters and decision variable mappings"
  }
}
