Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:54:53

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: battle_death

```sql
CREATE TABLE battle (
  id NUMBER,
  name TEXT,
  date TEXT,
  bulgarian_commander TEXT,
  latin_commander TEXT,
  result TEXT
);
```

```sql
CREATE TABLE ship (
  lost_in_battle NUMBER,
  id NUMBER,
  name TEXT,
  tonnage TEXT,
  ship_type TEXT,
  location TEXT,
  disposition_of_ship TEXT
);
```

```sql
CREATE TABLE death (
  caused_by_ship_id NUMBER,
  id NUMBER,
  note TEXT,
  killed NUMBER,
  injured 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": "battle_death",
  "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": "battle_death",
  "iteration": 0,
  "business_context": "Optimize the allocation of ships to battles to minimize the total number of deaths caused by ships, considering the constraints on ship availability and battle requirements.",
  "optimization_problem_description": "The goal is to allocate ships to battles in a way that minimizes the total number of deaths caused by ships. Each ship can be assigned to at most one battle, and each battle has a requirement for a certain number of ships. The number of deaths caused by each ship in a battle is known.",
  "optimization_formulation": {
    "objective": "minimize total_deaths = \u2211(deaths_caused_by_ship_in_battle[i,j] * x[i,j])",
    "decision_variables": "x[i,j] = 1 if ship i is assigned to battle j, 0 otherwise (binary)",
    "constraints": [
      "\u2211(x[i,j]) <= 1 for each ship i (each ship can be assigned to at most one battle)",
      "\u2211(x[i,j]) >= required_ships[j] for each battle j (each battle requires a minimum number of ships)",
      "x[i,j] \u2208 {0, 1} for all i, j (binary decision variables)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "deaths_caused_by_ship_in_battle[i,j]": {
        "currently_mapped_to": "death.killed",
        "mapping_adequacy": "partial",
        "description": "Number of deaths caused by ship i in battle j"
      }
    },
    "constraint_bounds": {
      "required_ships[j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of ships required for battle j"
      }
    },
    "decision_variables": {
      "x[i,j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if ship i is assigned to battle j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Data on the number of ships required for each battle",
    "Mapping of ships to specific battles to determine potential assignments"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping of decision variables and constraints to the existing schema"
  }
}
