Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:30:51

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: perpetrator

```sql
CREATE TABLE perpetrator (
  Perpetrator_ID NUMBER,
  People_ID NUMBER,
  Date TEXT,
  Year NUMBER,
  Location TEXT,
  Country TEXT,
  Killed NUMBER,
  Injured NUMBER
);
```

```sql
CREATE TABLE people (
  People_ID NUMBER,
  Name TEXT,
  Height NUMBER,
  Weight NUMBER,
  Home Town 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": "perpetrator",
  "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": "perpetrator",
  "iteration": 0,
  "business_context": "A security agency aims to minimize the total number of casualties (killed and injured) by optimally allocating resources to monitor and prevent incidents in different locations.",
  "optimization_problem_description": "The agency wants to minimize the total casualties (sum of killed and injured) by deciding how many resources to allocate to each location. The resources are limited, and each location has a different impact on reducing casualties based on historical data.",
  "optimization_formulation": {
    "objective": "minimize \u2211(killed[i] + injured[i])",
    "decision_variables": "x[i] = number of resources allocated to location i (continuous)",
    "constraints": [
      "\u2211(x[i]) \u2264 total_resources",
      "x[i] \u2265 0 for all i",
      "killed[i] \u2264 max_killed[i] for all i",
      "injured[i] \u2264 max_injured[i] for all i",
      "killed[i] + injured[i] \u2264 max_casualties[i] for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "killed[i]": {
        "currently_mapped_to": "perpetrator.Killed",
        "mapping_adequacy": "good",
        "description": "Number of people killed in location i"
      },
      "injured[i]": {
        "currently_mapped_to": "perpetrator.Injured",
        "mapping_adequacy": "good",
        "description": "Number of people injured in location i"
      }
    },
    "constraint_bounds": {
      "total_resources": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total resources available for allocation"
      },
      "max_killed[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum allowed killed in location i"
      },
      "max_injured[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum allowed injured in location i"
      },
      "max_casualties[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum allowed casualties in location i"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of resources allocated to location i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total resources available for allocation",
    "Maximum allowed killed per location",
    "Maximum allowed injured per location",
    "Maximum allowed casualties per location"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define the missing parameters and refine the constraints to better reflect the resource allocation problem."
  }
}
