Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 21:38:11

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 government agency wants to allocate resources to minimize the total number of casualties (killed and injured) in various locations over a year. The agency has a limited budget and resources that can be allocated to different locations to improve safety and reduce casualties.",
  "optimization_problem_description": "The goal is to minimize the total number of casualties (killed and injured) by optimally allocating resources to different locations. The resources are limited, and each location has a different impact on reducing casualties. The optimization will determine the optimal allocation of resources to minimize casualties while respecting budget constraints.",
  "optimization_formulation": {
    "objective": "minimize total_casualties = sum(c_killed[i] * x[i] + c_injured[i] * x[i])",
    "decision_variables": "x[i] represents the amount of resources allocated to location i (continuous)",
    "constraints": [
      "sum(cost[i] * x[i]) <= budget",
      "x[i] >= 0 for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "c_killed[i]": {
        "currently_mapped_to": "perpetrator.Killed",
        "mapping_adequacy": "good",
        "description": "represents the number of people killed in location i"
      },
      "c_injured[i]": {
        "currently_mapped_to": "perpetrator.Injured",
        "mapping_adequacy": "good",
        "description": "represents the number of people injured in location i"
      }
    },
    "constraint_bounds": {
      "budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the total budget available for resource allocation"
      }
    },
    "decision_variables": {
      "x[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the amount of resources allocated to location i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Cost of resources for each location",
    "Total budget available for allocation"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Determine the cost of resources for each location and the total budget available for allocation"
  }
}
