Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:28:18

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: voter_2

```sql
CREATE TABLE Student (
  StuID NUMBER,
  LName TEXT,
  Fname TEXT,
  Age NUMBER,
  Sex TEXT,
  Major NUMBER,
  Advisor NUMBER,
  city_code TEXT
);
```

```sql
CREATE TABLE Voting_record (
  StuID NUMBER,
  Registration_Date TEXT,
  Election_Cycle TEXT,
  President_Vote NUMBER,
  Vice_President_Vote NUMBER,
  Secretary_Vote NUMBER,
  Treasurer_Vote NUMBER,
  Class_President_Vote NUMBER,
  Class_Senator_Vote 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": "voter_2",
  "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": "voter_2",
  "iteration": 0,
  "business_context": "A university wants to maximize student participation in elections by allocating resources (e.g., campaign materials, reminders) to different majors based on historical voting patterns and student demographics.",
  "optimization_problem_description": "The goal is to maximize the total expected votes across all election positions by allocating resources to different majors. The decision variables represent the amount of resources allocated to each major. Constraints include budget limits, minimum resource allocations per major, and ensuring that resources are allocated based on the number of students in each major.",
  "optimization_formulation": {
    "objective": "maximize \u2211(expected_votes_per_major \u00d7 resource_allocation_per_major)",
    "decision_variables": "resource_allocation_per_major (continuous)",
    "constraints": [
      "\u2211(resource_allocation_per_major) \u2264 total_budget",
      "resource_allocation_per_major \u2265 minimum_allocation_per_major",
      "resource_allocation_per_major \u2264 maximum_allocation_per_major",
      "resource_allocation_per_major \u2264 (number_of_students_in_major \u00d7 resource_per_student)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "expected_votes_per_major[major]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Expected votes per major based on historical voting data"
      }
    },
    "constraint_bounds": {
      "total_budget[]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total budget available for resource allocation"
      },
      "minimum_allocation_per_major[major]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum resource allocation required per major"
      },
      "maximum_allocation_per_major[major]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum resource allocation allowed per major"
      },
      "number_of_students_in_major[major]": {
        "currently_mapped_to": "Student.Major",
        "mapping_adequacy": "partial",
        "description": "Number of students in each major"
      },
      "resource_per_student[]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Resource allocation per student"
      }
    },
    "decision_variables": {
      "resource_allocation_per_major[major]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Amount of resources allocated to each major",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Expected votes per major",
    "Total budget for resource allocation",
    "Minimum and maximum resource allocations per major",
    "Resource allocation per student"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the constraints and objective function based on additional data requirements"
  }
}
