Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:09:50

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: candidate_poll

```sql
CREATE TABLE candidate (
  Candidate_ID NUMBER,
  People_ID NUMBER,
  Poll_Source TEXT,
  Date TEXT,
  Support_rate NUMBER,
  Consider_rate NUMBER,
  Oppose_rate NUMBER,
  Unsure_rate NUMBER
);
```

```sql
CREATE TABLE people (
  People_ID NUMBER,
  Sex TEXT,
  Name TEXT,
  Date_of_Birth TEXT,
  Height NUMBER,
  Weight 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": "candidate_poll",
  "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": "candidate_poll",
  "iteration": 0,
  "business_context": "A political campaign wants to optimize the allocation of resources to maximize the overall support rate for their candidate across different poll sources. The campaign can decide how much effort to allocate to each poll source to influence the support rate.",
  "optimization_problem_description": "The goal is to maximize the total support rate for a candidate by optimally allocating resources across different poll sources. The decision variables represent the level of effort allocated to each poll source, which influences the support rate. Constraints include budget limits, minimum and maximum effort levels, and ensuring that the total effort does not exceed available resources.",
  "optimization_formulation": {
    "objective": "maximize total_support_rate = \u2211(effort[i] * support_rate[i])",
    "decision_variables": "effort[i] for each poll source i, representing the level of effort allocated (continuous)",
    "constraints": [
      "\u2211(effort[i]) <= total_available_resources",
      "effort[i] >= min_effort[i] for each poll source i",
      "effort[i] <= max_effort[i] for each poll source i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "support_rate[i]": {
        "currently_mapped_to": "candidate.Support_rate",
        "mapping_adequacy": "good",
        "description": "The support rate for the candidate from poll source i"
      }
    },
    "constraint_bounds": {
      "total_available_resources": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The total resources available for allocation"
      },
      "min_effort[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The minimum effort required for poll source i"
      },
      "max_effort[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum effort allowed for poll source i"
      }
    },
    "decision_variables": {
      "effort[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The level of effort allocated to poll source i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total available resources for allocation",
    "Minimum and maximum effort levels for each poll source"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping of decision variables and constraints to existing schema or identify additional data requirements"
  }
}
