Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-28 00:19:24

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: wedding

```sql
CREATE TABLE people (
  People_ID NUMBER,
  Name TEXT,
  Country TEXT,
  Is_Male TEXT,
  Age NUMBER
);
```

```sql
CREATE TABLE church (
  Church_ID NUMBER,
  Name TEXT,
  Organized_by TEXT,
  Open_Date NUMBER,
  Continuation_of TEXT
);
```

```sql
CREATE TABLE wedding (
  Church_ID NUMBER,
  Male_ID NUMBER,
  Female_ID NUMBER,
  Year 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": "wedding",
  "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": "wedding",
  "iteration": 0,
  "business_context": "Optimize the allocation of weddings to churches to maximize the number of weddings held while respecting church availability and gender balance.",
  "optimization_problem_description": "The goal is to maximize the number of weddings held in available churches, ensuring that each wedding has one male and one female participant, and that each church can host a limited number of weddings per year.",
  "optimization_formulation": {
    "objective": "maximize total_weddings = \u2211(wedding_allocation[church_id, male_id, female_id])",
    "decision_variables": "wedding_allocation[church_id, male_id, female_id] (binary: 1 if wedding is held, 0 otherwise)",
    "constraints": [
      "\u2211(wedding_allocation[church_id, male_id, female_id]) \u2264 church_capacity[church_id] for each church_id",
      "\u2211(wedding_allocation[church_id, male_id, female_id]) \u2264 1 for each male_id",
      "\u2211(wedding_allocation[church_id, male_id, female_id]) \u2264 1 for each female_id",
      "wedding_allocation[church_id, male_id, female_id] \u2208 {0, 1}"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "total_weddings": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the total number of weddings held"
      }
    },
    "constraint_bounds": {
      "church_capacity[church_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of weddings a church can host per year"
      }
    },
    "decision_variables": {
      "wedding_allocation[church_id, male_id, female_id]": {
        "currently_mapped_to": "wedding.Church_ID, wedding.Male_ID, wedding.Female_ID",
        "mapping_adequacy": "partial",
        "description": "binary variable indicating if a wedding is held at a specific church with specific male and female participants",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Church capacity data to define church_capacity[church_id]",
    "Data to ensure each male and female participates in at most one wedding"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data on church capacities and ensure unique participation of individuals in weddings"
  }
}
