Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:28:35

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: local_govt_in_alabama

```sql
CREATE TABLE Services (
  Service_ID NUMBER,
  Service_Type_Code TEXT
);
```

```sql
CREATE TABLE Participants (
  Participant_ID NUMBER,
  Participant_Type_Code TEXT,
  Participant_Details TEXT
);
```

```sql
CREATE TABLE Events (
  Event_ID NUMBER,
  Service_ID NUMBER,
  Event_Details TEXT
);
```

```sql
CREATE TABLE Participants_in_Events (
  Event_ID NUMBER,
  Participant_ID 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": "local_govt_in_alabama",
  "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": "local_govt_in_alabama",
  "iteration": 0,
  "business_context": "Optimizing the allocation of participants to events to maximize overall satisfaction while respecting event capacity and participant availability.",
  "optimization_problem_description": "The goal is to maximize the total satisfaction score of participants assigned to events, ensuring that no event exceeds its capacity and each participant is assigned to at most one event.",
  "optimization_formulation": {
    "objective": "maximize \u2211(satisfaction_score[Event_ID, Participant_ID] \u00d7 assign[Event_ID, Participant_ID])",
    "decision_variables": "assign[Event_ID, Participant_ID] (binary: 1 if participant is assigned to event, 0 otherwise)",
    "constraints": [
      "\u2211(assign[Event_ID, Participant_ID]) \u2264 event_capacity[Event_ID] for each Event_ID",
      "\u2211(assign[Event_ID, Participant_ID]) \u2264 1 for each Participant_ID",
      "assign[Event_ID, Participant_ID] \u2208 {0, 1} for each Event_ID, Participant_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "satisfaction_score[Event_ID, Participant_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "satisfaction score of participant in event"
      }
    },
    "constraint_bounds": {
      "event_capacity[Event_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of participants allowed in event"
      }
    },
    "decision_variables": {
      "assign[Event_ID, Participant_ID]": {
        "currently_mapped_to": "Participants_in_Events.Event_ID, Participants_in_Events.Participant_ID",
        "mapping_adequacy": "partial",
        "description": "assignment of participant to event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "satisfaction_score[Event_ID, Participant_ID]",
    "event_capacity[Event_ID]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify or create data sources for satisfaction scores and event capacities."
  }
}
