Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:41:29

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: party_people

```sql
CREATE TABLE region (
  Region_ID NUMBER,
  Region_name TEXT,
  Date TEXT,
  Label TEXT,
  Format TEXT,
  Catalogue TEXT
);
```

```sql
CREATE TABLE party (
  Party_ID NUMBER,
  Minister TEXT,
  Took_office TEXT,
  Left_office TEXT,
  Region_ID NUMBER,
  Party_name TEXT
);
```

```sql
CREATE TABLE member (
  Member_ID NUMBER,
  Member_Name TEXT,
  Party_ID TEXT,
  In_office TEXT
);
```

```sql
CREATE TABLE party_events (
  Event_ID NUMBER,
  Event_Name TEXT,
  Party_ID NUMBER,
  Member_in_charge_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": "party_people",
  "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": "party_people",
  "iteration": 0,
  "business_context": "A political organization wants to optimize the allocation of its members to various party events to maximize the overall effectiveness of the events. Each member has a certain effectiveness score for each event, and the goal is to assign members to events in a way that maximizes the total effectiveness while respecting constraints such as the number of members per event and availability.",
  "optimization_problem_description": "The problem is to maximize the total effectiveness of party events by optimally assigning members to events. Each member has a specific effectiveness score for each event, and the assignment must respect constraints such as the maximum number of members per event and the availability of members.",
  "optimization_formulation": {
    "objective": "maximize total_effectiveness = sum(efficiency_score[member_id, event_id] * x[member_id, event_id])",
    "decision_variables": "x[member_id, event_id] = 1 if member_id is assigned to event_id, 0 otherwise (binary)",
    "constraints": [
      "sum(x[member_id, event_id] for member_id) <= max_members_per_event for each event_id",
      "sum(x[member_id, event_id] for event_id) <= 1 for each member_id",
      "x[member_id, event_id] = 0 if member is not available for the event"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "efficiency_score[member_id, event_id]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Effectiveness score of a member for a specific event"
      }
    },
    "constraint_bounds": {
      "max_members_per_event": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of members that can be assigned to a single event"
      }
    },
    "decision_variables": {
      "x[member_id, event_id]": {
        "currently_mapped_to": "party_events.Member_in_charge_ID",
        "mapping_adequacy": "partial",
        "description": "Binary variable indicating if a member is assigned to an event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Effectiveness scores for each member-event pair",
    "Maximum number of members allowed per event",
    "Availability of each member for each event"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping of decision variables and gather missing data for effectiveness scores and constraints"
  }
}
