Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:32:36

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 party aims to maximize its influence across regions by strategically allocating its members to events. The party wants to ensure that each region is adequately represented while minimizing the total cost of organizing these events.",
  "optimization_problem_description": "The optimization problem involves maximizing the total influence of the party across regions by assigning members to events, while ensuring that the total cost of organizing events does not exceed a predefined budget. The influence is measured by the number of members assigned to events in each region, and the cost is determined by the number of events organized.",
  "optimization_formulation": {
    "objective": "maximize \u2211(influence_coefficient[region] \u00d7 number_of_members_assigned[region])",
    "decision_variables": "number_of_members_assigned[region] (integer), number_of_events_organized[region] (integer)",
    "constraints": [
      "\u2211(cost_per_event[region] \u00d7 number_of_events_organized[region]) \u2264 total_budget",
      "number_of_members_assigned[region] \u2264 total_members_available[region] for each region",
      "number_of_events_organized[region] \u2264 max_events_per_region[region] for each region",
      "number_of_members_assigned[region] \u2265 min_members_per_region[region] for each region",
      "number_of_events_organized[region] \u2265 min_events_per_region[region] for each region"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "influence_coefficient[region]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The influence coefficient represents the impact of assigning a member to an event in a specific region."
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The total budget available for organizing events."
      },
      "total_members_available[region]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The total number of members available in each region."
      },
      "max_events_per_region[region]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum number of events that can be organized in each region."
      },
      "min_members_per_region[region]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The minimum number of members that must be assigned to each region."
      },
      "min_events_per_region[region]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The minimum number of events that must be organized in each region."
      }
    },
    "decision_variables": {
      "number_of_members_assigned[region]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The number of members assigned to events in each region.",
        "variable_type": "integer"
      },
      "number_of_events_organized[region]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The number of events organized in each region.",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "influence_coefficient[region]",
    "total_budget",
    "total_members_available[region]",
    "max_events_per_region[region]",
    "min_members_per_region[region]",
    "min_events_per_region[region]",
    "cost_per_event[region]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "low",
    "next_focus": "Define and map the missing coefficients and constraints to the existing schema or business configuration logic."
  }
}
