Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-28 00:21:27

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: news_report

```sql
CREATE TABLE event (
  Event_ID NUMBER,
  Date TEXT,
  Venue TEXT,
  Name TEXT,
  Event_Attendance NUMBER
);
```

```sql
CREATE TABLE journalist (
  journalist_ID NUMBER,
  Name TEXT,
  Nationality TEXT,
  Age TEXT,
  Years_working NUMBER
);
```

```sql
CREATE TABLE news_report (
  journalist_ID NUMBER,
  Event_ID NUMBER,
  Work_Type TEXT
);
```



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": "news_report",
  "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": "news_report",
  "iteration": 0,
  "business_context": "A news agency wants to optimize the allocation of journalists to events to maximize the total event attendance covered by journalists, considering constraints on the number of events a journalist can cover and the total number of journalists available.",
  "optimization_problem_description": "The goal is to maximize the total event attendance covered by journalists. Each journalist can cover a limited number of events, and there is a limited number of journalists available. The decision is which journalist covers which event to maximize the total attendance covered.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Event_Attendance[Event_ID] \u00d7 x[journalist_ID, Event_ID])",
    "decision_variables": "x[journalist_ID, Event_ID] is a binary variable indicating whether journalist journalist_ID covers event Event_ID",
    "constraints": [
      "\u2211(x[journalist_ID, Event_ID]) \u2264 max_events_per_journalist for each journalist_ID",
      "\u2211(x[journalist_ID, Event_ID]) \u2264 1 for each Event_ID",
      "\u2211(x[journalist_ID, Event_ID] for all journalist_ID) \u2264 total_journalists"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Event_Attendance[Event_ID]": {
        "currently_mapped_to": "event.Event_Attendance",
        "mapping_adequacy": "good",
        "description": "represents the attendance of each event, which is the weight in the objective function"
      }
    },
    "constraint_bounds": {
      "max_events_per_journalist": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of events a journalist can cover"
      },
      "total_journalists": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "total number of journalists available"
      }
    },
    "decision_variables": {
      "x[journalist_ID, Event_ID]": {
        "currently_mapped_to": "news_report.journalist_ID and news_report.Event_ID",
        "mapping_adequacy": "partial",
        "description": "binary variable indicating if a journalist covers an event",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "max_events_per_journalist",
    "total_journalists"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping of decision variables and ensure all necessary parameters are available"
  }
}
