Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:34:23

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: movie_1

```sql
CREATE TABLE Movie (
  mID NUMBER,
  title TEXT,
  year NUMBER,
  director TEXT
);
```

```sql
CREATE TABLE Reviewer (
  rID NUMBER,
  name TEXT
);
```

```sql
CREATE TABLE Rating (
  rID NUMBER,
  mID NUMBER,
  stars NUMBER,
  ratingDate TIME
);
```



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": "movie_1",
  "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": "movie_1",
  "iteration": 0,
  "business_context": "A movie streaming service wants to optimize the allocation of promotional budget across different movies to maximize the average rating improvement, subject to budget constraints and minimum promotional requirements for each movie.",
  "optimization_problem_description": "The goal is to determine the optimal allocation of a fixed promotional budget to different movies to maximize the expected increase in their average ratings. Each movie has a different sensitivity to promotional spending, and there are minimum promotional requirements for each movie.",
  "optimization_formulation": {
    "objective": "maximize sum(promotion_sensitivity[mID] * budget_allocation[mID])",
    "decision_variables": "budget_allocation[mID] - continuous variables representing the amount of budget allocated to movie mID",
    "constraints": [
      "sum(budget_allocation[mID]) <= total_budget",
      "budget_allocation[mID] >= min_promotion_requirement[mID] for all mID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "promotion_sensitivity[mID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents how much the average rating of movie mID is expected to increase per unit of promotional budget"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "the total promotional budget available for allocation"
      },
      "min_promotion_requirement[mID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "the minimum promotional budget that must be allocated to movie mID"
      }
    },
    "decision_variables": {
      "budget_allocation[mID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "the amount of promotional budget allocated to movie mID",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Data on promotion_sensitivity for each movie",
    "Total promotional budget available",
    "Minimum promotional requirements for each movie"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gathering data on promotion sensitivity and budget constraints"
  }
}
