Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:27:36

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: restaurants

```sql
CREATE TABLE GEOGRAPHIC (
  CITY_NAME TEXT,
  COUNTY TEXT,
  REGION TEXT
);
```

```sql
CREATE TABLE RESTAURANT (
  ID NUMBER,
  NAME TEXT,
  FOOD_TYPE TEXT,
  CITY_NAME TEXT,
  RATING NUMBER
);
```

```sql
CREATE TABLE LOCATION (
  RESTAURANT_ID NUMBER,
  HOUSE_NUMBER NUMBER,
  STREET_NAME TEXT,
  CITY_NAME 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": "restaurants",
  "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": "restaurants",
  "iteration": 0,
  "business_context": "A restaurant chain wants to optimize the placement of new restaurants across different cities to maximize overall customer satisfaction, represented by the sum of ratings, while ensuring a balanced distribution across regions and limiting the number of new restaurants per city.",
  "optimization_problem_description": "The goal is to maximize the total customer satisfaction (sum of ratings) from new restaurant placements, subject to constraints on the number of new restaurants per city and ensuring a minimum number of restaurants in each region.",
  "optimization_formulation": {
    "objective": "maximize \u2211(RATING_i * X_i) where X_i is a binary decision variable indicating whether to place a new restaurant in city i.",
    "decision_variables": "X_i: binary variable (1 if a new restaurant is placed in city i, 0 otherwise).",
    "constraints": [
      "\u2211(X_i) \u2264 MAX_RESTAURANTS_PER_CITY for each city i.",
      "\u2211(X_i) \u2265 MIN_RESTAURANTS_PER_REGION for each region.",
      "\u2211(X_i) \u2264 TOTAL_BUDGET, where TOTAL_BUDGET is the maximum number of new restaurants that can be opened.",
      "X_i \u2208 {0, 1} for all i."
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "RATING_i": {
        "currently_mapped_to": "RESTAURANT.RATING",
        "mapping_adequacy": "partial",
        "description": "The rating of the restaurant, used to weight the decision variable."
      }
    },
    "constraint_bounds": {
      "MAX_RESTAURANTS_PER_CITY": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of new restaurants allowed per city."
      },
      "MIN_RESTAURANTS_PER_REGION": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of new restaurants required per region."
      },
      "TOTAL_BUDGET": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total budget constraint for the number of new restaurants."
      }
    },
    "decision_variables": {
      "X_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating whether to place a new restaurant in city i.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "MAX_RESTAURANTS_PER_CITY",
    "MIN_RESTAURANTS_PER_REGION",
    "TOTAL_BUDGET",
    "Binary decision variables X_i"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine constraints and decision variables to better align with the business context and ensure all necessary data is available."
  }
}
