Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:23:30

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: world_1

```sql
CREATE TABLE city (
  ID NUMBER,
  Name TEXT,
  CountryCode TEXT,
  District TEXT,
  Population NUMBER
);
```

```sql
CREATE TABLE sqlite_sequence (
  name TEXT,
  seq TEXT
);
```

```sql
CREATE TABLE country (
  Code TEXT,
  Name TEXT,
  Continent TEXT,
  Region TEXT,
  SurfaceArea NUMBER,
  IndepYear NUMBER,
  Population NUMBER,
  LifeExpectancy NUMBER,
  GNP NUMBER,
  GNPOld NUMBER,
  LocalName TEXT,
  GovernmentForm TEXT,
  HeadOfState TEXT,
  Capital NUMBER,
  Code2 TEXT
);
```

```sql
CREATE TABLE countrylanguage (
  CountryCode TEXT,
  Language TEXT,
  IsOfficial TEXT,
  Percentage 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": "world_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": "world_1",
  "iteration": 0,
  "business_context": "A global logistics company wants to optimize the distribution of goods across various cities in different countries to minimize transportation costs while ensuring demand is met in each city.",
  "optimization_problem_description": "The company needs to minimize the total transportation cost of distributing goods from a central warehouse to various cities. The objective is to determine the optimal quantity of goods to be shipped to each city, considering the demand in each city and the transportation cost per unit.",
  "optimization_formulation": {
    "objective": "minimize total_transportation_cost = sum(transportation_cost_per_unit[i] * quantity_shipped[i])",
    "decision_variables": "quantity_shipped[i] for each city i, representing the number of units shipped to city i (continuous)",
    "constraints": [
      "sum(quantity_shipped[i]) <= total_available_goods",
      "quantity_shipped[i] >= city_demand[i] for each city i",
      "quantity_shipped[i] <= max_capacity[i] for each city i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "transportation_cost_per_unit[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Transportation cost per unit to city i"
      }
    },
    "constraint_bounds": {
      "total_available_goods": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total number of goods available for distribution"
      },
      "city_demand[i]": {
        "currently_mapped_to": "city.Population",
        "mapping_adequacy": "partial",
        "description": "Demand in city i, approximated by its population"
      },
      "max_capacity[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum capacity of goods that can be shipped to city i"
      }
    },
    "decision_variables": {
      "quantity_shipped[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of units shipped to city i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Transportation cost per unit for each city",
    "Total available goods for distribution",
    "Maximum capacity for each city"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine mapping of transportation costs and capacity constraints"
  }
}
