Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 21:48:14

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: manufactory_1

```sql
CREATE TABLE Manufacturers (
  Code NUMBER,
  Name TEXT,
  Headquarter TEXT,
  Founder TEXT,
  Revenue NUMBER
);
```

```sql
CREATE TABLE Products (
  Code NUMBER,
  Name TEXT,
  Price NUMBER,
  Manufacturer 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": "manufactory_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": "manufactory_1",
  "iteration": 0,
  "business_context": "A manufacturing company wants to optimize the allocation of production resources to maximize revenue from product sales while considering production capacity and manufacturer-specific constraints.",
  "optimization_problem_description": "The goal is to maximize the total revenue from selling products produced by different manufacturers, subject to constraints on production capacity and manufacturer-specific production limits.",
  "optimization_formulation": {
    "objective": "maximize total_revenue = \u2211(Price[product] \u00d7 ProductionQuantity[product])",
    "decision_variables": "ProductionQuantity[product] - the number of units to produce for each product (continuous)",
    "constraints": [
      "\u2211(ProductionQuantity[product]) \u2264 TotalProductionCapacity",
      "ProductionQuantity[product] \u2264 ManufacturerCapacity[manufacturer] for each manufacturer"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Price[product]": {
        "currently_mapped_to": "Products.Price",
        "mapping_adequacy": "good",
        "description": "The selling price of each product"
      }
    },
    "constraint_bounds": {
      "TotalProductionCapacity": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The total production capacity available across all manufacturers"
      },
      "ManufacturerCapacity[manufacturer]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum production capacity for each manufacturer"
      }
    },
    "decision_variables": {
      "ProductionQuantity[product]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The number of units to produce for each product",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total production capacity data",
    "Manufacturer-specific production capacity data"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data on production capacities and refine constraints"
  }
}
