Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:29:20

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: manufacturer

```sql
CREATE TABLE manufacturer (
  Manufacturer_ID NUMBER,
  Open_Year NUMBER,
  Name TEXT,
  Num_of_Factories NUMBER,
  Num_of_Shops NUMBER
);
```

```sql
CREATE TABLE furniture (
  Furniture_ID NUMBER,
  Name TEXT,
  Num_of_Component NUMBER,
  Market_Rate NUMBER
);
```

```sql
CREATE TABLE furniture_manufacte (
  Manufacturer_ID NUMBER,
  Furniture_ID NUMBER,
  Price_in_Dollar 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": "manufacturer",
  "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": "manufacturer",
  "iteration": 0,
  "business_context": "A furniture manufacturer aims to maximize its profit by determining the optimal number of each furniture type to produce, considering production costs, market rates, and factory capacity constraints.",
  "optimization_problem_description": "The manufacturer needs to decide how many units of each furniture type to produce to maximize profit, given the production costs, market rates, and limited factory capacity. The objective is to maximize the total profit, which is the difference between the revenue from selling the furniture and the production costs.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Market_Rate \u00d7 Quantity_Produced - Price_in_Dollar \u00d7 Quantity_Produced)",
    "decision_variables": "Quantity_Produced[Furniture_ID] (integer)",
    "constraints": [
      "\u2211(Quantity_Produced[Furniture_ID]) \u2264 Total_Factory_Capacity",
      "Quantity_Produced[Furniture_ID] \u2265 0 for all Furniture_ID",
      "\u2211(Price_in_Dollar \u00d7 Quantity_Produced[Furniture_ID]) \u2264 Budget_Limit"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Market_Rate[Furniture_ID]": {
        "currently_mapped_to": "furniture.Market_Rate",
        "mapping_adequacy": "good",
        "description": "Market rate of each furniture type"
      },
      "Price_in_Dollar[Furniture_ID]": {
        "currently_mapped_to": "furniture_manufacte.Price_in_Dollar",
        "mapping_adequacy": "good",
        "description": "Production cost of each furniture type"
      }
    },
    "constraint_bounds": {
      "Total_Factory_Capacity": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total production capacity of all factories"
      },
      "Budget_Limit": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total budget available for production"
      }
    },
    "decision_variables": {
      "Quantity_Produced[Furniture_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of units to produce for each furniture type",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total_Factory_Capacity",
    "Budget_Limit",
    "Quantity_Produced[Furniture_ID]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map the missing constraints and decision variables to complete the optimization model."
  }
}
