Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:28:55

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: phone_market

```sql
CREATE TABLE phone (
  Name TEXT,
  Phone_ID NUMBER,
  Memory_in_G NUMBER,
  Carrier TEXT,
  Price NUMBER
);
```

```sql
CREATE TABLE market (
  Market_ID NUMBER,
  District TEXT,
  Num_of_employees NUMBER,
  Num_of_shops NUMBER,
  Ranking NUMBER
);
```

```sql
CREATE TABLE phone_market (
  Market_ID NUMBER,
  Phone_ID TEXT,
  Num_of_stock 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": "phone_market",
  "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": "phone_market",
  "iteration": 0,
  "business_context": "A phone distributor aims to optimize the allocation of phone stocks across different markets to maximize total revenue while respecting market capacities and minimizing stock shortages.",
  "optimization_problem_description": "The distributor needs to decide how many units of each phone model to allocate to each market to maximize total revenue, ensuring that the total stock allocated does not exceed the available stock for each phone model and that the total stock in each market does not exceed its capacity.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Price[Phone_ID] \u00d7 Num_of_stock[Market_ID, Phone_ID])",
    "decision_variables": "Num_of_stock[Market_ID, Phone_ID] (integer)",
    "constraints": [
      "\u2211(Num_of_stock[Market_ID, Phone_ID]) \u2264 Num_of_shops[Market_ID] for each Market_ID",
      "\u2211(Num_of_stock[Market_ID, Phone_ID]) \u2264 Num_of_stock[Market_ID, Phone_ID] for each Phone_ID",
      "Num_of_stock[Market_ID, Phone_ID] \u2265 0 for each Market_ID, Phone_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Price[Phone_ID]": {
        "currently_mapped_to": "phone.Price",
        "mapping_adequacy": "good",
        "description": "Price of each phone model"
      }
    },
    "constraint_bounds": {
      "Num_of_shops[Market_ID]": {
        "currently_mapped_to": "market.Num_of_shops",
        "mapping_adequacy": "good",
        "description": "Maximum number of shops in each market"
      },
      "Num_of_stock[Market_ID, Phone_ID]": {
        "currently_mapped_to": "phone_market.Num_of_stock",
        "mapping_adequacy": "good",
        "description": "Available stock of each phone model in each market"
      }
    },
    "decision_variables": {
      "Num_of_stock[Market_ID, Phone_ID]": {
        "currently_mapped_to": "phone_market.Num_of_stock",
        "mapping_adequacy": "good",
        "description": "Number of units of each phone model allocated to each market",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Maximum stock capacity for each market",
    "Minimum stock requirements for each phone model in each market"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine constraints to include minimum stock requirements and maximum market capacities"
  }
}
