Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:41:01

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain 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
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "business_context": "A retail chain wants to optimize the distribution of devices across its shops to minimize shipping costs while ensuring each shop meets its demand and does not exceed its storage capacity.",
  "optimization_problem": "The objective is to minimize the total shipping cost of devices from a central warehouse to various shops. The decision variables are the number of each device type to be shipped to each shop. Constraints include meeting the demand for each device at each shop, not exceeding the storage capacity of each shop, and ensuring non-negative shipments.",
  "objective": "minimize \u2211(Shipping_Cost[Device_ID, Shop_ID] \u00d7 Quantity_Shipped[Device_ID, Shop_ID])",
  "table_count": 3,
  "key_changes": [
    "Schema changes include creating tables for shipping costs, demand, and storage capacity. Business configuration logic updated with scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data for shipping costs, demand, and storage capacity.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for shipping costs, demand, and storage capacity. Business configuration logic updated with scalar parameters and formulas.

CREATE TABLE shipping_cost (
  device_id INTEGER,
  shop_id INTEGER,
  cost FLOAT
);

CREATE TABLE demand (
  device_id INTEGER,
  shop_id INTEGER,
  quantity INTEGER
);

CREATE TABLE storage_capacity (
  shop_id INTEGER,
  capacity INTEGER
);

CREATE TABLE stock (
  device_id INTEGER,
  shop_id INTEGER,
  quantity INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "shipping_cost": {
      "business_purpose": "Cost to ship a specific device to a specific shop",
      "optimization_role": "objective_coefficients",
      "columns": {
        "device_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the device",
          "optimization_purpose": "Links to device in optimization model",
          "sample_values": "1, 2, 3"
        },
        "shop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the shop",
          "optimization_purpose": "Links to shop in optimization model",
          "sample_values": "101, 102, 103"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "Shipping cost for the device to the shop",
          "optimization_purpose": "Used in objective function",
          "sample_values": "10.5, 15.0, 20.0"
        }
      }
    },
    "demand": {
      "business_purpose": "Demand for a specific device at a specific shop",
      "optimization_role": "constraint_bounds",
      "columns": {
        "device_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the device",
          "optimization_purpose": "Links to device in optimization model",
          "sample_values": "1, 2, 3"
        },
        "shop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the shop",
          "optimization_purpose": "Links to shop in optimization model",
          "sample_values": "101, 102, 103"
        },
        "quantity": {
          "data_type": "INTEGER",
          "business_meaning": "Demand quantity for the device at the shop",
          "optimization_purpose": "Used in demand constraint",
          "sample_values": "50, 75, 100"
        }
      }
    },
    "storage_capacity": {
      "business_purpose": "Maximum number of devices a shop can store",
      "optimization_role": "constraint_bounds",
      "columns": {
        "shop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the shop",
          "optimization_purpose": "Links to shop in optimization model",
          "sample_values": "101, 102, 103"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum storage capacity for the shop",
          "optimization_purpose": "Used in storage capacity constraint",
          "sample_values": "200, 250, 300"
        }
      }
    },
    "stock": {
      "business_purpose": "Number of devices to be shipped to a specific shop",
      "optimization_role": "decision_variables",
      "columns": {
        "device_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the device",
          "optimization_purpose": "Links to device in optimization model",
          "sample_values": "1, 2, 3"
        },
        "shop_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the shop",
          "optimization_purpose": "Links to shop in optimization model",
          "sample_values": "101, 102, 103"
        },
        "quantity": {
          "data_type": "INTEGER",
          "business_meaning": "Number of devices to be shipped",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "10, 20, 30"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "shipping_cost_formula": {
    "formula_expression": "Shipping_Cost[Device_ID, Shop_ID] * Quantity_Shipped[Device_ID, Shop_ID]",
    "data_type": "STRING",
    "business_meaning": "Total shipping cost calculation",
    "optimization_role": "Used in objective function",
    "configuration_type": "business_logic_formula"
  },
  "storage_capacity_threshold": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "Maximum storage capacity for a shop",
    "optimization_role": "Used in storage capacity constraint",
    "configuration_type": "scalar_parameter"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "device",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 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 still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "device",
  "iteration": 1,
  "business_context": "A retail chain aims to optimize the distribution of devices across its shops to minimize shipping costs while ensuring each shop meets its demand and does not exceed its storage capacity.",
  "optimization_problem_description": "The objective is to minimize the total shipping cost of devices from a central warehouse to various shops. The decision variables are the number of each device type to be shipped to each shop. Constraints include meeting the demand for each device at each shop, not exceeding the storage capacity of each shop, and ensuring non-negative shipments.",
  "optimization_formulation": {
    "objective": "minimize \u2211(Shipping_Cost[Device_ID, Shop_ID] \u00d7 Quantity_Shipped[Device_ID, Shop_ID])",
    "decision_variables": "Quantity_Shipped[Device_ID, Shop_ID] (integer)",
    "constraints": [
      "\u2211(Quantity_Shipped[Device_ID, Shop_ID]) \u2265 Demand[Device_ID, Shop_ID] for all Device_ID, Shop_ID",
      "\u2211(Quantity_Shipped[Device_ID, Shop_ID]) \u2264 Storage_Capacity[Shop_ID] for all Shop_ID",
      "Quantity_Shipped[Device_ID, Shop_ID] \u2265 0 for all Device_ID, Shop_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Shipping_Cost[Device_ID, Shop_ID]": {
        "currently_mapped_to": "shipping_cost.cost",
        "mapping_adequacy": "good",
        "description": "Shipping cost for each device to each shop"
      }
    },
    "constraint_bounds": {
      "Demand[Device_ID, Shop_ID]": {
        "currently_mapped_to": "demand.quantity",
        "mapping_adequacy": "good",
        "description": "Demand for each device at each shop"
      },
      "Storage_Capacity[Shop_ID]": {
        "currently_mapped_to": "storage_capacity.capacity",
        "mapping_adequacy": "good",
        "description": "Maximum storage capacity for each shop"
      }
    },
    "decision_variables": {
      "Quantity_Shipped[Device_ID, Shop_ID]": {
        "currently_mapped_to": "stock.quantity",
        "mapping_adequacy": "good",
        "description": "Number of devices to be shipped to each shop",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
