=== Problem Context ===
# Complete Optimization Problem and Solution: store_product

## 1. Problem Context and Goals

### Context  
A retail chain is focused on optimizing the allocation of products across its stores to maximize total sales revenue. The key decision involves determining the number of units of each product to allocate to each store. This decision must consider the sales potential of each product in each store, the total available units of each product, and the capacity of each store to handle inventory. Additionally, the allocation must adhere to business-defined thresholds: a minimum number of units must be allocated to ensure product presence in every store, and a maximum number of units must not be exceeded to prevent overstocking and maintain balanced inventory levels.

The sales potential of a product in a store represents the expected contribution of that product to total sales revenue. The total sales revenue is calculated by summing the product of the sales potential and the allocated units for each product-store combination. The business configuration includes a minimum allocation threshold of 10 units and a maximum allocation threshold of 100 units per product per store. These thresholds ensure operational efficiency and inventory balance across the retail chain.

### Goals  
The primary goal of this optimization is to maximize total sales revenue by strategically allocating products to stores. This is achieved by determining the optimal number of units of each product to allocate to each store, considering their sales potential, availability, and store capacities. Success is measured by the total sales revenue generated, which is directly influenced by the sales potential of each product in each store and the number of units allocated. The optimization ensures that the allocation respects store capacities, product availability, and the defined minimum and maximum allocation thresholds.

## 2. Constraints  

The optimization must adhere to the following constraints:  
1. **Store Capacity Constraint**: The total number of units allocated to a store across all products must not exceed the store's capacity. This ensures that the store can handle the allocated inventory without operational strain.  
2. **Product Availability Constraint**: The total number of units allocated for a product across all stores must not exceed the available units of that product. This ensures that the allocation does not exceed the available inventory.  
3. **Minimum Allocation Threshold**: The number of units allocated for a product to a store must be at least the minimum allocation threshold. This ensures a minimum presence of each product in every store.  
4. **Maximum Allocation Threshold**: The number of units allocated for a product to a store must not exceed the maximum allocation threshold. This prevents overstocking and ensures balanced inventory levels across stores.  

These constraints ensure that the allocation decisions are operationally feasible and aligned with business requirements.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Added allocation table for decision variables, updated business configuration logic with new scalar parameters, and ensured all mappings are complete.

CREATE TABLE sales_potential (
  store_id INTEGER,
  product_id INTEGER,
  sales_potential_value FLOAT
);

CREATE TABLE product_availability (
  product_id INTEGER,
  available_units INTEGER
);

CREATE TABLE store_capacity (
  store_id INTEGER,
  capacity INTEGER
);

CREATE TABLE allocation (
  store_id INTEGER,
  product_id INTEGER,
  allocation_value INTEGER
);
```

### Data Dictionary  
- **sales_potential**: Represents the expected sales contribution of a product in a specific store.  
  - *store_id*: Unique identifier for the store.  
  - *product_id*: Unique identifier for the product.  
  - *sales_potential_value*: The sales potential of the product in the store, used as a coefficient in the objective function.  

- **product_availability**: Represents the total available units of a product across all stores.  
  - *product_id*: Unique identifier for the product.  
  - *available_units*: The total available units of the product, used as an upper bound in the product availability constraint.  

- **store_capacity**: Represents the maximum number of units a store can handle.  
  - *store_id*: Unique identifier for the store.  
  - *capacity*: The maximum number of units the store can handle, used as an upper bound in the store capacity constraint.  

- **allocation**: Represents the number of units of a product allocated to a store.  
  - *store_id*: Unique identifier for the store.  
  - *product_id*: Unique identifier for the product.  
  - *allocation_value*: The number of units of the product allocated to the store, used as the decision variable in the optimization model.  


=== Schema ===
-- Iteration 2 Database Schema
-- Objective: Added allocation table for decision variables, updated business configuration logic with new scalar parameters, and ensured all mappings are complete.

CREATE TABLE sales_potential (
  store_id INTEGER,
  product_id INTEGER,
  sales_potential_value FLOAT
);

CREATE TABLE product_availability (
  product_id INTEGER,
  available_units INTEGER
);

CREATE TABLE store_capacity (
  store_id INTEGER,
  capacity INTEGER
);

CREATE TABLE allocation (
  store_id INTEGER,
  product_id INTEGER,
  allocation_value INTEGER
);



=== LLM Response ===
```sql
-- Query Description: Retrieve the sales potential for each product in each store.
-- This data is crucial for the objective function, as it represents the expected contribution of each product to total sales revenue.
SELECT store_id, product_id, sales_potential_value
FROM sales_potential;

-- Query Description: Retrieve the total available units for each product.
-- This data is essential for the product availability constraint, ensuring that the total allocation does not exceed the available inventory.
SELECT product_id, available_units
FROM product_availability;

-- Query Description: Retrieve the capacity for each store.
-- This data is necessary for the store capacity constraint, ensuring that the total allocation to a store does not exceed its capacity.
SELECT store_id, capacity
FROM store_capacity;

-- Query Description: Retrieve the current allocation of products to stores.
-- This data represents the decision variables in the optimization model and is used to ensure that the allocation respects the minimum and maximum thresholds.
SELECT store_id, product_id, allocation_value
FROM allocation;

-- Query Description: Retrieve the total allocated units per store to check against store capacity.
-- This aggregated data helps ensure that the store capacity constraint is not violated.
SELECT store_id, SUM(allocation_value) AS total_allocated_units
FROM allocation
GROUP BY store_id;

-- Query Description: Retrieve the total allocated units per product to check against product availability.
-- This aggregated data helps ensure that the product availability constraint is not violated.
SELECT product_id, SUM(allocation_value) AS total_allocated_units
FROM allocation
GROUP BY product_id;

-- Query Description: Retrieve the sales potential and current allocation for each product-store combination.
-- This data is useful for evaluating the current allocation against the sales potential and identifying opportunities for optimization.
SELECT sp.store_id, sp.product_id, sp.sales_potential_value, a.allocation_value
FROM sales_potential sp
LEFT JOIN allocation a ON sp.store_id = a.store_id AND sp.product_id = a.product_id;

-- Query Description: Retrieve the sales potential, current allocation, and store capacity for each store.
-- This data helps in understanding the relationship between sales potential, current allocation, and store capacity, which is crucial for optimizing the allocation.
SELECT sp.store_id, sp.product_id, sp.sales_potential_value, a.allocation_value, sc.capacity
FROM sales_potential sp
LEFT JOIN allocation a ON sp.store_id = a.store_id AND sp.product_id = a.product_id
LEFT JOIN store_capacity sc ON sp.store_id = sc.store_id;

-- Query Description: Retrieve the sales potential, current allocation, and product availability for each product.
-- This data helps in understanding the relationship between sales potential, current allocation, and product availability, which is crucial for optimizing the allocation.
SELECT sp.product_id, sp.sales_potential_value, a.allocation_value, pa.available_units
FROM sales_potential sp
LEFT JOIN allocation a ON sp.store_id = a.store_id AND sp.product_id = a.product_id
LEFT JOIN product_availability pa ON sp.product_id = pa.product_id;

-- Query Description: Retrieve the total sales potential per store.
-- This aggregated data helps in identifying stores with the highest sales potential, which can be prioritized in the allocation process.
SELECT store_id, SUM(sales_potential_value) AS total_sales_potential
FROM sales_potential
GROUP BY store_id;

-- Query Description: Retrieve the total sales potential per product.
-- This aggregated data helps in identifying products with the highest sales potential, which can be prioritized in the allocation process.
SELECT product_id, SUM(sales_potential_value) AS total_sales_potential
FROM sales_potential
GROUP BY product_id;
```

These queries are designed to retrieve the most relevant data for the optimization problem, including the decision variables, objective function coefficients, and constraint parameters. They also provide aggregated data and summary statistics that can help in making informed allocation decisions.
