Research Article

# A Hybrid Method for Modeling and Solving Supply Chain Optimization Problems with Soft and Logical Constraints

## Table 2

Indices, parameters, symbols, and decision variables.
 Symbol Description Indices Product item () Customer/retailer () Factory (manufacturer) () Distributor () Mode of transportation () Number of factories Number of customers/retailers Number of distributors Number of product items Number of ransportation modes Input parameters Distributorâ€™s cost (fixed) Volume/capacity occupied by product item Weight of product item Max capacity/volume of distributor Production capacity of factory for product item Cost of product item in factory If distributor can supply product item then ; otherwise Time required to prepare the dispatch of product item by distributor Cut-off time of supply of product item to customer/retailer Size of the order for product item placed by customer c Number of transportation units using transportation mode e Capacity of transportation unit using transportation mode e Tonnage of transportation unit using transportation mode e Supply time from factory (manufacturer) a to distributor b by transportation mode e Cost of supplying product item d from factory (manufacturer) a to distributor b by transportation mode e (variable) If factory (manufacturer) a can supply distributor b using transportation mode e, then ; otherwise Cost of supply from factory (manufacturer) a to distributor b by transportation mode e (fixed) Overall cost of supply from distributor b to customer c by transportation mode e Time of supply from distributor b to customer/retailer c by transportation mode e Variable cost of supply of product item d from distributor b to customer/retailer c by transportation mode e If distributor b can supply customer/retailer c by transportation mode e, then ; otherwise Fixed cost of supply from distributor b to customer/retailer c by transportation mode e Overall cost of supply from distributor b to customer/retailer c by transportation mode e Environmental cost of using transportation mode e Decision variables Quantity of a product item d supplied from factory (manufacturer) a to distributor b by transportation mode e to customer/retailer c If supply is from factory (manufacturer) a to distributor b of product d by transportation mode e to customer/retailer , then , otherwise Number of travels from factory (manufacturer) a to distributor b by transportation mode e Quantity of product item d supplied from distributor b to customer c by transportation mode e If supply is from distributor b to customer/retailer c for product d by transportation mode e, then ; otherwise Number of travels from distributor b to customer/retailer c by transportation mode e