Mathematical Problems in Engineering / 2016 / Article / Tab 2

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.

SymbolDescription

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

Distributor’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