Multibox Three-Dimensional Packing Problems for Heterogeneous Extrudable Items

Table 1

Description of symbols.

Symbols	Definitions
	The set of packages used for th order, where .
	The set of items packed in the th package used for the th order, where , .
	The number of packages used for the th order, .
	The volume of the th item, where .
	The length, width, and height of the th item, respectively.
	The new length, width, and height of the th item after extrusion and deformation, respectively.
	The maximum volume of the th package.
	The length, width, and height of the th package, respectively.
	The new length, width, and height of the th bag after the th item has been filled, respectively.
	The maximum length, width, and height of the th bag, respectively.
	The squeeze rate of the th order of the th squeezable item after packing, .
	The overall squeeze rate of the th order after packing.
	The overall squeeze rate of all orders.
	The squeezability factor of the items in the order, .
	The average space utilization per order after all orders are packed.
	The total number of orders.
	Be used to evaluate the goodness of a crating scheme. The higher the value, the better the crating scheme.