The Cast Design Problem

The cast design problem starts from a set of designed slabs, that is, slabs that have a specific dimension and to which orders have been assigned. (See the slab design problem.) The task is to sequence slabs into charges, and charges into casts such that the following constraints are satisifed

• the absolute difference between adjacent slab widths is less than some maximum value
• charge weight is within some minimum and maximum weight
• cast weight is within some minimum and maximum weight
• the slab width is monotonically increasing or decreasing within a charge
• the position of a slab within a charge and within a cast does not violate quality requirements of the orders assigned to the slab

• the use of surplus or stock slabs is minimized
• the average charge weight is close to some specified value
• the average of the absolute difference between adjacent slab widths is minimized
• grade substitution is is minimized
• orders in the same cast have similar due dates

The cast design problem has characteristics from the vehicle routing problem, bin packing, and the travelling saleperson problem, but cast design does not map onto any well-studied problem in operations research.