Bin Packing Problems with Variable Pattern Processing Times: A Proof-of-concept

In several real-world applications the time required to accomplish a job generally depends on the number of tasks that compose it. Although the same also holds for packing (or cutting) problems when the processing time of a bin depends by the number of its items, the approaches proposed in the literature usually do not consider variable bin processing times and therefore become inaccurate when time costs are worth more than raw material costs. In this paper we discuss this issue by considering a variant of the one-dimensional bin packing problem in which items are due by given dates and a convex combination of number of used bins and maximum lateness has to be minimized. An integer linear program that takes into account variable pattern processing times is proposed and used as proof-of-concept.