Just-in-time batch scheduling problem with two-dimensional bin packing constraints

Abstract

This paper introduces and approximately solves a multi-component problem where small rectangular items are produced from large rectangular bins via guillotine cuts. An item is characterized by its width, height, due date, and earliness and tardiness penalties per unit time. Each item induces a cost that is proportional to its earliness and tardiness. Items cut from the same bin form a batch, whose processing and completion times depend on its assigned items. The items of a batch have the completion time of their bin. The objective is to find a cutting plan that minimizes the weighted sum of earliness and tardiness penalties. We address this problem via a constraint programming (CP) based heuristic (CPH) and an agent based modelling heuristic (ABH). CPH is an impact-based search strategy, implemented in the general-purpose solver IBM CP Optimizer. ABH is constructive. It builds a solution through repeated negotiations between the set of agents representing the items and the set representing the bins. The agents cooperate to minimize the weighted earlinesstardiness penalties. The computational investigation shows that CPH outperforms ABH on small-sized instances while the opposite prevails for larger instances.

A lookahead matheuristic for the unweighed variable-sized two-dimensional bin packing problem

“…VS2BP is an extension of the classical two-dimensional bin packing problem (2BP) [16]. Yet, the difficulty of 2BP restricted solution approaches to approximate ones that varied from simple best/first fit algorithms [6] to meta-heuristics [16] to hyper-heuristics [18] to multi-agent based algorithms [25] to a combination of CP and iterative packing heuristics [24]. Obviously, any heuristic that solves VS2BP solves 2BP, but not vice versa.…”

A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates

“…The cutting pattern minimizes both material waste and the sum of earliness-tardiness of the items. Polyakovskiy et al (2017) consider another variant of BP. Items that are cut from the same bin form a batch, whose processing time depends on its assigned items.…”