# Just-in-Time Batch Scheduling Problem with Two-dimensional Bin Packing Constraints

## TL;DR

This paper addresses a complex scheduling and packing problem involving rectangular items and bins, proposing heuristics to minimize earliness and tardiness penalties, with CP excelling on small instances and AB on larger ones.

## Contribution

It introduces a novel multi-component problem combining bin packing and scheduling, and develops two heuristics, CP and AB, to approximate solutions.

## Key findings

- CP outperforms AB on small instances
- AB performs better on larger instances
- Heuristics effectively minimize earliness and tardiness penalties

## 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 based heuristic (CP) and an agent based modelling heuristic (AB). CP is an impact-based search strategy, implemented in the general-purpose solver IBM CP Optimizer. AB 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 earliness-tardiness penalties. The computational investigation shows that CP outperforms AB on small-sized instances while the opposite prevails for larger instances.