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

S. Polyakovskiy; A. Makarowsky; R. M'Hallah

doi:10.1145/3071178.3071223

Home/Archive/arXiv

arXiv · 1703.07290

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

S. Polyakovskiy·A. Makarowsky·R. M'Hallah

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

S. Polyakovskiy, A. Makarowsky, R. M'Hallah. 2017-03-21. Just-in-Time Batch Scheduling Problem with Two-dimensional Bin Packing Constraints. https://doi.org/10.1145/3071178.3071223

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗