Exact Methods for the Generalized Multiple Strip Packing Problem with Heterogeneous Costs

TL;DR

This paper introduces a new cost-weighted area objective for the Generalized Multiple Strip Packing Problem, proposing two exact formulations and a Benders decomposition algorithm, with extensive computational validation.

Contribution

It presents the first cost-weighted area objective for GMSPP, along with two exact formulations and a novel Benders decomposition algorithm for heterogeneous strips.

Findings

The normal-position formulation outperforms the big-M formulation in experiments.

BendM algorithm effectively solves instances across various cost structures.

Cost-weighted area objective unifies multiple packing objectives in a single framework.

Abstract

We study the Generalized Multiple Strip Packing Problem (GMSPP) with heterogeneous per-unit-area costs, in which rectangular items of fixed dimensions must be packed without overlap into multiple open-ended strips of different widths, each incurring a cost proportional to the area used. This cost-weighted area objective is introduced here for the first time and unifies several objectives studied separately in the literature, including total area, total height for identical strips, and makespan. We propose two exact integer programming formulations for this problem: a big-M formulation adapted from recent work, and a normal-position formulation extending an earlier single-strip approach to multiple heterogeneous strips. For the normal-position formulation, we develop an exact Benders decomposition algorithm, called BendM (Benders' Method for Multiple strips). Comprehensive computational experiments on 180 instances derived from standard strip-packing benchmarks compare both formulations and demonstrate the effectiveness of BendM across three cost structures.