One-dimensional bin packing with pattern-dependent processing time

In this paper the classical one-dimensional bin packing problem is integrated with scheduling elements: a due date is assigned to each item and the time required to process each bin depends on the pattern being used. The objective is to minimize a convex combination of the material waste and the del...

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Bibliographic Details
Published in:European journal of operational research Vol. 322; no. 3; pp. 770 - 782
Main Authors: Marinelli, Fabrizio, Pizzuti, Andrea, Wu, Wei, Yagiura, Mutsunori
Format: Journal Article
Language:English
Published: Elsevier B.V 01.05.2025
Subjects:
Batch scheduling
Branch-and-price
Dynamic programming
Mixed integer programming
Packing
Mixed integer programming
Branch-and-price
Dynamic programming
Packing
Batch scheduling
ISSN:0377-2217
Online Access:Get full text
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Summary:In this paper the classical one-dimensional bin packing problem is integrated with scheduling elements: a due date is assigned to each item and the time required to process each bin depends on the pattern being used. The objective is to minimize a convex combination of the material waste and the delay costs, both significant in many real-world contexts. We present a novel pattern-based mixed integer linear formulation suitable for different classical scheduling objective functions, and focus on the specific case where the delay cost corresponds to the maximum tardiness. The formulation is tackled by a branch-and-price algorithm where the pricing of the column generation scheme is a quadratic problem solved by dynamic programming. A sequential value correction heuristic (SVC) is used to feed with warm starting solutions the column generation which, in turn, feeds the SVC with optimal prices so as to compute refined feasible solutions during the enumeration. Computational tests show that both column generation and branch-and-price substantially outperform standard methods in computing dual bounds and exact solutions. Additional tests are presented to analyze the sensitivity to parameters’ changes. •Two pattern-based formulations for solving 1BP-VPT.•Ad-hoc dynamic programming methods for the special knapsack pricing problems.•Exact branch-and-price procedure embedding a robust branching scheme.•Proposed formulations outperform the benchmark assignment-based model for 1BP-VPT.•Sensitivity analysis to identify challenging instances.
ISSN:0377-2217
DOI:10.1016/j.ejor.2024.11.023