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Pereira, J. (2016). Procedures for the bin packing problem with precedence constraints. Eur. J. Oper. Res., 250(3), 794–806.
Abstract: The bin packing problem with precedence constraints (BPP-P) is a recently proposed variation of the classical bin packing problem (BPP), which corresponds to a basic model featuring many underlying characteristics of several scheduling and assembly line balancing problems. The formulation builds upon the BPP by incorporating precedence constraints among items, which force successor items to be packed into later bins than their predecessors. In this paper we propose a dynamic programming based heuristic, and a modified exact enumeration procedure to solve the problem. These methods make use of several new lower bounds and dominance rules tailored for the problem in hand. The results of a computational experiment show the effectiveness of the proposed methods, which are able to close all of the previous open instances from the benchmark instance set within very reduced running times. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
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Alvarez-Miranda, E., Pereira, J., & Vila, M. (2023). Analysis of the simple assembly line balancing problem complexity. Comput. Oper. Res., 159, 106323.
Abstract: The simple assembly line balancing problem (SALBP) involves the determination of the assignment of elementary assembly operations to the workstations of the assembly line for the manufacture of a final product, with the objective of maximising assembly efficiency. In addition to its practicality, the SALBP can be considered as an extension of the bin packing problem (BPP) to account for the precedence relations between items. These constraints introduce an ordering component to the problem, which increases the complexity of SALBP resolution. However, previous studies indicated that precedence constraints do not play an important role in the capacity of state-of-the-art procedures to solve benchmark instances to optimality. In this study, we analysed the influences of different features of an SALBP instance on the performance of state-of-the-art solution methods for the abovementioned problem. First, we provide an alternative proof of complexity for the SALBP that uses precedence constraints to demonstrate its non-deterministic polynomial time (NP)-complete status, followed by a new set of benchmark instances directed towards an empirical analysis of the different features of SALBP instances. The experimental results revealed that the packing features of the SALBP are a major source of the perceived difficulty for any instance; however, precedence constraints play a role in the performance of these solution procedures. Specifically, the number of precedence constraints plays an important role in the results obtained from state-of-the-art methods. In addition to the analysis, certain issues that were identified in the publicly available implementations of the state-of-the-art method for resolving this problem were addressed in this study.
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