Solving robust bin-packing problems with a branch-and-price approach

Schepler, Xavier; Rossi, André; Gurevsky, Evgeny; Dolgui, Alexandre

doi:10.1016/j.ejor.2021.05.041

Cited by 11 publications

(7 citation statements)

References 38 publications

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“…In recent years, many scholars from different angle have begun to consider the problems with the impact of uncertainty. For example, in the traditional packing problem, the size of each item and the capacity of the bin are assumed to be known in advance, but not for actual applications (Schepler et al, 2022). The capacity constraint under uncertainty also appears in the domain of supply-chain management (Crainic et al, 2016), hospital administration (Cardoen et al, 2010), vehicle routing (Lu and Gzara, 2019;Gounaris et al, 2013) and scheduling of batch plants in the chemical industry (Cui and Engell, 2009;Bonfill et al, 2004).…”

Section: Related Literaturementioning

confidence: 99%

“…Recently, there is a lot of literature on column-generation based algorithms to solve combinatorial optimization problems under uncertainty, for example, robust machine availability problem in a parallel machine environment (Song et al, 2018), robust vehicle routing problem with time windows under demand uncertainty (Lu and Gzara, 2019), robust bin packing problem (Schepler et al, 2022), robust single-source capacitated facility location problem (Ryu and Park, 2022), and cost-based feature selected (Lee et al, 2022). All these papers introduce a robust version of deterministic optimization problems with budgeted uncertainty, where at most Γ number of uncertain parameters can deviate from there nominal ones.…”

Section: Optimizing Intelligent Schedulingmentioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

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A branch-and-price algorithm for robust parallel batch scheduling problem with uncertain size

Wang

Shao

Yan

2022

IMDS

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PurposeIn intelligent scheduling, parallel batch processing can reasonably allocate production resources and reduce the production cost per unit product. Hence, the research on a parallel batch scheduling problem (PBSP) with uncertain job size is of great significance to realize the flexibility of product production and mass customization of personalized products.Design/methodology/approachThe authors propose a robust formulation in which the job size is defined by budget constrained support. For obtaining the robust solution of the robust PBSP, the authors propose an exact algorithm based on branch-and-price framework, where the pricing subproblem can be reduced to a robust shortest path problem with resource constraints. The robust subproblem is transformed into a deterministic mixed integer programming by duality. A series of deterministic shortest path problems with resource constraints is derived from the programming for which the authors design an efficient label-setting algorithm with a strong dominance rule.FindingsThe authors test the performance of the proposed algorithm on the extension of benchmark instances in literature and compare the infeasible rate of robust and deterministic solutions in simulated scenarios. The authors' results show the efficiency of the authors' algorithm and importance of incorporating uncertainties in the problem.Originality/valueThis work is the first to study the PBSP with uncertain size. To solve this problem, the authors design an efficient exact algorithm based on Dantzig–Wolfe decomposition. This can not only enrich the intelligent manufacturing theory related to parallel batch scheduling but also provide ideas for relevant enterprises to solve problems.

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Section: Related Literaturementioning

confidence: 99%

Section: Optimizing Intelligent Schedulingmentioning

confidence: 99%

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A branch-and-price algorithm for robust parallel batch scheduling problem with uncertain size

Wang

Shao

Yan

2022

IMDS

View full text Add to dashboard Cite

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“…Finally, a branch‐and‐price method for robust optimization is proposed in Schepler et al. (2022) to address one‐dimensional bin packing with items of uncertain sizes.…”

Section: Literature Reviewmentioning

confidence: 99%

“…A cutting stock problem with random customer demand and random cutting times is investigated in Krichagina et al (1998) and approximated by linear programming and a dynamic control problem involving Brownian motion. Finally, a branch-and-price method for robust optimization is proposed in Schepler et al (2022) to address one-dimensional bin packing with items of uncertain sizes.…”

Section: Production and Operations Managementmentioning

confidence: 99%

Robust stock assortment and cutting under defects in automotive glass production

Arbib

Marinelli

Pınar

et al. 2022

Production and Operations Management

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We address an assortment‐and‐cutting problem arising in the glass industry. The objective is to provide minimum waste solutions that are robust against such raw material imperfections as those possibly occurring with float glass production technology. The stochastic realization of defects is modeled as a spatial Poisson point process. A mixed integer program in the classical vein of robust optimization is presented and tested on data taken from a real plant application. Defective final products must in any case be discarded as waste but, if a recourse strategy is adopted, faults in glass sheets can sometimes be recovered. Closed forms for the computation of faulty item probabilities are provided in simple cases, and obtained via Monte Carlo simulation in more complex ones. The computational results demonstrate the benefits of the robust approach in terms of the reduction of back‐orders and overproduction, thereby showing that recourse strategies can enable nonnegligible improvements. Encouraged by this result, the management is presently evaluating the possibility of adopting the proposed model in plant operation.

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