Exact solutions for the two-machine robust flow shop with budgeted uncertainty

Levorato, Mario; Figueiredo, Rosa; Frota, Yuri

doi:10.1016/j.ejor.2021.10.021

Cited by 15 publications

(12 citation statements)

References 51 publications

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“…Scheduling a two-machine flow-shop has been a popular research topic since the seminal paper of Johnson (1954) until the present time, see, for example, the most recent publications of Gmys et al (2020), Levorato et al (2022), Gilenson and Shabtay (2021), and Zinder et al (2021). The main application area for these studies is the short-term planning of industrial and service operations in a sequential two-stage system.…”

Section: Relevant Literature Motivation and Summary Of Our Resultsmentioning

confidence: 99%

Maximizing total early work in a distributed two‐machine flow‐shop

Dolgui

Kovalyov

Lin

2022

Naval Research Logistics

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The problem of maximizing total early work in a two-machine flow-shop, in which n jobs are to be scheduled subject to a common due date d, has been recently studied in the scheduling literature. An O(n 2 d 4 ) time dynamic programming algorithm was presented first for the weighted case, and then for the unweighted case another O(n 2 d 2 ) running time dynamic programming algorithm was proposed and converted into an O ( n 4 𝜀 2 ) time fully polynomial time approximation scheme (FPTAS). By establishing new problem properties, we present an O(nd 2 ) time dynamic programming algorithm and an O ( n 3 𝜀 2) time FPTAS for the unweighted problem. We generalize the problem to a distributed setting of m parallel two-machine flow-shops, develop an O(nd 3m ) time dynamic programming algorithm, an O) time FPTAS, and three integer linear programming (ILP) formulations for it. Computational experiments are conducted to appraise the proposed ILP models.

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Section: Relevant Literature Motivation and Summary Of Our Resultsmentioning

confidence: 99%

Maximizing total early work in a distributed two‐machine flow‐shop

Dolgui

Kovalyov

Lin

2022

Naval Research Logistics

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“…Regarding the two-machine robust flow shop problem with the makespan objective, budgeted uncertainty and processing time intervals, Ying (2015) developed two metaheuristic algorithms to solve the problem (SA and IG), but with the makespan objective. Finally, in a recent work (Levorato et al, 2022), an exact solution approach was developed for the makespan problem, based on Column-and-Constraint Generation.…”

Section: Robust Optimization Approachesmentioning

confidence: 99%

“…This section presents an exact method for solving RPFS-TWCT under budgeted uncertainty. Our approach is based on a cutting plane procedure for two-stage RO problems, called Column-and-Constraint Generation (C&CG), recently applied in the efficient solution of robust scheduling problems (Ruiz Duarte et al, 2020;Silva et al, 2020;Levorato et al, 2022). Besides generating new constraints, as usual in this kind of method, each cutting plane of C&CG is also associated with a set of new decision variables for the recourse problem (Zeng & Zhao, 2013).…”

Section: Column-and-constraint Generation Applied To the Rpfs-twctmentioning

confidence: 99%

“…To the best of our knowledge, this is the first work to treat the m-machine robust permutation flow shop problem under budgeted uncertainty, which minimizes the worst-case weighted sum of job completion times. The solution method is partly based on a previous work (Levorato et al, 2022), developed for the two-machine robust permutation flow shop problem, with the makespan objective. This text adopts the following structure.…”

Section: Introductionmentioning

confidence: 99%

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Robust permutation flow shop total weighted completion time problem: Solution and application to the oil and gas industry

Levorato

Sotelo

Figueiredo

et al. 2023

Computers & Operations Research

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“…For a given sequence of jobs σ, there exists a worst-case scenario, maximizing the value of the makespan. Levorato et al [6] developed a polynomial-time (O(n 2 )) worst-case determination procedure, using dynamic programming, for machinedependent budget Γ = (Γ 1 , Γ 2 ). The same idea is now used when considering a global budget Γ .…”

Section: 1 Worst-case Evaluationmentioning

confidence: 99%

Constraint Programming for the Robust Two-Machine Flow-Shop Scheduling Problem with Budgeted Uncertainty

Juvin

Houssin

López

2023

Lecture Notes in Computer Science

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This paper addresses the robust two-machine permutation flow-shop scheduling problem considering non-deterministic operation processing times associated with an uncertainty budget. The objective is to minimize the makespan of the schedule. Exact solution methods incorporated within the framework of a twostage robust optimization are proposed to solve the problem. We first prove that under particular conditions the robust two-machine permutation flow-shop scheduling problem can be solved in polynomial time by the well-known Johnson's algorithm usually dedicated to the deterministic version. Then we tackle the general problem, for which we propose a column and constraint generation algorithm. We compare two versions of the algorithm. In the first version, a mixed-integer linear programming formulation is used for the master problem. In the second version, we use a constraint programming model for the master problem. To the best of our knowledge, the use of constraint programming for a master problem in a two-stage robust optimization problem is innovative. The experimental results show the very good performance of the method based on the constraint programming formulation. We also notice that Johnson's algorithm is surprisingly efficient for the robust version of the general problem.

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Exact solutions for the two-machine robust flow shop with budgeted uncertainty

Cited by 15 publications

References 51 publications

Maximizing total early work in a distributed two‐machine flow‐shop

Maximizing total early work in a distributed two‐machine flow‐shop

Robust permutation flow shop total weighted completion time problem: Solution and application to the oil and gas industry

Constraint Programming for the Robust Two-Machine Flow-Shop Scheduling Problem with Budgeted Uncertainty

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