Admission control in queue-time loop production-mixed integer programming with Lagrangian relaxation (MIPLAR)

Hong, I‐Hsuan; Chou, Chin-Chen; Lee, Pin-Kuan

doi:10.1016/j.cie.2019.02.002

Cited by 11 publications

(4 citation statements)

References 32 publications

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“…Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines such as mathematics, operations research, engineering, and computer science as well as within a range of areas of strategic importance to society such as biology 1,2 , healthcare 3,4 , humanitarian applications [5][6][7][8] , manufacturing [9][10][11][12] , pharmacy [13][14][15][16] , power and energy systems [17][18][19] , transportation and logistics 20,21 and many others.…”

mentioning

confidence: 99%

Surrogate “Level-Based” Lagrangian Relaxation for mixed-integer linear programming

Bragin

Tucker

2022

Sci Rep

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Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity. Because of integer decision variables, as the problem size increases, the number of possible solutions increases super-linearly thereby leading to a drastic increase in the computational effort. To efficiently solve MILP problems, a “price-based” decomposition and coordination approach is developed to exploit 1. the super-linear reduction of complexity upon the decomposition and 2. the geometric convergence potential inherent to Polyak’s stepsizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set stepsizes heuristically by adjusting hyperparameters, the key novel way to obtain stepsizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate stepsizes are inferred. Testing results for large-scale Generalized Assignment Problems demonstrate that for the majority of instances, certifiably optimal solutions are obtained. For stochastic job-shop scheduling as well as for pharmaceutical scheduling, computational results demonstrate the two orders of magnitude speedup as compared to Branch-and-Cut. The new method has a major impact on the efficient resolution of complex Mixed-Integer Programming problems arising within a variety of scientific fields.

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mentioning

confidence: 99%

Surrogate “Level-Based” Lagrangian Relaxation for mixed-integer linear programming

Bragin

Tucker

2022

Sci Rep

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“…MILP has multiple applications in problems of importance to society: ambulance relocation (Lee et al, 2022), balanced item placement (Gasse et al, 2022), cost-sharing for ride-sharing (Hu et al, 2021), drop box location (Schmidt and Albert, 2022), efficient failure detection in large-scale distributed systems (Er-Rahmadi and Ma, 2022), home healthcare routing (Dastgoshade et al, 2020), home service routing and appointment scheduling (Tsang and Shehadeh, 2022), inventory control under demand and lead time uncertainty (Thorsen and Yao, 2017), job-shop scheduling (Liu et al, 2021), facility location (Basciftci et al, 2021), flow-shop scheduling (Hong et al, 2019;Balogh et al, 2022;Öztop et al, 2022), freight transportation (Archetti et al, 2021), location and inventory prepositioning of disaster relief supplies (Shehadeh and Tucker, 2022), machine scheduling with sequence-dependent setup times (Yalaoui and Nguyen, 2021), maritime inventory routing (Gasse et al, 2022), multi-agent path finding with conflict-based search (Huang et al, 2021), multi-depot electric bus scheduling (Gkiotsalitis et al, 2023), multi-echelon/multi-facility green reverse logistics network design (Reddy et al, 2022), optimal physician staffing (Prabhu et al, 2021), optimal search path with visibility (Morin et al, 2023), oral cholera vaccine distribution (Smalley et al, 2015), outpatient colonoscopy scheduling (Shehadeh et al, 2020), pharmaceutical distribution (Zhu and Ursavas, 2018), plant factory crop scheduling (Huang et al, 2020), post-disaster blood supply (Hamdan and Diabat, 2020;Kamyabniya et al, 2021), real assembly line balancing with human-robot collaboration (Nourmohammadi et al, 2022), reducing vulnerability to human trafficking (Kaya et al, 2022), restoration planning and crew routing (Morshedlou et al, 2021)...…”

Section: Importance and Difficulties Of Milp Problemsmentioning

confidence: 99%

Lagrangian Relaxation for Mixed-Integer Linear Programming: Importance, Challenges, Recent Advancements, and Opportunities

Bragin¹

2023

Preprint

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Operations in areas of importance to society are frequently modeled as Mixed-Integer Linear Programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve the associated difficulties through decomposition. Due to the non-smooth nature of Lagrangian dual functions, the coordination aspect of the method has posed serious challenges. This paper presents several significant historical milestones (beginning with Polyak's pioneering work in 1967) toward improving Lagrangian Relaxation coordination through improved optimization of non-smooth functionals. Finally, this paper presents the most recent developments in Lagrangian Relaxation for fast resolution of MILP problems. The paper also briefly discusses the opportunities that Lagrangian Relaxation can provide at this point in time.

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“…Zheng et al [54], Heidari-Fathian and Pasandideh [53], and Yousefi-Babadi et al [55] are some examples of the usage of the Lagrangian relaxation based method in supply chain management. Hong et al [56] adopted this method in the manufacturing systems. Regarding the efficiency of this approach in the several problems, it has been adapted to our problem.…”

Section: Lagrangian Relaxation-based Approachmentioning

confidence: 99%

Process and production planning for sustainable reconfigurable manufacturing systems (SRMSs): multi-objective exact and heuristic-based approaches

Yazdani

Khezri²,

Benyoucef

2022

Int J Adv Manuf Technol

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In today's competitive environments, companies need to be cost-effective, environmental-friendly, and social-friendly to deal with several challenges that exist in markets. In this context, reconfigurable manufacturing systems (RMSs) have emerged to fulfil these requirements. RMS is one of the attractive manufacturing paradigms. Machine components, software, or material handling units can be added, removed, modified, or interchanged as needed and imposed by the necessity to react rapidly and cost-effectively to changing. A multi-objective multi-product process and production planning problem in a sustainable reconfigurable manufacturing environment (SRMS) is considered in this paper. Three pillars of sustainability, respectively social, environmental, and economic are formulated and optimised. First, a linear mixed-integer model is proposed. Second, a Lagrangian relaxation-based approach is developed to solve the problem on the large scales, where an exact method is used to solve the problem in small and medium cases with GAMS software. To illustrate the applicability of the proposed approaches, some numerical examples and analyses are presented. Finally, a sensibility study of the problem according to some parameters is performed.

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Admission control in queue-time loop production-mixed integer programming with Lagrangian relaxation (MIPLAR)

Cited by 11 publications

References 32 publications

Surrogate “Level-Based” Lagrangian Relaxation for mixed-integer linear programming

Surrogate “Level-Based” Lagrangian Relaxation for mixed-integer linear programming

Lagrangian Relaxation for Mixed-Integer Linear Programming: Importance, Challenges, Recent Advancements, and Opportunities

Process and production planning for sustainable reconfigurable manufacturing systems (SRMSs): multi-objective exact and heuristic-based approaches

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