Optimal job-shop scheduling with random operations and cost objectives

Golenko‐Ginzburg, Dimitri; Gonik, Aharon

doi:10.1016/s0925-5273(01)00140-2

Cited by 40 publications

(7 citation statements)

References 11 publications

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“…Multipliers are initialized by using LP dual solutions. The following hyperparameters are used: within the step-sizing formula (23), parameters γ and ζ are chosen to be 1 I (the inverse of the number of machines) and 1 1.5 , respectively; within (24), parameter ν is chosen to be 2. As demonstrated in Table 1, the method's performance is appreciably stable for the given range of initial step-sizes used.…”

Section: Example 1: Generalized Assignment Problemsmentioning

confidence: 99%

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

Bragin

Tucker

2022

Preprint

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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 step-sizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set step-sizes heuristically by adjusting hyper-parameters, the key novel way to obtain step-sizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate step-sizes are inferred. Testing results for large-scale Generalized Assignment Problems (GAP) 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 frequently used Branch-and-Cut (B&C). SLBLR has a major impact on the efficient resolution of complex Mixed-Integer Programming (MIP) problems arising within a variety of scientific fields.

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Section: Example 1: Generalized Assignment Problemsmentioning

confidence: 99%

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

Bragin

Tucker

2022

Preprint

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“…In the extant research, uncertain processing times have been considered (Luh et al 1999, Golenko-Ginzburg and Gonik 2002, Lei and Xiong 2007, Lei 2011, Horng et al 2012, Zhang et al 2013, Yang et al 2014, Shen and Zhu 2016, Jamili 2019, Horng and Lin 2021). 4 Within these papers, while the processing time is uncertain, a job is assumed to be processed with certainty.…”

Section: Supply Chain Management Downstream Procurementmentioning

confidence: 99%

Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Bragin¹,

Wilhelm²,

Yu³

et al. 2022

Preprint

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Motivated by the presence of uncertainties as well as combinatorial complexity within the links of supply chains, this paper addresses the outstanding and timely challenge illustrated through a case study of stochastic job-shop scheduling problems arising within low-volume high-variety manufacturing. These problems have been classically formulated as integer linear programs (ILPs), which are known to be NP-hard, and are computationally intractable. Yet, optimal or near-optimal solutions must be obtained within strict computational time requirements. While the deterministic cases have been efficiently solved by state-of-the-art methods such as branch-and-cut (B&C), uncertainties may compromise the entire schedule thereby potentially affecting the entire supply chain downstream, thus, uncertainties must be explicitly captured to ensure the feasibility of operations. The stochastic nature of the resulting problem adds a layer of computational difficulty on top of an already intractable problem, as evidenced by the presented case studies with some cases taking hours without being able to find a "near-optimal" schedule. To efficiently solve the stochastic JSS problem, a recent Surrogate "Level-Based" Lagrangian Relaxation is used to reduce computational effort while efficiently exploiting geometric convergence potential inherent to Polyak's step-sizing formula thereby leading to fast convergence. Computational results demonstrate that the new method is more than two orders of magnitude faster compared to B&C. Moreover, insights based on a small intuitive example are provided through simulations demonstrating an advantage of scholastic scheduling.

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“…In Ref. [9], the authors study the SJSSP with just-in-time objective (completion before or after the due date will both result in a cost). Several decision-making rules are proposed for selecting a job when several jobs are competing for a machine.…”

Section: The Stochastic Job Shop Scheduling Problemmentioning

confidence: 99%