A Novel Integer Linear Programming Formulation for Job-Shop Scheduling Problems

Liu, Anbang; Luh, Peter B.; Yan, Bing; Bragin, Mikhail A.

doi:10.1109/lra.2021.3086422

Cited by 18 publications

(49 citation statements)

References 20 publications

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“…The gist of the tightening is to delineate facets of the convex hull; if successful, then the combinatorial problem reduces to a much easier-to-solve LP problem; even if a problem is "partially" tightened, the CPU time is greatly reduced (Yan et al 2018(Yan et al , 2021. One of the most recent advancements to reduce the number of decision variables and constraints, compared to previous ILP formulation, is proven to be tighter compared to previous formulations (Liu et al 2021): only the beginning times of operations are decision variables thereby reducing the number of decision variables and constraints compared to those within the previous formulations. Since the formulation has few decision variables and constraints, for a problem instance from (Hoitomt et al 1993), the formulation leads to several orders of magnitude improvement over previously-used approaches in terms of CPU time and to optimality of solution obtained (from 3,600 s and 3.72% gap down to 3.31 s and 0% gap) when solved by using standard B&C (Liu et al 2021).…”

Section: Supply Chain Management Downstream Procurementmentioning

confidence: 99%

“…Supported by the work "Surrogate" Lagrangian Relaxation (SLR) (Bragin et al 2015) whereby the difficulties of the sub-gradient method (such as zigzagging of multipliers and high computational effort) were overcome, the JSS problem was formulated as an MILP problem and efficiently solved by using the SLR method (Yan et al 2018). To further improve computational efficiency, supported by the work of Bragin et al (2019) whereby convergence of SLR was improved by using two-segment absolutevalue penalties for constraint violations, the JSS problem (as mentioned before) was formulated as a tighter MILP problem and the resulting problem was solved by using a version of the SLR method with three-segment penalties for faster convergence (Liu et al 2021).…”

Section: Supply Chain Management Downstream Procurementmentioning

confidence: 99%

“…These two attempts will be captured probabilistically and will be modeled within one problem formulation. The formulation developed by Liu et al (2021) will be used as a basis, and stochastic elements due to scrap and rework will be added, as explained in the following sections. Once a feasible schedule is obtained, the schedule corresponding to the first attempt is generated at the beginning of a shift: which job is to be assigned to what machine group and at what time.…”

Section: Job-shop Scheduling Problem Description and Formulationmentioning

confidence: 99%

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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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Section: Supply Chain Management Downstream Procurementmentioning

confidence: 99%

Section: Supply Chain Management Downstream Procurementmentioning

confidence: 99%

Section: Job-shop Scheduling Problem Description and Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Bragin¹,

Wilhelm²,

Yu³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…where S is the set of all part-operation pairs. Range [li,j, ui,j] contains all eligible beginning times, and can be derived based on part arrival times ai, operation processing times {pi,j}, and T following ( 9) and ( 10) of [7].…”

Section: Problem Formulation and Surrogate Lagrangian Relaxationmentioning

confidence: 99%

“…Coupling machine capacity (Constraints ( 7) of [7]) Decision variables of different parts are coupled by machine capacity constraints, i.e., the number of "active" operations (i.e., being processed) on a machine group at each time slot cannot exceed the capacity of that machine group. To formulate these constraints based on {bi,j,t}, a fact is novelly exploited that if operation (i, j) is processing on time slot t, then it must begin within [t-pi,j+1].…”

Section: Problem Formulation and Surrogate Lagrangian Relaxationmentioning

confidence: 99%

Integrating Machine Learning and Mathematical Optimization for Job Shop Scheduling

Liu¹,

Luh²,

Sun³

2022

Preprint

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<p>Job-shop scheduling is an important but difficult integer optimization problem for low-volume and high-variety manufacturing, with solutions required to be obtained quickly at the beginning of each shift. In view of the increasing demand of customized products, problem sizes are growing. Machine learning (ML) is a promising solution methodology. Direct learning solutions, however, is difficult because of the NP-hard nature of the problem. In this paper, ML and the decomposition and coordination approach of Surrogate Lagrangian Relaxation are synergistically integrated. ML is used to learn and predict “good enough” solutions of part subproblems, which are not NP-hard. Nevertheless, the task is still challenging in view of the quite different parts to be scheduled from shift to shift, the complicated tardiness-related objective function, and many part-level constraints. To address these issues, a generic pointer network is developed for all parts after part subproblems are innovatively reformulated to be at a much simplified and streamlined level. The pointer network is also novelly enhanced with a masking mechanism so that predictions satisfy all part-level constraints. Numerical results demonstrate that the enhanced pointer network can learn and predict subproblem solutions well, and that near-optimal solutions of large problems are efficiently obtained. The performance of the method is expected to further improve through continual learning. </p>

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A simulation‐based integrated virtual testbed for dynamic optimization in smart manufacturing systems

Sun

Bragin

et al. 2022

J Adv Manuf & Process

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In a manufacturing system, production control-related decision-making activities occur at different levels. At the process level, one of the main control activities is to tune the parameters of individual manufacturing equipment. At the system level, the main activity is to coordinate production resources and to route parts to appropriate workstations based on their processing requirement, priority indices, and control policy. At the factory level, the goal is to plan and schedule the processing of parts at different operations for the entire system in order to optimize certain objectives. Note that the results of such activities at different levels are closely coupled and affect the overall performance of the manufacturing system as a whole. Therefore, it is important to systematically integrate these control and optimization activities into one unified platform to ensure the goal of each individual activity is aligned with the overall performance of the system. In this paper, we develop a simulation-based virtual testbed that implements dynamic optimization, automatic information exchange, and decision-making from the process-level, system-level, and factory-level of a manufacturing system into an integrated computation environment. This is demonstrated by connecting a Python-based numerical computation program, discrete-event simulation software (Simul8), and an optimization solver (CPLEX) via a third-party master program. The application of this simulation-based virtual testbed is illustrated by a case study in a machining shop.

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A Novel Integer Linear Programming Formulation for Job-Shop Scheduling Problems

Cited by 18 publications

References 20 publications

Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Integrating Machine Learning and Mathematical Optimization for Job Shop Scheduling

A simulation‐based integrated virtual testbed for dynamic optimization in smart manufacturing systems

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