Minimizing the Total Weighted Waiting Times and Instability in a Rescheduling Problem with Dynamic Jobs Weight

Thanks to smart technological tools, customers can at any moment create or modify their commands. This reality forced many production firms to become sensitive in rescheduling processes. In the literature, most of rescheduling problems consider classical efficiency measures. However, some existing works also consider stability as a measure for limiting the deviation from initial schedule. In this work, we aim to bridge the gap in existing works on rescheduling by investigating a new approach to measure simultaneously efficiency by the total weighted waiting times and stability by the total weighted completion time deviation. This combination of criteria is very significant in industrial and hospital environments. In this paper, a single machine rescheduling problem with jobs arriving over time is considered. A mixed integer linear programming (MILP) model is designed for this problem and an iterative predictive-reactive strategy for dealing with the online part. Numerical results show that, at each time the jobs are rescheduled, the low weight ones move forward. Consequently, a new concept consisting in increasing the jobs weight as function of time is established. The effect of this new conception is evaluated by the evolution of the maximum flowtime. Eventually, the computing time of the MILP resolution is studied to explore its limitations.

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Single-Machine Scheduling with Fixed Periodic Preventive Maintenance to Minimise the Total Weighted Completion Times

Mathematical Problems in Engineering ◽

10.1155/2021/8891322 ◽

2021 ◽

Vol 2021 ◽

pp. 1-15

Author(s):

Hongming Zhou ◽

Ya-Chih Tsai ◽

Shenquan Huang ◽

Yarong Chen ◽

Fuh-Der Chou

Keyword(s):

Single Machine ◽

Preventive Maintenance ◽

Completion Time ◽

Machine Scheduling ◽

Single Machine Scheduling ◽

Mixed Integer ◽

Total Weighted Completion Time ◽

Machine Failure ◽

Periodic Preventive Maintenance ◽

Weighted Completion Time

The single-machine scheduling problem with fixed periodic preventive maintenance, in which preventive maintenance is implemented periodically to maintain good machine operational status and decrease the cost caused by sudden machine failure, is studied in this paper. The adopted objective function is to minimise the total weighted completion time, which is representative of the minimisation of the global holding/inventory cost in the system. This problem is proven to be NP-hard; a position-based mixed integer programming model and an efficient heuristic algorithm with local improvement strategy are developed for the total weighted completion time problem. To evaluate the performances of the proposed heuristic algorithms, two new lower bounds are further developed. Computational experiments show that the proposed heuristic can rapidly achieve optimal results for small-sized problems and obtain near-optimal solutions with tight average relative percentage deviation for large-sized problems.

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A new approach to select the best subset of predictors in linear regression modelling: bi-objective mixed integer linear programming

ANZIAM Journal ◽

10.21914/anziamj.v61i0.12784 ◽

2019 ◽

Vol 61 ◽

pp. 64

Author(s):

Hadi Charkhgard ◽

Ali Eshragh

Keyword(s):

Linear Programming ◽

Linear Regression ◽

Integer Linear Programming ◽

Mixed Integer Linear Programming ◽

Mixed Integer ◽

New Approach ◽

Regression Modelling

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Algorithms for the single machine total weighted completion time scheduling problem with release times and sequence-dependent setups

The International Journal of Advanced Manufacturing Technology ◽

10.1007/s00170-008-1762-4 ◽

2008 ◽

Vol 43 (7-8) ◽

pp. 810-821 ◽

Cited By ~ 14

Author(s):

Fuh-Der Chou ◽

Hui-Mei Wang ◽

Tzu-Yun Chang

Keyword(s):

Single Machine ◽

Completion Time ◽

Total Weighted Completion Time ◽

Scheduling Problem ◽

Release Times ◽

Sequence Dependent ◽

Time Scheduling ◽

Weighted Completion Time

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Scheduling Jobs with Truncated Exponential Sum-of-Logarithm-Processing-Times Based and Position-based Learning Effects

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595915500268 ◽

2015 ◽

Vol 32 (04) ◽

pp. 1550026 ◽

Cited By ~ 6

Author(s):

Yuan-Yuan Lu ◽

Fei Teng ◽

Zhi-Xin Feng

Keyword(s):

Single Machine ◽

Minimization Problem ◽

Completion Time ◽

Heuristic Algorithms ◽

Exponential Sum ◽

Total Weighted Completion Time ◽

Learning Effects ◽

Processing Times ◽

Time Minimization ◽

Weighted Completion Time

In this study, we consider a scheduling problem with truncated exponential sum-of-logarithm-processing-times based and position-based learning effects on a single machine. We prove that the shortest processing time (SPT) rule is optimal for the makespan minimization problem, the sum of the θth power of job completion times minimization problem, and the total lateness minimization problem, respectively. For the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, we present heuristic algorithms (the worst-case bound of these heuristic algorithms are also given) according to the corresponding single machine scheduling problems without learning considerations. It also shows that the problems of minimizing the total tardiness, the total weighted completion time and the discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.

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Online bounded-batch scheduling to minimize total weighted completion time on parallel machines

International Journal of Production Economics ◽

10.1016/j.ijpe.2014.05.012 ◽

2014 ◽

Vol 156 ◽

pp. 31-38 ◽

Cited By ~ 4

Author(s):

Ran Ma ◽

Long Wan ◽

Lijun Wei ◽

Jinjiang Yuan

Keyword(s):

Completion Time ◽

Parallel Machines ◽

Batch Scheduling ◽

Total Weighted Completion Time ◽

Weighted Completion Time

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Automatic 3-D Crack Propagation Calculations in Industrial Components: A Pure Hexahedral versus a Combined Hexahedral-Tetrahedral Approach

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.348-349.45 ◽

2007 ◽

Vol 348-349 ◽

pp. 45-48

Author(s):

Guido Dhondt

Keyword(s):

Crack Propagation ◽

Computing Time ◽

Propagation Direction ◽

Hexahedral Elements ◽

Crack Propagation Direction ◽

Low Weight ◽

Out Of Plane ◽

Hexahedral Meshes ◽

Crack Faces

In recent years, increased loading and low weight requirements have led to the need for automatic crack tracing software. At MTU a purely hexahedral code has been developed in the nineties for Mode-I applications. It has been used extensively for all kinds of components and has proven to be very flexible and reliable. Nevertheless, in transition regions between complex components curved cracks have been observed, necessitating the development of mixed-mode software. Due to the curvature of the crack faces, purely hexahedral meshes are not feasible, and therefore a mixture of hexahedral elements at the crack tip, combined with tetrahedral in the remaining structure has been selected. The intention of the present paper is to compare both methods and to point out the strength and weaknesses of each regarding accuracy, complexity, flexibility and computing time. Furthermore, difficulties arising from the out-of-plane growth of the crack such as the determination of the crack propagation direction are discussed.

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RASON: A new approach to the scheduling radiotherapy problem that considers the current waiting times

Expert Systems with Applications ◽

10.1016/j.eswa.2016.07.045 ◽

2016 ◽

Vol 64 ◽

pp. 287-295 ◽

Cited By ~ 8

Author(s):

María-Cristina Riff ◽

Juan Pablo Cares ◽

Bertrand Neveu

Keyword(s):

Waiting Times ◽

New Approach

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MINIMIZING TOTAL WEIGHTED COMPLETION TIME ON A SINGLE BATCH PROCESSING MACHINE

Production and Operations Management ◽

10.1111/j.1937-5956.1997.tb00415.x ◽

2009 ◽

Vol 6 (1) ◽

pp. 57-73 ◽

Cited By ~ 56

Author(s):

Reha Uzsoy ◽

Yaoyu Yang

Keyword(s):

Completion Time ◽

Batch Processing ◽

Total Weighted Completion Time ◽

Processing Machine ◽

Batch Processing Machine ◽

Weighted Completion Time ◽

Single Batch

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Modeling and scheduling hybrid open shops for makespan minimization

Journal of Modelling in Management ◽

10.1108/jm2-11-2020-0302 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Kennedy Anderson Guimarães de Araújo ◽

Tiberius Oliveira e Bonates ◽

Bruno de Athayde Prata

Keyword(s):

Programming Model ◽

Computing Time ◽

Iterated Local Search ◽

Mixed Integer ◽

Scheduling Problems ◽

Priority Rules ◽

Production Flow ◽

Solution Quality ◽

Content Type ◽

Constructive Heuristics

Purpose This study aims to address the hybrid open shop problem (HOSP) with respect to the minimization of the overall finishing time or makespan. In the HOSP, we have to process n jobs in stages without preemption. Each job must be processed once in every stage, there is a set of mk identical machines in stage k and the production flow is immaterial. Design/methodology/approach Computational experiments carried out on a set of randomly generated instances showed that the minimal idleness heuristic (MIH) priority rule outperforms the longest processing time (LPT) rule proposed in the literature and the other proposed constructive methods on most instances. Findings The proposed mathematical model outperformed the existing model in the literature with respect to computing time, for small-sized instances, and solution quality within a time limit, for medium- and large-sized instances. The authors’ hybrid iterated local search (ILS) improved the solutions of the MIH rule, drastically outperforming the models on large-sized instances with respect to solution quality. Originality/value The authors formalize the HOSP, as well as argue its NP-hardness, and propose a mixed integer linear programming model to solve it. The authors propose several priority rules – constructive heuristics based on priority measures – for finding feasible solutions for the problem, consisting of adaptations of classical priority rules for scheduling problems. The authors also propose a hybrid ILS for improving the priority rules solutions.

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