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Mathematics
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Mathematical Models and Methods of Scheduling Theory
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Mathematical Models and Methods of Scheduling Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 8769

Special Issue Editor

Dr. Amir Elalouf

E-Mail Website
Guest Editor
Department of Management, Bar Ilan University, Ramat Gan, Israel
Interests: scheduling; queueing theory; operation research; approximation algorithms; optimization

Special Issue Information

Dear Colleagues,

Scheduling theory is an important topic within the wide area of combinatorial optimization and operation management that examines questions on developing optimal schedules for performing finite or repetitive sets of operations. Its application encompasses diverse fields such as management, production, transportation, computer systems, and construction. Mathematical aspects of scheduling tackle the perennial problem of optimal utilization of finite resources in accomplishing an assortment of tasks or objectives. While some of the problems have polynomial time solutions, the vast majority of the problems are NP-hard. Hence, this Special Issue strives to publish original papers on mathematical models of scheduling theory, which describe new methods for overcoming current problems and weaknesses. Submitted studies should present mathematical exact or approximate solutions to core problems or to introduce and analyze efficient heuristics. For example, they may focus on some new trends in deterministic scheduling and related combinatorial problems, probabilistic scheduling models, the complexity of scheduling in practice and optimization, system design, and implementation. The research field is vast; thus, papers can address network problems, machine sequencing problems and techniques, flow-shop scheduling problems under different objectives and constraints, and the job-shop-scheduling problem.

The Special Issue aims to exhibit innovative articles reflecting the latest developments and findings of mathematical models and methods of scheduling theory. Therefore, we are eager to display pioneering and original techniques and approaches to improve current practices.

Dr. Amir Elalouf
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • scheduling theory
  • operations research
  • mathematics
  • computer science
  • management
  • flow-shop scheduling
  • network problems
  • machine sequencing problems

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Published Papers (5 papers)

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Research

15 pages, 477 KiB  
Article
Novel Approaches to the Formulation of Scheduling Problems
by José Manuel García-Sánchez and Plácido Moreno
Mathematics 2024, 12(7), 1035; https://doi.org/10.3390/math12071035 - 30 Mar 2024
Viewed by 839
Abstract
This paper presents two novel formulations for scheduling problems, namely order-position hybrid formulation (OPH) and order-disjunctive hybrid formulation (ODH), which extend and combine parts of existing formulation strategies. The first strategy (OPH) is based on sequence position and linear ordering formulations, adding relationships [...] Read more.
This paper presents two novel formulations for scheduling problems, namely order-position hybrid formulation (OPH) and order-disjunctive hybrid formulation (ODH), which extend and combine parts of existing formulation strategies. The first strategy (OPH) is based on sequence position and linear ordering formulations, adding relationships between constraints that allow relaxing some decision variables. The second approach (ODH) is based on linear ordering and disjunctive formulations. In this work, we prove ODH to be the most efficient formulation known so far. The experiments have been carried out with a large set of problems, which consider single machines and identical parallel machines. Computational results show that OPH is better than the rest of the existing formulations for the case of weighted completion objectives, while ODH turns out to be the best approach for most scenarios studied. Full article
(This article belongs to the Special Issue Mathematical Models and Methods of Scheduling Theory)
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12 pages, 287 KiB  
Article
The Expected Competitive Ratio on a Kind of Stochastic-Online Flowtime Scheduling with Machine Subject to an Uncertain Breakdown
by Zhenpeng Li and Congdian Cheng
Mathematics 2023, 11(11), 2413; https://doi.org/10.3390/math11112413 - 23 May 2023
Viewed by 1078
Abstract
We consider the problem of scheduling jobs on a single machine subject to an uncertain breakdown to minimize the flowtime. Assuming the machine is unavailable during the breakdown, the starting time of the breakdown is a random variable s with distribution function [...] Read more.
We consider the problem of scheduling jobs on a single machine subject to an uncertain breakdown to minimize the flowtime. Assuming the machine is unavailable during the breakdown, the starting time of the breakdown is a random variable s with distribution function D(s) and the terminating time of the breakdown has no any other information; jobs are non-resumable. Under these assumptions and starting from the perspective of statistical optimization, we first establish the scheduling problem HSONRP, which contains deterministic information, stochastic information, and online information and then define the expected competitive ratio of an algorithm to find the optimized solution of the problem HSONRP. In addition, then, we propose and prove certain results on the expected competitive ratio of the SPT rule. In particular, we prove the expected competitive ratio of SPT rule is less than 1+max{pi}2P when s is the uniform distribution on interval (0,P], where pi is the processing time of job i, P=∑i=1npi, and show that it is no more than 54 under a quite loose condition. Meanwhile, we also make some discussions about our studies. What we have performed will enrich and improve the research results on the area of scheduling to minimize flowtime and advance the development of online optimization and stochastic optimization. Full article
(This article belongs to the Special Issue Mathematical Models and Methods of Scheduling Theory)
22 pages, 2120 KiB  
Article
Managing Disruptions in a Flow-Shop Manufacturing System
by Ajay Surendrarao Bhongade, Prakash Manohar Khodke, Ateekh Ur Rehman, Manoj Dattatray Nikam, Prathamesh Dattatray Patil and Pramod Suryavanshi
Mathematics 2023, 11(7), 1731; https://doi.org/10.3390/math11071731 - 4 Apr 2023
Cited by 5 | Viewed by 2019
Abstract
There is a manufacturing system where several parts are processed through machining workstations and later assembled to form final products. In the event of disruptions such as machine failure, the original flow-shop schedule needs to be revised and/or rescheduled. In such a scenario, [...] Read more.
There is a manufacturing system where several parts are processed through machining workstations and later assembled to form final products. In the event of disruptions such as machine failure, the original flow-shop schedule needs to be revised and/or rescheduled. In such a scenario, rescheduling methods based on right-shift rescheduling and affected operations rescheduling work very well. Here in this study, the deviation of the make-span of the revised schedule from the original schedule is used as a performance measure. We have proposed three rescheduling methods. There are multiple factors that influence the performance of the rescheduling methodology. One of them is the make-span deviation of the schedule, and the factors influencing it are optimality of the initial solution, failure duration, deviation of make-span, rescheduling method, size, and instant of failure. The initial schedule and problem size depend on the flow-shop manufacturing system for which scheduling is performed, but the method of rescheduling depends on the decision as to which rescheduling methodology is to be selected. Computations are performed using full factorial experimentation. We also observed that right-shift rescheduling is the preferred rescheduling method in the majority of situations. In contrast, the affected operation rescheduling method is also equally suitable when the initial solution is created using modified bottleneck minimum idleness. Full article
(This article belongs to the Special Issue Mathematical Models and Methods of Scheduling Theory)
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13 pages, 724 KiB  
Article
Scheduling BCG and IL-2 Injections for Bladder Cancer Immunotherapy Treatment
by Amit Yaniv-Rosenfeld, Elizaveta Savchenko, Ariel Rosenfeld and Teddy Lazebnik
Mathematics 2023, 11(5), 1192; https://doi.org/10.3390/math11051192 - 28 Feb 2023
Cited by 4 | Viewed by 1674
Abstract
Cancer is one of the most common families of diseases today with millions of new patients every year around the world. Bladder cancer (BC) is one of the most prevalent types of cancer affecting both genders, and it is not known to be [...] Read more.
Cancer is one of the most common families of diseases today with millions of new patients every year around the world. Bladder cancer (BC) is one of the most prevalent types of cancer affecting both genders, and it is not known to be associated with a specific group in the population. The current treatment standard for BC follows a standard weekly Bacillus Calmette–Guérin (BCG) immunotherapy-based therapy protocol which includes BCG and IL-2 injections. Unfortunately, due to the biological and clinical complexity of the interactions between the immune system, treatment, and cancer cells, clinical outcomes vary significantly among patients. Unfortunately, existing models are commonly developed for a non-existing average patient or pose strict, unrealistic, expectations on the treatment process. In this work, we propose the most extensive ordinary differential equation-based biological model of BCG treatment to date and a deep learning-based scheduling approach to obtain a personalized treatment schedule. Our results show that resulting treatment schedules favorably compare with the current standard practices and the current state-of-the-art scheduling approach. Full article
(This article belongs to the Special Issue Mathematical Models and Methods of Scheduling Theory)
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16 pages, 1209 KiB  
Article
The Extended David-Yechiali Rule for Kidney Allocation
by Amir Elalouf, Ariel Rosenfeld and Ofir Rockach
Mathematics 2023, 11(2), 331; https://doi.org/10.3390/math11020331 - 8 Jan 2023
Viewed by 1951
Abstract
The First Come First Served (FCFS) queuing policy is routinely assumed to be the benchmark policy for “fairness” in waiting-time performance. In this article, we propose a slight modification of the FCFS policy based on a natural extension of the well-established David and [...] Read more.
The First Come First Served (FCFS) queuing policy is routinely assumed to be the benchmark policy for “fairness” in waiting-time performance. In this article, we propose a slight modification of the FCFS policy based on a natural extension of the well-established David and Yechiali (DY) rule and analyze it in the context of managing a waiting list for kidney transplants. In the proposed policy, the queuing agents are sequentially offered a stochastically arriving organ on a “first come, first served” basis while applying the individually optimal DY stopping rule. Through a realistic simulation, we show that the proposed policy, which we term Extended David and Yechiali (EDY), favorably compares to the FCFS policy in terms of medical efficiency while maintaining a comparable level of equity (i.e., fairness). Possible implications and practical aspects of the EDY are discussed. Full article
(This article belongs to the Special Issue Mathematical Models and Methods of Scheduling Theory)
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