Common Due-Date Problem: Exact Polynomial Algorithms for a Given Job Sequence

This paper considers the problem of scheduling jobs on single and parallel machines where all the jobs possess different processing times but a common due date. There is a penalty involved with each job if it is processed earlier or later than the due date. The objective of the problem is to find the assignment of jobs to machines, the processing sequence of jobs and the time at which they are processed, which minimizes the total penalty incurred due to tardiness or earliness of the jobs. This work presents exact polynomial algorithms for optimizing a given job sequence or single and parallel machines with the run-time complexities of $O(n \log n)$ and $O(mn^2 \log n)$ respectively, where $n$ is the number of jobs and $m$ the number of machines. The algorithms take a sequence consisting of all the jobs $(J_i, i=1,2,\dots,n)$ as input and distribute the jobs to machines (for $m>1$) along with their best completion times so as to get the least possible total penalty for this sequence. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we present the results for the benchmark instances and compare with previous work for single and parallel machine cases, up to $200$ jobs.Comment: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computin

A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page

Dynamic resource constrained multi-project scheduling problem with weighted earliness/tardiness costs

In this study, a conceptual framework is given for the dynamic multi-project scheduling problem with weighted earliness/tardiness costs (DRCMPSPWET) and a mathematical programming formulation of the problem is provided. In DRCMPSPWET, a project arrives on top of an existing project portfolio and a due date has to be quoted for the new project while minimizing the costs of schedule changes. The objective function consists of the weighted earliness tardiness costs of the activities of the existing projects in the current baseline schedule plus a term that increases linearly with the anticipated completion time of the new project. An iterated local search based approach is developed for large instances of this problem. In order to analyze the performance and behavior of the proposed method, a new multi-project data set is created by controlling the total number of activities, the due date tightness, the due date range, the number of resource types, and the completion time factor in an instance. A series of computational experiments are carried out to test the performance of the local search approach. Exact solutions are provided for the small instances. The results indicate that the local search heuristic performs well in terms of both solution quality and solution time

Minimizing weighted total earliness, total tardiness and setup costs

The paper considers a (static) portfolio system that satisfies adding-up contraints and the gross substitution theorem. The paper shows the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables to investigate the impact of simultaneous changes in interest rates on the asset demands.

BASA: An improved hybrid bees algorithm for the single machine scheduling with early/tardy jobs

[EN] In this paper, we present a novel hybrid meta-heuristic by enhancing the Basic Bees Algorithm through the integration of a local search method namely Simulated Annealing and Variable Neighbourhood Search like algorithm. The resulted hybrid bees algorithm (BASA) is used to solve the Single Machine Scheduling Problem with Early/Tardy jobs, where the generated outcomes are compared against the Basic Bees Algorithm (BA), and against some stat-of-the-art meta-heuristics. Computational results reveal that our proposed framework outperforms the Basic Bees Algorithm, and demonstrates a competitive performance compared with some algorithms extracted from the literature.Abdessemed, AA.; Mouss, LH.; Benaggoune, K. (2023). BASA: An improved hybrid bees algorithm for the single machine scheduling with early/tardy jobs. International Journal of Production Management and Engineering. 11(2):167-177. https://doi.org/10.4995/ijpme.2023.18077167177112Abdul-Razaq, T. S., & Potts, C. N. (1988). Dynamic programming state-space relaxation for single-machine scheduling. Journal of the Operational Research Society, 39(2), 141-152. https://doi.org/10.1057/jors.1988.26Abdullah, S., & Alzaqebah, M. (2013). A hybrid self-adaptive bees algorithm for examination timetabling problems. Applied Soft Computing, 13(8), 3608-3620. https://doi.org/10.1016/j.asoc.2013.04.010Baker, K. R., & Scudder, G. D. (1990). Sequencing with earliness and tardiness penalties: a review. Operations research, 38(1), 22-36. https://doi.org/10.1287/opre.38.1.22Castellani, M., Pham, Q. T., & Pham, D. T. (2012). Dynamic optimisation by a modified bees algorithm. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 226(7), 956-971. https://doi.org/10.1177/0959651812443462Dereli, T., & Das, G. S. (2011). A hybrid 'bee (s) algorithm'for solving container loading problems. Applied Soft Computing, 11(2), 2854-2862. https://doi.org/10.1016/j.asoc.2010.11.017Dowsland, K. A., & Thompson, J. (2012). Simulated annealing. Handbook of natural computing, 1623-1655. https://doi.org/10.1007/978-3-540-92910-9_49Hansen, P., Mladenović, N., & Moreno Pérez, J. A. (2010). Variable neighbourhood search: methods and applications. Annals of Operations Research, 175(1), 367-407. https://doi.org/10.1007/s10479-009-0657-6Ho, Y. C., & Pepyne, D. L. (2001). Simple explanation of the no free lunch theorem of optimization. In Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No. 01CH37228) (Vol. 5, pp. 4409-4414). IEEE.Kirkpatrick, S., Gelatt Jr, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. science, 220(4598), 671-680. https://doi.org/10.1126/science.220.4598.671Lara, C., Flores, J. J., & Calderón, F. (2008). Solving a school timetabling problem using a bee algorithm. In Mexican International Conference on Artificial Intelligence (pp. 664-674). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88636-5_63Lim, C. H., Lim, S., How, B. S., Ng, W. P. Q., Ngan, S. L., Leong, W. D., & Lam, H. L. (2021). A review of industry 4.0 revolution potential in a sustainable and renewable palm oil industry: HAZOP approach. Renewable and Sustainable Energy Reviews, 135, 110223. https://doi.org/10.33932/rir.44.3.2Mei, C. A., Pham, D. T., Anthony, J. S., & Kok, W. N. (2010, November). PCB assembly optimisation using the Bees Algorithm enhanced with TRIZ operators. In IECON 2010-36th Annual Conference on IEEE Industrial Electronics Society (pp. 2708-2713). IEEE. https://doi.org/10.1109/IECON.2010.5675114M'Hallah, R., & Alhajraf, A. (2016). Ant colony systems for the single-machine total weighted earliness tardiness scheduling problem. Journal of Scheduling, 19(2), 191-205. https://doi.org/10.1007/s10951-015-0429-xNguyen, K., Nguyen, P., & Tran, N. (2012). A hybrid algorithm of harmony search and bees algorithm for a university course timetabling problem. International Journal of Computer Science Issues (IJCSI), 9(1), 12.Pham, D. T., Ghanbarzadeh, A., Koç, E., Otri, S., Rahim, S., & Zaidi, M. (2006). The bees algorithm-a novel tool for complex optimisation problems. In Intelligent production machines and systems (pp. 454-459). Elsevier Science Ltd. https://doi.org/10.1177/0959651811422759Pham, D. T., Koc, E., Lee, J. Y., & Phrueksanant, J. (2007a). Using the bees algorithm to schedule jobs for a machine. In Proceedings Eighth International Conference on Laser Metrology, CMM and Machine Tool Performance, LAMDAMAP, Euspen, UK, Cardiff (pp. 430-439).Pham, D. T., Otri, S., & Darwish, A. H. (2007b). Application of the Bees Algorithm to PCB assembly optimisation. In Proceedings of the 3rd virtual international conference on intelligent production machines and systems (IPROMS 2007) (pp. 511-516).Pham, D. T., Castellani, M., & Fahmy, A. A. (2008). Learning the inverse kinematics of a robot manipulator using the bees algorithm. In 2008 6th IEEE International Conference on Industrial Informatics (pp. 493-498). IEEE. https://doi.org/10.1109/INDIN.2008.4618151Pham, Q. T., Pham, D. T., & Castellani, M. (2012). A modified bees algorithm and a statistics-based method for tuning its parameters. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 226(3), 287-301. https://doi.org/10.1177/0959651811422759Seeley, T. D. (2009). The wisdom of the hive: the social physiology of honey bee colonies. Harvard University Press. https://doi.org/10.2307/j.ctv1kz4h15Sourd, F. (2009). New exact algorithms for one-machine earliness-tardiness scheduling. INFORMS Journal on Computing, 21(1), 167-175. https://doi.org/10.1287/ijoc.1080.0287Sourd, F., & Kedad-Sidhoum, S. (2008). A faster branch-and-bound algorithm for the earliness-tardiness scheduling problem. Journal of Scheduling, 11(1), 49-58. https://doi.org/10.1007/s10951-007-0048-2Tanaka, S., Fujikuma, S., & Araki, M. (2009). An exact algorithm for single-machine scheduling without machine idle time. Journal of Scheduling, 12(6), 575-593. https://doi.org/10.1007/s10951-008-0093-5Von Frisch, K. (2014). Bees: their vision, chemical senses, and language. Cornell University Press.Wan, L., & Yuan, J. (2013). Single-machine scheduling to minimize the total earliness and tardiness is strongly NP-hard. Operations Research Letters, 41(4), 363-365. https://doi.org/10.1016/j.orl.2013.04.007Yau, H., Pan, Y., & Shi, L. (2008). New solution approaches to the general single-machine earliness-tardiness problem. IEEE Transactions on Automation Science and Engineering, 5(2), 349-360. https://doi.org/10.1109/TASE.2007.895219Yuce, B., Packianather, M. S., Mastrocinque, E., Pham, D. T., & Lambiase, A. (2013). Honey bees inspired optimization method: the bees algorithm. Insects, 4(4), 646-662. https://doi.org/10.3390/insects4040646Yuce, B., Fruggiero, F., Packianather, M. S., Pham, D. T., Mastrocinque, E., Lambiase, A., & Fera, M. (2017). Hybrid Genetic Bees Algorithm applied to single machine scheduling with earliness and tardiness penalties. Computers & Industrial Engineering, 113, 842-858. https://doi.org/10.1016/j.cie.2017.07.018Yurtkuran, A., & Emel, E. (2016). A discrete artificial bee colony algorithm for single machine scheduling problems. International Journal of Production Research, 54(22), 6860-6878. https://doi.org/10.1080/00207543.2016.118555

Iterated search methods for earliness and tardiness minimization in hybrid flowshops with due windows

[EN] In practice due dates usually behave more like intervals rather than specific points in time. This paper studies hybrid flowshops where jobs, if completed inside a due window, are considered on time. The objective is therefore the minimization of the weighted earliness and tardiness from the due window. This objective has seldom been studied and there are almost no previous works for hybrid flowshops. We present methods based on the simple concepts of iterated greedy and iterated local search. We introduce some novel operators and characteristics, like an optimal idle time insertion procedure and a two stage local search where, in the second stage, a limited local search on a exact representation is carried out. We also present a comprehensive computational campaign, including the reimplementation and comparison of 9 competing procedures. A thorough evaluation of all methods with more than 3000 instances shows that our presented approaches yield superior results which are also demonstrated to be statistically significant. Experiments also show the contribution of the new operators in the presented methods. (C) 2016 Elsevier Ltd. All rights reserved.The authors would like to thank Professors Lofti Hidri and Mohamed Haouari for sharing with us the source codes and explanations of the lower bounds. Quan-Ke Pan is supported by the National Natural Science Foundation of China (Grant No. 51575212), Program for New Century Excellent Talents in University (Grant No. NCET-13-0106), Science Foundation of Hubei Province in China (Grant No. 2015CFB560), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20130042110035), Key Laboratory Basic Research Foundation of Education Department of Liaoning Province (LZ2014014), Open Research Fund Program of the State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, China. Ruben Ruiz and Pedro Alfaro-Fernandez are supported by the Spanish Ministry of Economy and Competitiveness, under the project "SCHEYARD Optimization of Scheduling Problems in Container Yards" (No. DPI2015-65895-R) financed by FEDER funds.Pan, Q.; Ruiz García, R.; Alfaro-Fernandez, P. (2017). Iterated search methods for earliness and tardiness minimization in hybrid flowshops with due windows. Computers & Operations Research. 80:50-60. https://doi.org/10.1016/j.cor.2016.11.022S50608

A new hybrid meta-heuristic algorithm for solving single machine scheduling problems

A dissertation submitted in partial ful lment of the degree of Master of Science in Engineering (Electrical) (50/50) in the Faculty of Engineering and the Built Environment Department of Electrical and Information Engineering May 2017Numerous applications in a wide variety of elds has resulted in a rich history of research into optimisation for scheduling. Although it is a fundamental form of the problem, the single machine scheduling problem with two or more objectives is known to be NP-hard. For this reason we consider the single machine problem a good test bed for solution algorithms. While there is a plethora of research into various aspects of scheduling problems, little has been done in evaluating the performance of the Simulated Annealing algorithm for the fundamental problem, or using it in combination with other techniques. Speci cally, this has not been done for minimising total weighted earliness and tardiness, which is the optimisation objective of this work. If we consider a mere ten jobs for scheduling, this results in over 3.6 million possible solution schedules. It is thus of de nite practical necessity to reduce the search space in order to nd an optimal or acceptable suboptimal solution in a shorter time, especially when scaling up the problem size. This is of particular importance in the application area of packet scheduling in wireless communications networks where the tolerance for computational delays is very low. The main contribution of this work is to investigate the hypothesis that inserting a step of pre-sampling by Markov Chain Monte Carlo methods before running the Simulated Annealing algorithm on the pruned search space can result in overall reduced running times. The search space is divided into a number of sections and Metropolis-Hastings Markov Chain Monte Carlo is performed over the sections in order to reduce the search space for Simulated Annealing by a factor of 20 to 100. Trade-o s are found between the run time and number of sections of the pre-sampling algorithm, and the run time of Simulated Annealing for minimising the percentage deviation of the nal result from the optimal solution cost. Algorithm performance is determined both by computational complexity and the quality of the solution (i.e. the percentage deviation from the optimal). We nd that the running time can be reduced by a factor of 4.5 to ensure a 2% deviation from the optimal, as compared to the basic Simulated Annealing algorithm on the full search space. More importantly, we are able to reduce the complexity of nding the optimal from O(n:n!) for a complete search to O(nNS) for Simulated Annealing to O(n(NMr +NS)+m) for the input variables n jobs, NS SA iterations, NM Metropolis- Hastings iterations, r inner samples and m sections.MT 201

Available-to-promise (ATP) systems: a classification and framework for analysis

Available-to-promise (ATP) systems deal with a number of managerial decisions related to order capture activities in a company, including order acceptance/rejection, due date setting, and resource scheduling. These different but interrelated decisions have often been studied in an isolated manner, and, to the best of our knowledge, no framework has been presented to integrate them into the broader perspective of order capture. This paper attempts to provide a general framework for ATP-related decisions. By doing so, we: (1) identify the different decision problems to be addressed; (2) present the different literature-based models supporting related decisions into a coherent framework; and (3) review the main contributions in the literature for each one of these. We first describe different approaches for order capture available in the literature, depending on two parameters related to the application context of ATP systems, namely the inclusion of explicit information about due dates in the decision model, and the level of integration among decisions. According to these parameters, up to six approaches for ATP-related decisions are identified. Secondly, we show the subsequent decision problems derived from the different approaches, and describe the main issues and key references involving each one of these decision problems. Finally, a number of conclusions and future research lines are discussed.Ministerio de Ciencia e Innovación DPI2007-6134