The robust single machine scheduling problem with uncertain release and processing times

In this work, we study the single machine scheduling problem with uncertain release times and processing times of jobs. We adopt a robust scheduling approach, in which the measure of robustness to be minimized for a given sequence of jobs is the worst-case objective function value from the set of all possible realizations of release and processing times. The objective function value is the total flow time of all jobs. We discuss some important properties of robust schedules for zero and non-zero release times, and illustrate the added complexity in robust scheduling given non-zero release times. We propose heuristics based on variable neighborhood search and iterated local search to solve the problem and generate robust schedules. The algorithms are tested and their solution performance is compared with optimal solutions or lower bounds through numerical experiments based on synthetic data

Min-Max Regret Scheduling To Minimize the Total Weight of Late Jobs With Interval Uncertainty

We study the single machine scheduling problem with the objective to minimize the total weight of late jobs. It is assumed that the processing times of jobs are not exactly known at the time when a complete schedule must be dispatched. Instead, only interval bounds for these parameters are given. In contrast to the stochastic optimization approach, we consider the problem of finding a robust schedule, which minimizes the maximum regret of a solution. Heuristic algorithm based on mixed-integer linear programming is presented and examined through computational experiments

Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments

In the current work we introduce a novel estimation of distribution algorithm to tackle a hard combinatorial optimization problem, namely the single-machine scheduling problem, with uncertain delivery times. The majority of the existing research coping with optimization problems in uncertain environment aims at finding a single sufficiently robust solution so that random noise and unpredictable circumstances would have the least possible detrimental effect on the quality of the solution. The measures of robustness are usually based on various kinds of empirically designed averaging techniques. In contrast to the previous work, our algorithm aims at finding a collection of robust schedules that allow for a more informative decision making. The notion of robustness is measured quantitatively in terms of the classical mathematical notion of a norm on a vector space. We provide a theoretical insight into the relationship between the properties of the probability distribution over the uncertain delivery times and the robustness quality of the schedules produced by the algorithm after a polynomial runtime in terms of approximation ratios

Flow shop rescheduling under different types of disruption

This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Production Research on 2013, available online:http://www.tandfonline.com/10.1080/00207543.2012.666856Almost all manufacturing facilities need to use production planning and scheduling systems to increase productivity and to reduce production costs. Real-life production operations are subject to a large number of unexpected disruptions that may invalidate the original schedules. In these cases, rescheduling is essential to minimise the impact on the performance of the system. In this work we consider flow shop layouts that have seldom been studied in the rescheduling literature. We generate and employ three types of disruption that interrupt the original schedules simultaneously. We develop rescheduling algorithms to finally accomplish the twofold objective of establishing a standard framework on the one hand, and proposing rescheduling methods that seek a good trade-off between schedule quality and stability on the other.The authors would like to thank the anonymous referees for their careful and detailed comments that helped to improve the paper considerably. This work is partially financed by the Small and Medium Industry of the Generalitat Valenciana (IMPIVA) and by the European Union through the European Regional Development Fund (FEDER) inside the R + D program "Ayudas dirigidas a Institutos tecnologicos de la Red IMPIVA" during the year 2011, with project number IMDEEA/2011/142.Katragjini Prifti, K.; Vallada Regalado, E.; Ruiz García, R. (2013). Flow shop rescheduling under different types of disruption. International Journal of Production Research. 51(3):780-797. https://doi.org/10.1080/00207543.2012.666856S780797513Abumaizar, R. J., & Svestka, J. A. (1997). Rescheduling job shops under random disruptions. International Journal of Production Research, 35(7), 2065-2082. doi:10.1080/002075497195074Adiri, I., Frostig, E., & Kan, A. H. G. R. (1991). Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs. Naval Research Logistics, 38(2), 261-271. doi:10.1002/1520-6750(199104)38:23.0.co;2-iAkturk, M. S., & Gorgulu, E. (1999). Match-up scheduling under a machine breakdown. European Journal of Operational Research, 112(1), 81-97. doi:10.1016/s0377-2217(97)00396-2Allahverdi, A. (1996). Two-machine proportionate flowshop scheduling with breakdowns to minimize maximum lateness. Computers & Operations Research, 23(10), 909-916. doi:10.1016/0305-0548(96)00012-3Arnaout, J. P., & Rabadi, G. (2008). Rescheduling of unrelated parallel machines under machine breakdowns. International Journal of Applied Management Science, 1(1), 75. doi:10.1504/ijams.2008.020040Artigues, C., Billaut, J.-C., & Esswein, C. (2005). Maximization of solution flexibility for robust shop scheduling. European Journal of Operational Research, 165(2), 314-328. doi:10.1016/j.ejor.2004.04.004Azizoglu, M., & Alagöz, O. (2005). Parallel-machine rescheduling with machine disruptions. IIE Transactions, 37(12), 1113-1118. doi:10.1080/07408170500288133Bean, J. C., Birge, J. R., Mittenthal, J., & Noon, C. E. (1991). Matchup Scheduling with Multiple Resources, Release Dates and Disruptions. Operations Research, 39(3), 470-483. doi:10.1287/opre.39.3.470Caricato, P., & Grieco, A. (2008). An online approach to dynamic rescheduling for production planning applications. International Journal of Production Research, 46(16), 4597-4617. doi:10.1080/00207540601136225CHURCH, L. K., & UZSOY, R. (1992). Analysis of periodic and event-driven rescheduling policies in dynamic shops. International Journal of Computer Integrated Manufacturing, 5(3), 153-163. doi:10.1080/09511929208944524Cowling, P., & Johansson, M. (2002). Using real time information for effective dynamic scheduling. European Journal of Operational Research, 139(2), 230-244. doi:10.1016/s0377-2217(01)00355-1Curry, J., & Peters *, B. (2005). Rescheduling parallel machines with stepwise increasing tardiness and machine assignment stability objectives. International Journal of Production Research, 43(15), 3231-3246. doi:10.1080/00207540500103953DUTTA, A. (1990). Reacting to Scheduling Exceptions in FMS Environments. IIE Transactions, 22(4), 300-314. doi:10.1080/07408179008964185Ghezail, F., Pierreval, H., & Hajri-Gabouj, S. (2010). Analysis of robustness in proactive scheduling: A graphical approach. Computers & Industrial Engineering, 58(2), 193-198. doi:10.1016/j.cie.2009.03.004Goren, S., & Sabuncuoglu, I. (2008). Robustness and stability measures for scheduling: single-machine environment. IIE Transactions, 40(1), 66-83. doi:10.1080/07408170701283198Hall, N. G., & Potts, C. N. (2004). Rescheduling for New Orders. Operations Research, 52(3), 440-453. doi:10.1287/opre.1030.0101Herrmann, J. W., Lee, C.-Y., & Snowdon, J. L. (1993). A Classification of Static Scheduling Problems. Complexity in Numerical Optimization, 203-253. doi:10.1142/9789814354363_0011Herroelen, W., & Leus, R. (2005). Project scheduling under uncertainty: Survey and research potentials. European Journal of Operational Research, 165(2), 289-306. doi:10.1016/j.ejor.2004.04.002Hozak, K., & Hill, J. A. (2009). Issues and opportunities regarding replanning and rescheduling frequencies. International Journal of Production Research, 47(18), 4955-4970. doi:10.1080/00207540802047106Huaccho Huatuco, L., Efstathiou, J., Calinescu, A., Sivadasan, S., & Kariuki, S. (2009). Comparing the impact of different rescheduling strategies on the entropic-related complexity of manufacturing systems. International Journal of Production Research, 47(15), 4305-4325. doi:10.1080/00207540701871036Jensen, M. T. (2003). Generating robust and flexible job shop schedules using genetic algorithms. IEEE Transactions on Evolutionary Computation, 7(3), 275-288. doi:10.1109/tevc.2003.810067King, J. R. (1976). The theory-practice gap in job-shop scheduling. Production Engineer, 55(3), 137. doi:10.1049/tpe.1976.0044Kopanos, G. M., Capón-García, E., Espuña,, A., & Puigjaner, L. (2008). Costs for Rescheduling Actions: A Critical Issue for Reducing the Gap between Scheduling Theory and Practice. Industrial & Engineering Chemistry Research, 47(22), 8785-8795. doi:10.1021/ie8005676Lee, C.-Y., Leung, J. Y.-T., & Yu, G. (2006). Two Machine Scheduling under Disruptions with Transportation Considerations. Journal of Scheduling, 9(1), 35-48. doi:10.1007/s10951-006-5592-7Li, Z., & Ierapetritou, M. (2008). Process scheduling under uncertainty: Review and challenges. Computers & Chemical Engineering, 32(4-5), 715-727. doi:10.1016/j.compchemeng.2007.03.001Liao, C. J., & Chen, W. J. (2004). Scheduling under machine breakdown in a continuous process industry. Computers & Operations Research, 31(3), 415-428. doi:10.1016/s0305-0548(02)00224-1Mehta, S. V. (1999). Predictable scheduling of a single machine subject to breakdowns. International Journal of Computer Integrated Manufacturing, 12(1), 15-38. doi:10.1080/095119299130443MUHLEMANN, A. P., LOCKETT, A. G., & FARN, C.-K. (1982). Job shop scheduling heuristics and frequency of scheduling. International Journal of Production Research, 20(2), 227-241. doi:10.1080/00207548208947763Nawaz, M., Enscore, E. E., & Ham, I. (1983). A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, 11(1), 91-95. doi:10.1016/0305-0483(83)90088-9O’Donovan, R., Uzsoy, R., & McKay, K. N. (1999). Predictable scheduling of a single machine with breakdowns and sensitive jobs. International Journal of Production Research, 37(18), 4217-4233. doi:10.1080/002075499189745Özlen, M., & Azizoğlu, M. (2009). Generating all efficient solutions of a rescheduling problem on unrelated parallel machines. International Journal of Production Research, 47(19), 5245-5270. doi:10.1080/00207540802043998Pfeiffer, A., Kádár, B., & Monostori, L. (2007). Stability-oriented evaluation of rescheduling strategies, by using simulation. Computers in Industry, 58(7), 630-643. doi:10.1016/j.compind.2007.05.009Pierreval, H., & Durieux-Paris, S. (2007). Robust simulation with a base environmental scenario. European Journal of Operational Research, 182(2), 783-793. doi:10.1016/j.ejor.2006.07.045Damodaran, P., Hirani, N. S., & Gallego, M. C. V. (2009). Scheduling identical parallel batch processing machines to minimise makespan using genetic algorithms. European J. of Industrial Engineering, 3(2), 187. doi:10.1504/ejie.2009.023605Qi, X., Bard, J. F., & Yu, G. (2006). Disruption management for machine scheduling: The case of SPT schedules. International Journal of Production Economics, 103(1), 166-184. doi:10.1016/j.ijpe.2005.05.021Rangsaritratsamee, R., Ferrell, W. G., & Kurz, M. B. (2004). Dynamic rescheduling that simultaneously considers efficiency and stability. Computers & Industrial Engineering, 46(1), 1-15. doi:10.1016/j.cie.2003.09.007Ruiz, R., & Stützle, T. (2007). A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research, 177(3), 2033-2049. doi:10.1016/j.ejor.2005.12.009Sabuncuoglu, I., & Goren, S. (2009). Hedging production schedules against uncertainty in manufacturing environment with a review of robustness and stability research. International Journal of Computer Integrated Manufacturing, 22(2), 138-157. doi:10.1080/09511920802209033Sabuncuoglu, I., & Kizilisik, O. B. (2003). Reactive scheduling in a dynamic and stochastic FMS environment. International Journal of Production Research, 41(17), 4211-4231. doi:10.1080/0020754031000149202Salveson, M. E. (1952). On a Quantitative Method in Production Planning and Scheduling. Econometrica, 20(4), 554. doi:10.2307/1907643Samarghandi, H., & ElMekkawy, T. Y. (2011). An efficient hybrid algorithm for the two-machine no-wait flow shop problem with separable setup times and single server. European J. of Industrial Engineering, 5(2), 111. doi:10.1504/ejie.2011.039869Subramaniam *, V., Raheja, A. S., & Rama Bhupal Reddy, K. (2005). Reactive repair tool for job shop schedules. International Journal of Production Research, 43(1), 1-23. doi:10.1080/0020754042000270412Taillard, E. (1990). Some efficient heuristic methods for the flow shop sequencing problem. European Journal of Operational Research, 47(1), 65-74. doi:10.1016/0377-2217(90)90090-xTaillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64(2), 278-285. doi:10.1016/0377-2217(93)90182-mValente, J. M. S., & Schaller, J. E. (2010). Improved heuristics for the single machine scheduling problem with linear early and quadratic tardy penalties. European J. of Industrial Engineering, 4(1), 99. doi:10.1504/ejie.2010.029572Vallada, E., & Ruiz, R. (2010). Genetic algorithms with path relinking for the minimum tardiness permutation flowshop problem☆. Omega, 38(1-2), 57-67. doi:10.1016/j.omega.2009.04.002Vieira, G. E., Herrmann, J. W., & Lin, E. (2000). Predicting the performance of rescheduling strategies for parallel machine systems. Journal of Manufacturing Systems, 19(4), 256-266. doi:10.1016/s0278-6125(01)80005-4Vieira, G. E., Herrmann, J. W., & Lin, E. (2003). Journal of Scheduling, 6(1), 39-62. doi:10.1023/a:1022235519958Yang, J., & Yu, G. (2002). Journal of Combinatorial Optimization, 6(1), 17-33. doi:10.1023/a:1013333232691Zandieh, M., & Gholami, M. (2009). An immune algorithm for scheduling a hybrid flow shop with sequence-dependent setup times and machines with random breakdowns. International Journal of Production Research, 47(24), 6999-7027. doi:10.1080/0020754080240063

Robust job-sequencing with an uncertain flexible maintenance activity

In this study, the problem of scheduling a set of jobs and one uncertain maintenance activity on a single machine, with the objective of minimizing the makespan is addressed. The maintenance activity has a given duration and must be executed within a given time window. Furthermore, duration and time window of the maintenance are uncertain, and can take different values which can be described by different scenarios. The problem is to determine a job sequence which performs well, in terms of makespan, independently on the possible variation of the data concerning the maintenance. A robust scheduling approach is used for the problem, in which four different measures of robustness are considered, namely, maximum absolute regret, maximum relative regret, worst-case scenario, and ordered weighted averaging. Complexity and approximation results are presented. In particular, we show that, for all the four robustness criteria, the problem is strongly NP-hard. A number of special cases are explored, and an exact pseudopolynomial algorithm based on dynamic programming is devised when the number of scenarios is fixed. Two Mixed Integer Programming (MIP) models are also presented for the general problem. Several computational experiments have been conducted to evaluate the efficiency and effectiveness of the MIP models and of the dynamic programming approach

Random Keys Genetic Algorithms Scheduling and Rescheduling Systems for Common Production Systems

The majority of scheduling research deals with problems in specific production environments with specific objective functions. However, in many cases, more than one problem type and/or objective function exists, resulting in the need for a more generic and flexible system to generate schedules. Furthermore, most of the published scheduling research focuses on creating an optimal or near optimal initial schedule during the planning phase. However, after production processes start, circumstances like machine breakdowns, urgent jobs, and other unplanned events may render the schedule suboptimal, obsolete or even infeasible resulting in a rescheduling problem, which is typically also addressed for a specific production environment, constraints, and objective functions. This dissertation introduces a generic framework consisting of models and algorithms based on Random Keys Genetic Algorithms (RKGA) to handle both the scheduling and rescheduling problems in the most common production environments and for various types of objective functions. The Scheduling system produces predictive (initial) schedules for environments including single machines, flow shops, job shops and parallel machine production systems to optimize regular objective functions such as the Makespan and the Total Tardiness as well as non-regular objective functions such as the Total Earliness and Tardiness. To deal with the rescheduling problem, and using as a basis the same RKGA, a reactive Rescheduling system capable of repairing initial schedules after the occurrence of unexpected events is introduced. The reactive Rescheduling system was designed not only to optimize regular and non-regular objective functions but also to minimize the instability, a very important aspect in rescheduling to avoid shop chaos due to disruptions. Minimizing both schedule inefficiency and instability, however, turns the problem into a multi-objective optimization problem, which is even more difficult to solve. The computational experiments for the predictive model show that it is able to produce optimal or near optimal schedules to benchmark problems for different production environments and objective functions. Additional computational experiments conducted to test the reactive Rescheduling system under two types of unexpected events, machine breakdowns and the arrival of a rush job, show that the proposed framework and algorithms are robust in handling various problem types and computationally reasonable

Algorithmic Developments in Two-Stage Robust Scheduling

This thesis considers the modelling and solving of a range of scheduling problems, with a particular focus on the use of robust optimisation for scheduling in two-stage decision-making contexts. One key contribution of this thesis is the development of a new compact robust counterpart for the resource-constrained project scheduling problem with uncertain activity durations. Resource conflicts must be resolved under the assumption of budgeted uncertainty, but start times can be determined once the activity durations become known. This formulation is also applied to the multi-mode version of this problem. In both cases, computational results show the clear dominance of the new formulation over the prior decomposition-based state-of-the-art methods. This thesis also demonstrates the first application of the recoverable robust framework to single machine scheduling. Two variants of this problem are considered, in which a first-stage schedule is constructed subject to uncertain job processing times, but can be amended in some limited way following the realisation of these processing times. The first of these problems is considered under general polyhedral uncertainty. Key results concerning the second-stage subproblem are derived, resulting in three formulations to the full problem which are compared computationally. The second of these problems considers interval uncertainty but allows for a more general recovery action. A 2-approximation is derived and the performance of a proposed greedy algorithm is examined in a series of computational experiments. In addition to these results on two-stage robust scheduling problems, a new deterministic resource-constrained project scheduling model is developed which, for the first time, combines both generalised precedence constraints and flexible resource allocation. This model is introduced specifically for the application of scheduling the decommissioning of the Sellafield nuclear site. A genetic algorithm is proposed to solve this model, and its performance is compared against a mixedinteger programming formulation

An Efficient Heuristic for a Discrete Optimization Problem

In this paper we deal with a discrete optimization problem, which, among many other such problems, is computationally intractable. Since the existence of an exact solution algorithm for our problem is highly unlikely, the development of heuristic and approximation algorithms is of a great importance. Here we briefly discuss this issue and describe a robust 2-approximation heuristic that is used for getting an approximation solution for the problem of scheduling jobs with release times and due-dates on a single machine to minimize the maximum job lateness