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

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 State-of-the-Art Survey of Due Date Assignment and Scheduling Research: Common Due Date

In this paper, we aim at providing a unified framework of the common due date assignment and scheduling problems in the deterministic case by surveying the literature concerning the models involving single machine and parallel machines. We focus on static production settings in which a fixed set of is available for processing as opposed to dynamic production settings where jobs continuously arrive in the system and should be scheduled on-line. The problems with due date determination have received considerable attention in the last ten years due to the introduction of new methods of inventory management such as Just-In-Time (JIT) systems. The common due date model which is also known in scheduling literature as CON model, where CON stands for constant flow allowance, corresponds, for instance, to an assembly system in which the components of the product should be ready at the same time, or to a shop where several jobs constitute a single customer's order. In the problems under consideration, the objective is to find an optimal value of the common due date and the related optimal schedule in order to optimize a given criterion based on the due date and the completion times of jobs. The results on the algorithms and complexity of the common due date assignment and scheduling problems are summarized

Scheduling unrelated parallel machines with resource-assignable sequence-dependent setup times

[EN] A novel scheduling problem that results from the addition of resource-assignable setups is presented in this paper. We consider an unrelated parallel machine problem with machine and job sequence-dependent setup times. The new characteristic is that the amount of setup time does not only depend on the machine and job sequence but also on the amount of resources assigned, which can vary between a minimum and a maximum. The aim is to give solution to real problems arising in several industries where frequent setup operations in production lines have to be carried out. These operations are indeed setups whose length can be reduced or extended according to the amount of resources assigned to them. The objective function considered is a linear combination of total completion time and the total amount of resources assigned. We present a mixed integer program (MIP) model and some fast dispatching heuristics. We carry out careful and comprehensive statistical analyses to study what characteristics of the problem affect the MIP model performance. We also study the effectiveness of the different heuristics proposed. © 2011 Springer-Verlag London Limited.The authors are indebted to the referees and editor for a close examination of the paper, which has increased its quality and presentation. This work is partially funded by the Spanish Ministry of Science and Innovation, under the project "SMPA-Advanced Parallel Multiobjective Sequencing: Practical and Theoretical Advances" with reference DPI2008-03511/DPI. The authors should also thank the IMPIVA-Institute for the Small and Medium Valencian Enterprise, for the project OSC with references IMIDIC/2008/137, IMIDIC/2009/198, and IMIDIC/2010/175.Ruiz García, R.; Andrés Romano, C. (2011). Scheduling unrelated parallel machines with resource-assignable sequence-dependent setup times. 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Eur J Oper Res 47(3):271–292Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326Grigoriev E, Sviridenko M, Uetz M (2007) Unrelated parallel machine scheduling with resource dependent processing times. Math Program Ser A and B 110(1):209–228Guinet A (1991) Textile production systems: a succession of non-identical parallel processor shops. J Oper Res Soc 42(8):655–671Guinet A, Dussauchoy A (1993) Scheduling sequence dependent jobs on identical parallel machines to minimize completion time criteria. Int J Prod Res 31(7):1579–1594Horn WA (1973) Minimizing average flow time with parallel machines. Oper Res 21(3):846–847Kass GV (1980) An exploratory technique for investigating large quantities of categorical data. Appl Stat 29(2):119–127Kim DW, Kim KH, Jang W, Chen FF (2002) Unrelated parallel machine scheduling with setup times using simulated annealing. Robot Comput-Integr Manuf 18(3–4):223–231Lam K, Xing W (1997) New trends in parallel machine scheduling. Int J Oper Prod Manage 17(3):326–338Lee YH, Pinedo M (1997) Scheduling jobs on parallel machines with sequence dependent setup times. Eur J Oper Res 100(3):464–474Marsh JD, Montgomery DC (1973) Optimal procedures for scheduling jobs with sequence-dependent changeover times on parallel processors. AIIE Technical Papers, pp 279–286Mokotoff E (2001) Parallel machine scheduling problems: a survey. Asia-Pac J Oper Res 18(2):193–242Morgan JA, Sonquist JN (1963) Problems in the analysis of survey data and a proposal. J Am Stat Assoc 58:415–434Ng CT, Edwin Cheng TC, Janiak A, Kovalyov MY (2005) Group scheduling with controllable setup and processing times: minimizing total weighted completion time. Ann Oper Res 133:163–174Nowicki E, Zdrzalka S (1990) A survey of results for sequencing problems with controllable processing times. Discrete Appl Math 26(2–3):271–287Pinedo M (2002) Scheduling: theory, algorithms, and systems, 2nd edn. Prentice Hall, Upper SaddleRabadi G, Moraga RJ, Al-Salem A (2006) Heuristics for the unrelated parallel machine scheduling problem with setup times. J Intell Manuf 17(1):85–97Radhakrishnan S, Ventura JA (2000) Simulated annealing for parallel machine scheduling with earliness-tardiness penalties and sequence-dependent set-up times. Int J Prod Res 38(10):2233–2252Ruiz R, Sivrikaya Şerifoğlu F, Urlings T (2008) Modeling realistic hybrid flexible flowshop scheduling problems. Comput Oper Res 35(4):1151–1175Sivrikaya-Serifoglu F, Ulusoy G (1999) Parallel machine scheduling with earliness and tardiness penalties. Comput Oper Res 26(8):773–787Webster ST (1997) The complexity of scheduling job families about a common due date. Oper Res Lett 20(2):65–74Weng MX, Lu J, Ren H (2001) Unrelated parallel machines scheduling with setup consideration and a total weighted completion time objective. 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New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove that, for a subclass of these problems, the completion times of all jobs can be ordered in an optimal solution. Using these two results, we provide new results on polynomially solvable problems and hence refine the boundary between P and NP for these problems

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan

Dynamic scheduling in a multi-product manufacturing system

To remain competitive in global marketplace, manufacturing companies need to improve their operational practices. One of the methods to increase competitiveness in manufacturing is by implementing proper scheduling system. This is important to enable job orders to be completed on time, minimize waiting time and maximize utilization of equipment and machineries. The dynamics of real manufacturing system are very complex in nature. Schedules developed based on deterministic algorithms are unable to effectively deal with uncertainties in demand and capacity. Significant differences can be found between planned schedules and actual schedule implementation. This study attempted to develop a scheduling system that is able to react quickly and reliably for accommodating changes in product demand and manufacturing capacity. A case study, 6 by 6 job shop scheduling problem was adapted with uncertainty elements added to the data sets. A simulation model was designed and implemented using ARENA simulation package to generate various job shop scheduling scenarios. Their performances were evaluated using scheduling rules, namely, first-in-first-out (FIFO), earliest due date (EDD), and shortest processing time (SPT). An artificial neural network (ANN) model was developed and trained using various scheduling scenarios generated by ARENA simulation. The experimental results suggest that the ANN scheduling model can provided moderately reliable prediction results for limited scenarios when predicting the number completed jobs, maximum flowtime, average machine utilization, and average length of queue. This study has provided better understanding on the effects of changes in demand and capacity on the job shop schedules. Areas for further study includes: (i) Fine tune the proposed ANN scheduling model (ii) Consider more variety of job shop environment (iii) Incorporate an expert system for interpretation of results. The theoretical framework proposed in this study can be used as a basis for further investigation

Flow shop scheduling with earliness, tardiness and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding) and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two di erent, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two di erent lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with di erent types of strongly NP-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs