Showing papers on "Tardiness published in 1998"
TL;DR: In this paper, the problem of scheduling n jobs on a batching machine to minimize regular scheduling criteria that are non-decreasing in the job completion times was studied, and it was shown that minimizing the weighted number of tardy jobs and the total weighted tardiness are NP-hard problems.
Abstract: We address the problem of scheduling n jobs on a batching machine to minimize regular scheduling criteria that are non-decreasing in the job completion times A batching machine is a machine that can handle up to b jobs simultaneously The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time The processing time of a batch is equal to the largest processing time of any job in the batch We analyse two variants: the unbounded model, where b⩾n; and the bounded model, where b1; for the case with m different processing times, we give a dynamic programming algorithm that requires O(b2m22m) time Moreover, we prove that due date based scheduling criteria give rise to NP-hard problems Finally, we show that an arbitrary regular cost function can be minimized in polynomial time for a fixed number of batches © 1998 John Wiley & Sons, Ltd
389 citations
TL;DR: This paper introduces a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations into actual sequences, and compares it to the usual "natural" permutation representation for descent, simulated annealing, threshold accepting, tabu search and genetic algorithms on a large set of test problems.
Abstract: This paper presents several local search heuristics for the problem of scheduling a single machine to minimize total weighted tardiness. We introduce a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations into actual sequences. This binary encoding scheme is compared to the usual "natural" permutation representation for descent, simulated annealing, threshold accepting, tabu search and genetic algorithms on a large set of test problems. Computational results indicate that all of the heuristics which employ our binary encoding are very robust in that they consistently produce good quality solutions, especially when multistart implementations are used instead of a single long run. The binary encoding is also used in a new genetic algorithm which performs very well and requires comparatively little computation time. A comparison of neighborhood search methods which use the permutation and binary representations shows that the permutation-based methods have a higher likelihood of generating an optimal solution, but are less robust in that some poor solutions are obtained. Of the neighborhood search methods, tabu search clearly dominates the others. Multistart descent performs remarkably well relative to simulated annealing and threshold accepting.
184 citations
TL;DR: A dynamic programming algorithm is presented which has polynomial time complexity when the number of job families and the batch machine capacity are fixed and which can provide near optimal solutions in a reasonable amount of computation time.
Abstract: Motivated by an application in semiconductor manufacturing, we study the problem of minimizing total tardiness on a batch processing machine with incompatibl8e job families, where all jobs of the same family have identical processing times and jobs of different families cannot be processed together. We present a dynamic programming algorithm which has polynomial time complexity when the number of job families and the batch machine capacity are fixed. We also examine various heuristic solution procedures which can provide near optimal solutions in a reasonable amount of computation time.
172 citations
TL;DR: An O(n log n) algorithm is proposed to solve a single machine static and deterministic scheduling problem in which jobs have a common due window and the objective is to find the optimal size and location of the window as well as an optimal sequence to minimise a cost function.
Abstract: We consider a single machine static and deterministic scheduling problem in which jobs have a common due window. Jobs completed within the window incur no penalties, other jobs incur either earliness or tardiness penalties. The objective is to find the optimal size and location of the window as well as an optimal sequence to minimise a cost function based on earliness, tardiness, window size, and window location. We propose an O(n log n) algorithm to solve the problem.
125 citations
TL;DR: In this article, the authors consider the problem of scheduling jobs on identical parallel machines to minimize total tardiness, and propose a branch and bound algorithm that incorporates the properties along with an efficient lower bounding scheme.
111 citations
TL;DR: In this paper, the authors present and compare a number of branch and bound algorithms for minimizing the total weighted tardiness in job shops, and obtain optimal solutions for all the instances with ten jobs and ten machines that they consider, including three tardy versions of a well-known 10 × 10 instance introduced by Muth and Thompson [1] in 1963.
Abstract: We present and compare a number of branch and bound algorithms for minimizing the total weighted tardiness in job shops. There are basically two types of branching schemes. The first one inserts operations in a partial schedule, while the second one fixes arcs in the disjunctive graph formulation of the problem. The bounding schemes are based on the analysis of precedence constraints, and on the solution of nonpreemptive single machine subproblems that are subject to so-called delayed precedence constraints. We obtain optimal solutions for all the instances with ten jobs and ten machines that we consider, including three tardiness versions of a well-known 10 × 10 instance introduced by Muth and Thompson [1] in 1963.
102 citations
TL;DR: The capacitated lot sizing and loading problem (CLSLP) as discussed by the authors deals with the issue of determining the lot sizes of product families/end items and loading them on parallel facilities to satisfy dynamic demand over a given planning horizon.
95 citations
TL;DR: In this article, the authors investigated the concurrent deployment of different priority rules at different processing stages of a manufacturing system by combining three simple priority rules with a combinatorial rule and found that the rule combinations are a better strategy than their pure forms when various performance measures are jointly evaluated.
Abstract: Several recent studies have explored the concurrent deployment of different priority rules at different processing stages of a manufacturing system. This study investigates the same issue by combining three popular simple priority rules with a combinatorial rule. In a three-stage flow shop, these rules are combined into 64 combination schemes and their performance compared under two shop load levels with two due date setting methods. The performance criteria considered are: mean lateness; mean tardiness; maximum tardiness; and per cent of tardy jobs. The results indicate that the rule combinations are a better strategy than their pure forms when various performance measures are jointly evaluated. Particularly, selected combinations of the Modified Shortest Processing Time, Shortest Processing Time, and the Earliest Due Date rules appear to be very effective. While the extent of shop load level shows little impact on the relative performance of the schemes, the endogenous method of due date setting consistently yields better results than the exogenous method.
57 citations
TL;DR: A polynomial time heuristic procedure, which provides efficient solutions to the problem of scheduling a set of independent jobs on parallel unrelated processors under a common due-date, is developed.
50 citations
TL;DR: In this paper, a genetic algorithm for scheduling jobs about an unrestricted common due date on a single machine is proposed and investigated, where the objective is to minimize total earliness and tardiness cost where early and tardy penalty rates are allowed to be arbitrary for each job.
Abstract: We propose and investigate a genetic algorithm for scheduling jobs about an unrestricted common due date on a single machine. The objective is to minimize total earliness and tardiness cost where early and tardy penalty rates are allowed to be arbitrary for each job. Jobs are classified into families and a family setup time is required between jobs from two different families. Results from a computational study are promising with close to optimal solutions obtained rather easily and quickly.
49 citations
TL;DR: In this article, a heuristic algorithm for minimizing job earliness and tardiness cost in a multimachine scheduling problem is proposed, which explicitly separates machine setup times from processing times.
Abstract: We provide a heuristic algorithm for minimizing job earliness and tardiness cost in a multimachine scheduling problem. Our formulation explicitly separates machine setup times from processing times, assumes that setup times may depend on the job-to-job sequence, and assumes that processing times may depend on the job-machine combination. The new algorithm can easily provide approximate solutions to problems involving about 10 machines and 100 jobs when using a personal computer. The accuracy of the solutions was measured using a large variety of problem types taken from the literature. Relative accuracy was measured by comparing the new algorithm's results with those from other heuristics, and absolute accuracy was measured by comparing with results obtained using integer programming methods. The new algorithm was significantly more accurate than the other heuristics, and its average deviation was only about 10% when compared to the optimal solutions. In many cases the new algorithm yielded the optimal so...
TL;DR: This paper outlines the fundamental issues of the manufacturing design in a genetic algorithm formulation and results indicate that this new scheduling scheme is an effective and efficient technique to tackle the problem of earliness and tardiness production scheduling and planning.
TL;DR: In this article, a heuristic algorithm based on the simulated annealing (SA) technique is developed for scheduling in flow shop and flowline-based manufacturing cell with the objective of minimizing mean tardiness of jobs.
01 Apr 1998
TL;DR: This paper develops assignment heuristics which iteratively update the problem parameters using lower and upper bounds computed from the corresponding schedule, and shows that the proposed approach provides a means for extending traditional scheduling capabilities to a much wider spectrum of shop conditions and production scenarios.
Abstract: In this paper, we present an approach to weighted tardiness job-shop scheduling problems (JSP) using a graph decomposition technique. Our method decomposes a JSP into a series of sub-problems by solving a variant of the generalized assignment problem which we term "VAP". Given a specified assignment cost, VAP assigns operations to mutually exclusive and exhaustive subsets, identifying a partially specified schedule, Compared to a conventional, completely specified schedule, this partial schedule is more robust to shop disturbances, and therefore more useful for planning and control. We have developed assignment heuristics which iteratively update the problem parameters using lower and upper bounds computed from the corresponding schedule. The heuristics are tested on standard test problems. We show that the proposed approach provides a means for extending traditional scheduling capabilities to a much wider spectrum of shop conditions and production scenarios.
TL;DR: In this article, a dynamic programming formulation is presented for determining an optimal solution to a problem where n jobs are to be sequenced in a multi-stage production environment, conditions are such that the job sequence is the same in all stages, each job requires setups at each stage and setup times are sequence dependent.
Abstract: A dynamic programming formulation is presented for determining an optimal solution to a problem where n jobs are to be sequenced in a multi-stage production environment. An application of a developed formulation to a plastic pipe manufacturing factory is also presented. Conditions are such that the job sequence is the same in all stages, each job requires setups at each stage and setup times are sequence dependent. An optimal solution is such that the minimum total tardiness is achieved. A listing of the developed computer program is also provided.
TL;DR: It is proved that even when the machine works at a variable rate, the pair-wise interchange of jobs minimizes the maximum tardiness and a simple modification to the well-known Moore-Hodgson's algorithm yields the minimum number of tardy jobs.
TL;DR: A new partition theorem is derived which generalises Lawler’s decomposition rule and leads to a new double decomposition procedure which applies a new lower bound based on due dates reassignment.
Abstract: This paper deals with the single machine total tardiness problem. From Emmons’ basic dominance conditions a new partition theorem is derived which generalises Lawler’s decomposition rule and leads to a new double decomposition procedure. This procedure is embedded into a branch and bound method which applies a new lower bound based on due dates reassignment. The branch and bound method is tested on problems with size up to 150 jobs.
TL;DR: A new composite heuristic is presented that combines tabu search, simulated annealing and steepest descent techniques to generate near optimal schedules for the single machine early/tardy job scheduling problem.
TL;DR: The objective is makespanminimization if there are no tardy jobs, and tardiness minimization otherwise, and the procedure is heuristic and exhibits a good trade-off between computing time and solution quality.
Abstract: In this paper we deal with a variant of the Job ShopScheduling Problem. We consider the addition of release dates anddeadlines to be met by all jobs. The objective is makespanminimization if there are no tardy jobs, and tardiness minimizationotherwise. The problem is approached by using a Shifting Bottleneckstrategy. The presence of deadlines motivates an iterative use of aparticular one machine problem which is solved optimally. Theoverall procedure is heuristic and exhibits a good trade-off betweencomputing time and solution quality.
TL;DR: It is shown that if the penalties meet a certain criterion, called the Dominance Condition, then there exists an extremal optimal solution to the LP-relaxation that is integral, leading to a polynomial-time solution procedure.
Abstract: The problem of determining a schedule of jobs with unit-time lengths on a single machine that minimizes the total weighted earliness and tardiness penalties with respect to arbitrary rational due-dates is formulated as an integer programming problem. We show that if the penalties meet a certain criterion, called the Dominance Condition, then there exists an extremal optimal solution to the LP-relaxation that is integral, leading to a polynomial-time solution procedure. The general weighted symmetric penalty structure is one cost structure that satisfies the Dominance Condition; we point out other commonly found penalty structures that also fall into this category.
TL;DR: Considers the resource‐constrained project scheduling problem where cash inflows and outflows are tied to the occurrence of events and develops hybrid scheduling rules with both NPV and tardiness considerations to enhance both objectives.
Abstract: Considers the resource‐constrained project scheduling problem where cash inflows and outflows are tied to the occurrence of events. The objective is the maximization of the project net present value (NPV) as well as the minimization of project tardiness in the presence of a project due date. Develops hybrid scheduling rules with both NPV and tardiness considerations to enhance both objectives. Experiments extensively with a set of benchmark problems originally designed for the objective of minimizing the project duration. Demonstrates that thje hybrid rules developed here are superior in performance with respect to both objectives when compared with well known rules which are developed for the two objective of minimizing the project duration. Demonstrates that the hybrid rules developed here are superior in performance with respect to both objectives when compared with well‐known rules which are developed for the two objectives taken individually. Furthermore, the iterative algorithm improves the performance of all tested rules significantly.
TL;DR: This paper proves the NP-hardness of unit-time job-shop scheduling problems which had unknown complexity status before by employing a general reduction of any scheduling problem for m identical parallel machines to minimize a criterion of the class.
01 Oct 1998
TL;DR: In this paper, the authors investigate how dispatching rules affect the performance of stochastic simulation-based finite capacity scheduling systems and provide guidance for schedulers to determine effective dispatching rule for such systems, and support the concept that the more randomness the system is subject to, the simpler the scheduling rules should be.
Abstract: In his paper, we investigate how dispatching rules affect the performance of stochastic simulation-based finite capacity scheduling systems and provide guidance for schedulers to determine effective dispatching rules for stochastic simulation-based finite capacity scheduling systems. To investigate the performance of dispatching rules in stochastic simulation-based finite capacity scheduling systems, extensive simulation experiments have been conducted through a two-stage simulation process. The experimental simulation results show that the schedules generated by the stochastic simulations with the dispatching rule, FIFO, outperform the schedules with some other well-known dispatching rules on the criteria of tardiness and proportion of jobs tardy. In addition, the simulation results support the concept that the more randomness the system is subject to, the simpler the scheduling rules should be.
TL;DR: In this paper, the problem of scheduling a single mask shop under a predetermined Earliest Due-Due-Date (EDD) dispatch policy is investigated. And the problem can be solved for an optimal solution in polynomial time.
Abstract: Reducing wafer fabrication cycle time and providing on-time wafer deliveries are among the top priorities of semiconductor companies. Mask manufacturing is essential to the overall wafer fabrication process since on-time delivery of masks significantly affects wafer fabrication cycle times. Moreover, delivering wafers on time means deliveries of masks must be on time as well. This research studies the scheduling problem of the bottleneck machine-the Electrical Beam (E-beam) Writer-of a mask shop. The criterion of minimum total tardiness is used as our performance measure to schedule this bottleneck operation. Using a predetermined Earliest-Due-Date (EDD) dispatch policy set by management, this study first addresses the problem of scheduling batches of a single mask size on a single machine. The approach is extended to the problem of scheduling batches of two mask sizes on a single machine; finally, a heuristic for a multiple-machine problem is developed. For the problem of a single machine under EDD dispatching policy, the problem can be formulated as a Dynamic Program (DP). Thus, it can be solved for an optimal solution in polynomial time. For the multiple machines problem, we heuristically allocate the masks to each machine. Each machine with allocated masks can then be solved by the DP formulation designed for the single machine problem. Based on the computational experiments in this study, the proposed DP approach reduces total tardiness by an average of 55% from the method currently in use at a major IC manufacturing foundry. Furthermore, in the case that due dates are set realistically, the DP approach reduces the tardiness about 95% from the shop's current method and about 88% from a simple full-batch method of scheduling.
TL;DR: A heuristic algorithm is developed using a Lagrangian relaxation technique to solve the problem of selecting orders to be produced in each period during the upcoming planning horizon with the objective of minimising earliness and tardiness costs and subcontracting costs.
Abstract: We consider a multi-period order selection problem in flexible manufacturing systems, which is the problem of selecting orders to be produced in each period during the upcoming planning horizon with the objective of minimising earliness and tardiness costs and subcontracting costs. The earliness and tardiness costs are incurred if an order is not finished on time, while subcontracting cost is incurred if an order is not selected within the planning horizon (and must be subcontracted) due to processing time capacity or tool magazine capacity. This problem is formulated as a 0–1 integer program which can be transformed into a generalised assignment problem. To solve the problem, a heuristic algorithm is developed using a Lagrangian relaxation technique. Effectiveness of the algorithm is tested on randomly generated problems and results are reported.
TL;DR: The qualities of stochastic algorithms, mainly genetic and simulated annealing-type algorithms, against heuristic methods, in the scheduling of workshops are evaluated and can be used for when scheduling more complicated real workshops.
Abstract: We evaluate in this paper the qualities of stochastic algorithms, mainly genetic and simulated annealing-type algorithms, against heuristic methods, in the scheduling of workshops. We are particularly interested in flow-shops (minimizing makespan) and one machine schedules (minimizing total tardiness, or minimizing total flow time). Many numerical results for various samples are given, and our conclusions are supported by statistical tests. When the initial population is randomly generated, genetic algorithms are shown to be statistically less efficient than annealing-type algorithms, and better than heuristic methods. But, as soon as at least one good item (e.g.,heuristicallyfound) belongs to the initial population, genetic algorithms become as good, or better than annealing-type algorithms. The resolution methods we propose are evaluated and can be used for when scheduling more complicated real workshops.
TL;DR: A guaranteed accuracy shifting bottleneck algorithm is developed for the two-machine flowshop total tardiness problem by exploiting its relationship to its single machine counterpart and it is shown that this bound is tight.
12 Oct 1998
TL;DR: This paper presents an algorithm for scheduling unit-execution-time instructions on machines with multiple pipelines, in the presence of precedence constraints, release-times, deadlines, and latencies l/sub ij/ between any pairs of instructions i and j.
Abstract: Instruction scheduling is central to achieving performance in modern processors with instruction level parallelism (ILP). Classical work in this area has spanned the theoretical foundations of algorithms for instruction scheduling with provable optimality, as well as heuristic approaches with experimentally validated performance improvements. Typically, the theoretical foundations are developed in the context of basic-blocks of code. In this paper, we provide the theoretical foundations for scheduling basic-blocks of instructions with time-constraints, which can play an important role in compile-time ILP optimizations in embedded applications. We present an algorithm for scheduling unit-execution-time instructions on machines with multiple pipelines, in the presence of precedence constraints, release-times, deadlines, and latencies $l_{ij}$ between any pairs of instructions $i$ and $j$. Our algorithm runs in time $O(n^3\alpha(n))$, where $\alpha(n)$ is the functional inverse of the Ackermann function. It can be used construct feasible schedules for two classes of instances:one pipeline and the latencies between instructions are restricted to the values of 0 and 1, and arbitrary number of pipelines and monotone-interval order precedences. %The algorithm can also be used to construct minimal tardiness %schedules in polynomial time. Our result can be seen as a natural extension of previous work on instruction scheduling for pipelined machines in the presence of deadlines.
TL;DR: The purpose of this paper is to investigate and analyse complex fuzzy interactions of variables affecting a scheduling system and its performance measure under current operating conditions, i.e., to expose the "hidden rules" that are operating under day to day implementation of the company procedures by the schedulers of theCompany.
TL;DR: In this paper, the authors focus on multi-period order selection and loading problems in flexible manufacturing systems and develop four iterative procedures to solve the two problems simultaneously, which are solved repeatedly until a good solution is obtained.
Abstract: This paper focuses on multi-period order selection and loading problems in flexible manufacturing systems. The multi-period order selection problem is the problem of selecting orders to be produced in each period during the upcoming planning horizon, and the loading problem involves allocation of operations and required tools to machines for orders selected in each period. The objective is to minimize earliness and tardiness costs and subcontracting costs. The earliness and tardiness costs are incurred if an order is not finished on time, while subcontracting cost is incurred if an order is not selected within the planning horizon (and must be subcontracted) due to limits in processing time capacity and the tool magazine capacity of the machines. To solve the two problems simultaneously, we develop four iterative procedures in which the multi-period order selection and loading problems are solved repeatedly until a good solution is obtained. To compare the four iterative procedures, computational experime...