Two branch-and-bound algorithms for the robust parallel machine scheduling problem

Uncertainty is an inevitable element in many practical production planning and scheduling environments. When a due date is predetermined for performing a set of jobs for a customer, production managers are often concerned with establishing a schedule with the highest possible confidence of meeting the due date. In this paper, we study the problem of scheduling a given number of jobs on a specified number of identical parallel machines when the processing time of each job is stochastic. Our goal is to find a robust schedule that maximizes the customer service level, which is the probability of the makespan not exceeding the due date. We develop two branch-and-bound algorithms for finding an optimal solution; the two algorithms differ mainly in their branching scheme. We generate a set of benchmark instances and compare the performance of the algorithms based on this dataset.     

Optimal algorithms for the batch scheduling problem in OBS networks

This paper introduces optimal batch scheduling algorithms for the problem of scheduling batches of bursts in optical burst switching networks. The problem is modelled as a job scheduling problem with identical machines. The consideration of previously scheduled bursts in the scheduling allows such modeling. Two optimal algorithms with polynomial time complexity are derived and evaluated. Results show that the algorithm that allows re-scheduling of previously scheduled bursts leads to preferred solutions.Moreover, an extended version of the JET reservation protocol is proposed for efficient handling of batches of bursts. Results obtained via simulation prove the superior performance of the BATCHOPT algorithm.     

Optimal algorithms for semi-online preemptive scheduling problems on two uniform machines

This paper investigates two preemptive semi-online scheduling problems to minimize makespan on two uniform machines. In the first semi-online problem, we know in advance that all jobs have their processing times in between p and rp . In the second semi-online problem, we know the size of the largest job in advance. We design an optimal semi-online algorithm which is optimal for every combination of machine speed ratio and job processing time ratio for the first problem, and an optimal semi-online algorithm for every machine speed ratio for the second problem.Received: 2 December 2003, Published online: 16 January 2004This research is supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China, and National Natural Science Foundation of China (10271110).     

Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups

In this paper, we consider the single machine weighted tardiness scheduling problem with sequence-dependent setups. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Previous beam search implementations use fixed beam and filter widths. We consider the usual fixed width algorithms, and develop new versions that use variable beam and filter widths.     

Preemptive online algorithms for scheduling with machine cost

For most scheduling problems the set of machines is fixed initially and remains unchanged. Recently Imreh and Noga proposed adding the concept of machine cost to scheduling problems and considered the so-called List Model problem. For this problem, we are given a sequence of independent jobs with positive sizes, which must be processed non-preemptively on a machine. No machines are initially provided, and when a job is revealed the algorithm has the option to purchase new machines. The objective is to minimize the sum of the makespan and cost of machines. In this paper, a modified model of List Model is presented where preemption is allowed. For this model, it is shown that better performance is possible. We present an online algorithm with a competitive ratio of while the lower bound is 4/3. For the semi-online problem with decreasing sizes, we design an optimal algorithm with a competitive ratio of 4/3, which improves the known upper bound of 3/2. The algorithm does not introduce any preemption, and hence is also an optimal semi-online algorithm for the non-preemptive semi-online problem. For the semi-online problem with known largest size, we present an optimal algorithm with a competitive ratio of 4/3.Received: 7 June 2004, Published online: 11 November 2004This research is supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China, and National Natural Science Foundation of China (10271110, 60021201).     

Optimal and heuristic solution methods for a multiprocessor machine scheduling problem

This paper deals with the scheduling of operations on a multiprocessor machine in the context of shoe manufacturing. Multiprocessor machines are composed of several parallel processors. Unlike parallel machines, the entire machine needs to be stopped whenever a single processor needs a setup. Our industrial partner, one of the major winter-shoe manufacturers in Canada, offers a relatively large variety of models. For each of these models, all the sizes proposed by this manufacturer must be produced in various quantities. Our objective is to schedule the production of the required sizes on the machine's different processors in order to minimize the global makespan, which includes both the production time and the set up time. We first present a mathematical formulation of the problem. Then, we introduce a decomposition procedure based on the mathematical model, and we demonstrate that this procedure is very efficient for small- and medium-size instances. We also propose two construction heuristics and two improvement heuristics for larger problems, and we report the results of our extensive computational experiments to demonstrate the quality of the proposed heuristics in terms of reducing production time and computational effort.     

Ordinal algorithms for parallel machine scheduling with nonsimultaneous machine available times

This paper considers ordinal algorithms for parallel machine scheduling with nonsimultaneous machine available times. Two objects of minimizing the latest job completion time and minimizing the latest machine completion time are studied. For the first objective, we present the optimal algorithms for m = 2, 3, 4 machine cases. For m ≥ 5, we propose an algorithm with competitive ratio 2 - 1/(m - 1) while the lower bound is 5/3. For the second objective, the optimal algorithm is also given. Furthermore, for a special case, an algorithm with significantly improved competitive ratio is given.     

A study of hybrid evolutionary algorithms for single machine scheduling problem with sequence-dependent setup times

We present a systematic comparison of hybrid evolutionary algorithms (HEAs), which independently use six combinations of three crossover operators and two population updating strategies, for solving the single machine scheduling problem with sequence-dependent setup times. Experiments show the competitive performance of the combination of the linear order crossover operator and the similarity-and-quality based population updating strategy. Applying the selected HEA to solve 120 public benchmark instances of the single machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness widely used in the literature, we achieve highly competitive results compared with the exact algorithm and other state-of-the-art metaheuristic algorithms in the literature. Meanwhile, we apply the selected HEA in its original form to deal with the unweighted 64 public benchmark instances. Our HEA is able to improve the previous best known results for one instance and match the optimal or the best known results for the remaining 63 instances in a reasonable time.     

Genetic algorithms for task scheduling problem

The scheduling and mapping of the precedence-constrained task graph to processors is considered to be the most crucial NP-complete problem in parallel and distributed computing systems. Several genetic algorithms have been developed to solve this problem. A common feature in most of them has been the use of chromosomal representation for a schedule. However, these algorithms are monolithic, as they attempt to scan the entire solution space without considering how to reduce the complexity of the optimization process. In this paper, two genetic algorithms have been developed and implemented. Our developed algorithms are genetic algorithms with some heuristic principles that have been added to improve the performance. According to the first developed genetic algorithm, two fitness functions have been applied one after the other. The first fitness function is concerned with minimizing the total execution time (schedule length), and the second one is concerned with the load balance satisfaction. The second developed genetic algorithm is based on a task duplication technique to overcome the communication overhead. Our proposed algorithms have been implemented and evaluated using benchmarks. According to the evolved results, it has been found that our algorithms always outperform the traditional algorithms.     

Optimal admission control algorithms for scheduling burst data in CDMA multimedia systems

The third generation mobile communication systems are widely envisioned to be based on wideband code division multiple access (CDMA) technologies to support high data rate (HDR) packet data services. To effectively harness the precious bandwidth while satisfying the HDR requests from users, it is crucial to use a judicious burst admission control algorithm. In this paper, we propose and evaluate the performance of a novel jointly adaptive burst admission algorithm, called the synergistic burst admission control algorithm to allocate valuable resources (i.e., channels) in wideband CDMA systems to burst HDR requests. We consider the spatial dimension only, and by that we mean the algorithm performs scheduling and admission control, for the current frame only, based solely on the selection diversity in the geographical and mobility aspects. The scheduler does not exploit the temporal dimension in that it does not make allocation decisions about future frames (i.e., requests that do not get allocation are simply ignored and such requests will be treated as new request in future frames). In the physical layer, we use a variable rate channel-adaptive modulation and coding system which offers variable throughput depending on the instantaneous channel condition. In the MAC layer, we use the proposed optimal multiple-burst admission algorithm, induced by our novel integer programming formulation of the admission control and scheduling problem. We demonstrate that synergy could be attained by interactions between the adaptive physical layer and the burst admission layer. Both the forward link and the reverse link burst requests are considered and the system is evaluated by dynamic simulations which takes into account of the user mobility, power control and soft handoff. We found that significant performance improvement, in terms of average packet delay, data user capacity and coverage, could be achieved by our scheme compared to the existing burst assignment algorithms.     

A linear compound algorithm for uniform machine scheduling

In this paper, we consider the classical two uniform machine scheduling problem. We present a compound algorithm which consists of three Greedy-like subprocedures running independently. We prove that the algorithm has a worst-case bound of 7/6 and runs in linear time. Partially supported by SFB F003 “Optimierung und Kontrolle”, Projektbereich Diskrete Optimierung and by the National Natural Science Foundation of China.     

Memetic algorithms for the job shop scheduling problem with operators

The job-shop scheduling problem with operators (JSO) is an extension of the classic job-shop problem in which an operation must be assisted by one of a limited set of human operators, so it models many real life situations. In this paper we tackle the JSO by means of memetic algorithms with the objective of minimizing the makespan. We define and analyze a neighborhood structure which is then exploited in local search and tabu search algorithms. These algorithms are combined with a conventional genetic algorithm to improve a fraction of the chromosomes in each generation. We also consider two different schedule builders for chromosome decoding. All these elements are combined to obtain memetic algorithms which are evaluated over an extensive set of instances. The results of the experimental study show that they reach high quality solutions in very short time, comparing favorably with the state-of-the-art methods.     

The optimal on-line parallel machine scheduling

This paper investigates on-line parallel machine scheduling problems. We show the optimality of the classical LS algorithm.     

A note on longest processing time algorithms for the two uniform parallel machine makespan minimization problem

This note considers the longest processing time heuristic for scheduling n independent jobs on two uniform parallel machines to minimize the makespan. A posterior worst-case performance ratio, by depending on the index of the latest job inserted in the machine where the makespan takes place, is developed for this heuristic, and some examples demonstrate that the ratio is tight.     

Heuristic algorithms for solving earliness-tardiness scheduling problems with machine vacations

The earliness and tardiness (E/T) penalty problem in scheduling gained more importance in part due to its application in Just-In-Time (JIT) production system. Inorder to meet JIT production schedules preventive maintenance plan must be in place. During the maintenance periods machine is not available for processing. The time duration planned for preventive maintenance or meal breaks is called machine vacation. Incorporating E/T penalty and machine vacation a single machine scheduling model is developed. Heuristic methods for solving this problem and computational results are also presented.     

Ordinal scheduling problem and its asymptotically optimal algorithms on parallel machine system

Consider a resource allocation problem on the following system. A system consists of m identical parallel machines and is alive only when all the machines are alive. To keep a machine alive, it requires resources (material, fuel, etc.). Resources with various sizes arrive one by one and the goal is to keep the system alive as long as possible. The problem has applications in many areas such as sequencing of maintenance actions for modular gas turbine aircraft engines[1]. Using scheduling term…