Unit-time open-shop scheduling problems with symmetric objective functions

The paper deals with the open??shop problems with unit??time operations and nonde??creasing symmetric objective functions depending on job completion times??. We construct two schedules??, one of them is optimal for any symmetric convex function??, the other is optimal for any symmetric concave function.?? Each of these two schedules is given by an analytically defined function which assigns to each operation the number of a unit-??time slot for its processing??

Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper

Scheduling coupled-operation jobs with exact time-lags

AbstractScheduling coupled-operation jobs with exact time-lags on a single machine has a wide range of applications. In that problem, each job consists of two operations with given processing times, which should be scheduled on a single machine observing a given time-lag. The general case of the problem with arbitrary processing times of operations and arbitrary time lags is known to be NP-hard in the strong sense and the problem remains NP-hard for many special cases. In order to develop a local search algorithm for the problem, we first explore two possible approaches for representing feasible solutions and their neighborhoods based on maintaining a permutation of first operations of the jobs or maintaining a full permutation of all operations. The first representation appears to be unpromising since, as we prove, the problem of finding an optimal sequence of second operations for a fixed sequence of first operations is NP-hard in the strong sense even in the case of unit processing times. We elaborate the second approach by developing a tabu search heuristic based on efficient job re-insertion. Empirical evaluation demonstrates superiority of the developed algorithm in comparison with the earlier published algorithms

Three-machine shop scheduling with partially ordered processing routes

This paper considers the problem of sequencing n jobs in a three-machine shop with the objective of minimising the maximum completion time. The shop consists of three machines, M1,M2 and M_{3}. A job is first processed on M1 and then is assigned either the route (M2,M_{3}) or the route (M_{3},M2). Thus, for our model the processing route is given by a partial order of machines, as opposed to the linear order of machines for a job shop, or to an arbitrary sequence of machines for an open shop. The main result is on O(nlog n) time heuristic, which generates a schedule with the makespan that is at most 5/3 times the optimum value

An adaptive scheduling algorithm based on the mixed graph model

This paper deals with an adaptive approach for scheduling problems. The main idea is to produce for a class of similar problems a special heuristic rule, which is successful for problems of this class. It is realized by 'tuning' the parameters of the algorithm while 'learning' on the peculiarities of considering class of problems. Once trained on the sample problems (in our experiments a well-known test problem with 10 jobs and 10 machines has been considered), the adaptive algorithm solves 'close' problems better than an exact algorithm (both in running time and in accuracy of the constructed schedule) and better than 25 heuristics (in accuracy), which were used in the learning stage. However, the adaptive algorithm is unable to perform better than the exact one for such scheduling problem, which are not sufficiently close to the sample problem. (orig.)Available from TIB Hannover: RR 4487(1995,11) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Shop-scheduling problems with fixed and non-fixed machine orders of the jobs

The paper deals with the determination of an optimal schedule for the so-called mixed-shop problem when the makespan has to be minimized. In such a problem, some jobs have fixed machine orders (as in the job-shop), while the operations of the other jobs may be processed in arbitrary orders (as in the open-shop). We prove binary NP-hardness of the preemptive problem case with three machines and three jobs (two jobs have fixed machine orders and one may have an arbitrary machine order). We answer all other remaining open questions on the complexity status of mixed-shop problems with the makespan criterion by presenting different polynomial and pseudopolynomial algorithms. (orig.)SIGLEAvailable from TIB Hannover: RR 4487(1997,14) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekInternational Association for the Promotion of Co-Operation with Scientists from the Independent States of the Former Soviet Union (INTAS); Deutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman

The Assignment Problem with Nearly Monge Arrays and Incompatible Partner Indices

In this paper we study the d-dimensional assignment problem in which entries of the cost array satisfy the Monge property, except for ∞-entries, which may violate it. We assume that the ∞-entries are incurred by incompatible partner indices and their number is bounded by an upper bound λ for each index. We show that the problem can be solved in linear time for fixed d and λ, and it becomes strongly NP-hard if d or λ is part of the input