An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.

Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation

We consider various single machine scheduling problems in which the processing time of a job depends either on its position in a processing sequence or on its start time. We focus on problems of minimizing the makespan or the sum of (weighted) completion times of the jobs. In many situations we show that the objective function is priority-generating, and therefore the corresponding scheduling problem under series-parallel precedence constraints is polynomially solvable. In other situations we provide counter-examples that show that the objective function is not priority-generating.

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({\rm T}_{\rm feas}(n) \times\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.

Approximation results for flow shop scheduling problems with machine availability constraints

This paper considers two-machine flow shop scheduling problems with machine availability constraints. When the processing of a job is interrupted by an unavailability period of a machine, we consider both the resumable scenario in which the processing can be resumed when the machine next becomes available, and the semi-resumable scenario in which some portion of the processing is repeated but the job is otherwise resumable. For the problem with several non-availability intervals on the first machine under the resumable scenario, we present a fast (3/2)-approximation algorithm. For the problem with one non-availability interval under the semi-resumable scenario, a polynomial-time approximation scheme is developed.

Scheduling parallel dedicated machines with the speeding-up resource

We consider a problem of scheduling jobs on m parallel machines. The machines are dedicated, i.e., for each job the processing machine is known in advance. We mainly concentrate on the model in which at any time there is one unit of an additional resource. Any job may be assigned the resource and this reduces its processing time. A job that is given the resource uses it at each time of its processing. No two jobs are allowed to use the resource simultaneously. The objective is to minimize the makespan. We prove that the two-machine problem is NP-hard in the ordinary sense, describe a pseudopolynomial dynamic programming algorithm and convert it into an FPTAS. For the problem with an arbitrary number of machines we present an algorithm with a worst-case ratio close to 3/2, and close to 3, if a job can be given several units of the resource. For the problem with a fixed number of machines we give a PTAS. Virtually all algorithms rely on a certain variant of the linear knapsack problem (maximization, minimization, multiple-choice, bicriteria). © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008

Single machine scheduling and due date assignment with positionally dependent processing times

We consider single machine scheduling and due date assignment problems in which the processing time of a job depends on its position in a processing sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and, possibly, the total earliness of the scheduled jobs. We present polynomial-time dynamic programming algorithms in the case of two popular due date assignment methods: CON and SLK. The considered problems are related to mathematical models of cooperation between the manufacturer and the customer in supply chain scheduling.

Fifty years of scheduling: a survey of milestones

Scheduling has become a major field within operational research with several hundred publications appearing each year. This paper explores the historical development of the subject since the mid-1950s when the landmark publications started to appear. A discussion of the main topics of scheduling research for the past five decades is provided, highlighting the key contributions that helped shape the subject. The main topics covered in the respective decades are combinatorial analysis, branch and bound, computational complexity and classification, approximate solution algorithms and enhanced scheduling models.

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.

Investigation into a modular rule-based testing method for testing business rules in scheduling applications

Rule testing in transport scheduling is a complex and potentially costly business problem. This paper proposes an automated method for the rule-based testing of business rules using the extensible Markup Language for rule representation and transportation. A compiled approach to rule execution is also proposed for performance-critical scheduling systems.

Scheduling and Platforming Trains at Busy Complex Stations

We consider the problem of train planning or scheduling for large, busy, complex train stations, which are common in Europe and elsewhere, though not in North America. We develop the constraints and objectives for this problem, but these are too computationally complex to solve by standard combinatorial search or integer programming methods. Also, the problem is somewhat political in nature, that is, it does not have a clear objective function because it involves multiple train operators with conflicting interests. We therefore develop scheduling heuristics analogous to those successfully adopted by train planners using ''manual'' methods. We tested the model and algorithms by applying to a typical large station that exhibits most of the complexities found in practice. The results compare well with those found by traditional methods, and take account of cost and preference trade-offs not handled by those methods. With successive refinements, the algorithm eventually took only a few seconds to run, the time depending on the version of the algorithm and the scheduling problem. The scheduling models and algorithms developed and tested here can be used on their own, or as key components for a more general system for train scheduling for a rail line or network.Train scheduling for a busy station includes ensuring that there are no conflicts between several hundred trains per day going in and out of the station on intersecting paths from multiple in-lines and out-lines to multiple platforms, while ensuring that each train is allowed at least its minimum required headways, dwell time, turnaround time and trip time. This has to be done while minimizing (costs of) deviations from desired times, platforms or lines, allowing for conflicts due to through-platforms, dead-end platforms, multiple sub-platforms, and possible constraints due to infrastructure, safety or business policy.

Dynamic Job Scheduling on the Grid Environment using the Great Deluge Algorithm

The utilization of the computational Grid processor network has become a common method for researchers and scientists without access to local processor clusters to avail of the benefits of parallel processing for compute-intensive applications. As a result, this demand requires effective and efficient dynamic allocation of available resources. Although static scheduling and allocation techniques have proved effective, the dynamic nature of the Grid requires innovative techniques for reacting to change and maintaining stability for users. The dynamic scheduling process requires quite powerful optimization techniques, which can themselves lack the performance required in reaction time for achieving an effective schedule solution. Often there is a trade-off between solution quality and speed in achieving a solution. This paper presents an extension of a technique used in optimization and scheduling which can provide the means of achieving this balance and improves on similar approaches currently published.