Jacek Blazewicz

Scheduling subject to resource constraints: classification and complexity

Abstract In deterministic sequencing and scheduling problems, jobs are to be processed on machines of limited capacity. We consider an extension of this class of problems, in which the jobs require the use of additional scarce resources during their execution. A classification scheme for resource constraints is proposed and the computational complexity of the extended problem class is investigated in terms of this classification. Models involving parallel machines, unit-time jobs and the maximum completion time criterion are studied in detail; other models are briefly discussed.

Scheduling Computer and Manufacturing Processes

No abstract

The Job Shop Scheduling Problem: Conventional and new Solution Techniques

A job shop consists of a set of different machines that perform operations on jobs. Each job has a specified processing order through the machines, i.e. a job is composed of an ordered list of operations each of which is determined by the machine required and the processing time on it. There are no precedence constraints among operations of different jobs. Operations can not be interrupted (non-preemption) and each machine can handle only one job at a time. Consequently, each job can be performed on only one machine at a time. The operation sequences on the machines are unknown and have to be determined in order to minimize the makespan, i. e. the time required to complete all jobs.

Scheduling in Computer and Manufacturing Systems

A theoretical and application-oriented analysis of deterministic scheduling problems arising in computer and manufacturing environments. The important classical results are surveyed with particular attention paid to single-processor scheduling, along with general models such as resource-constrained scheduling, flexible flow shops, dynamic job shops, and special flexible manufacturing systems. Polynomial and exponential-time optimization algorithms as well as approximation and heuristic ones are presented using a Pascal-like notation, before being discussed in the light of particular problems. Basic concepts from scheduling theory and related fields are described to assist less advanced readers.

Sequencing of parts and robot moves in a robotic cell

In this paper, we deal with the problem of sequencing parts and robot moves in a robotic cell where the robot is used to feed machines in the cell. The robotic cell, which produces a set of parts of the same or different types, is a flow-line manufacturing system. Our objective is to maximize the long-run average throughput of the system subject to the constraint that the parts are to be produced in proportion of their demand. The cycle time formulas are developed and analyzed for this purpose for cells producing a single part type using two or three machines. A state space approach is used to address the problem. Both necessary and sufficient conditions are obtained for various cycles to be optimal. Finally, in the case of many part types, the problem of scheduling parts for a specific sequence of robot moves in a two machine cell is formulated as a solvable case of the traveling salesman problem.

Automated 3D structure composition for large RNAs

Understanding the numerous functions that RNAs play in living cells depends critically on knowledge of their three-dimensional structure. Due to the difficulties in experimentally assessing structures of large RNAs, there is currently great demand for new high-resolution structure prediction methods. We present the novel method for the fully automated prediction of RNA 3D structures from a user-defined secondary structure. The concept is founded on the machine translation system. The translation engine operates on the RNA FRABASE database tailored to the dictionary relating the RNA secondary structure and tertiary structure elements. The translation algorithm is very fast. Initial 3D structure is composed in a range of seconds on a single processor. The method assures the prediction of large RNA 3D structures of high quality. Our approach needs neither structural templates nor RNA sequence alignment, required for comparative methods. This enables the building of unresolved yet native and artificial RNA structures. The method is implemented in a publicly available, user-friendly server RNAComposer. It works in an interactive mode and a batch mode. The batch mode is designed for large-scale modelling and accepts atomic distance restraints. Presently, the server is set to build RNA structures of up to 500 residues.

Mathematical programming formulations for machine scheduling: a survey

Abstract Machine scheduling was and still is a rich and promising field for research with applications in manufacturing, logistics, computer architecture, communications, etc. Combinatorial complexity theory has now classified the great majority of known machine scheduling problems as ‘easy’ or ‘very hard’. However, in most cases, mathematical programming models have not accompanied the algorithmic developments for solving ‘easy’ scheduling problems, nor have they facilitates solutions for ‘hard’ problems. Nevertheless, the analysis of the mathematical programming models for some hard combinatorial problems together with their polyhedral properties has enabled important computational advances for such problems as the TSP. In order to assess the present status and the solution potential of mathematical programming formulations for machine scheduling, we have compiled a systematic, consistent survey of formulations. The discussion has been developed in tandem with the classification of a given problems complexity, since ‘solvability’ (i.e., the status of a problem as P or NP-hard) generally cannot be easily assessed from the formulation itself. A number of excellent survey papers on machine scheduling have appeared over the years (see the reference list), but none of them has been focused on mathematical formulations. This survey is the first one that attempts to compile a large number of mathematical programming formulations for scheduling into a single paper to ease the task of model building and testing scheduling formulations. Both, a newcomer and experienced researcher can use it as a reference point. Ultimately, mathematical programming formulations for scheduling problems might be used as a stepping stone to computational advances for some hard problems.

An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints

In this paper, we study the single machine total completion scheduling problem subject to a period of maintenance. We propose an approximation algorithm to solve the problem with a worst case error bound of 3/17. Furthermore, an example is provided to show that the bound is tight. Computational experiments and an analysis are given afterwards.

Two-machine flow shops with limited machine availability

Abstract This paper studies a flow shop where machines have some periods of limited availability. The limited availability may be due to preschedules, preventive maintenance, or overlap of two consecutive time horizons in the rolling time horizon planning algorithm. It is shown that the problem of minimizing makespan in such a flow shop is NP-hard in the strong sense, and that no polynomial time heuristic with constant relative error exists for the problem unless P=NP. Some important properties of optimal schedules are proved for two-machine flow shops. A branch and bound algorithm based on these properties is proposed, and results of computational experiments with the algorithm are presented.

Selected Topics in Scheduling Theory

Publisher Summary This chapter discusses the deterministic problems of scheduling tasks on machines (processors), which is one of the most rapidly expanding areas of combinatorial optimization. These problems are stated as follows: A given set of tasks is to be processed on a set of available processors, so that all processing conditions are satisfied and a certain objective function is minimized (or maximized). It is assumed, in contrast to stochastic scheduling problems, that all task parameters are known a priori in a deterministic way. This assumption is well justified in many practical situations. On the other hand, it permits the solving of scheduling problems having a different practical interpretation from that of the stochastic approach. This interpretation is a valuable complement to the stochastic analysis and is often imposed by certain applications as—for example, in computer control systems working in a hard-real-time environment and in many industrial applications. The chapter focuses on the applications of this model in computer systems. It also points out some other interpretations, because tasks and machines may also represent ships and dockyards, classes and teachers, patients and hospital equipment, or dinners and cooks.