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Sequencing and scheduling: algorithms and complexity

We consider the problem of scheduling n jobs to minimize the total earliness and tardiness penalty. We review the literature on this topic, providing a framework to show how results have been generalized starting with a basic model that contains symmetric penalties, one machine and a common due date. To this base we add such features as parallel machines, complex penalty functions and distinct due dates. We also consolidate many of the existing results by proving general forms of two key properties of earliness/tardiness models.

Sequencing with Earliness and Tardiness Penalties: A Review

Publisher Summary This chapter discusses different types of sequencing and scheduling problems, and describes different types of algorithms and the concepts of complexity theory. A class of deterministic machine scheduling problems has been introduced in the chapter. The chapter also deals with the single machine, parallel machine and multi-operation problems in this class, respectively. The two generalizations of the deterministic machine-scheduling model have been presented in the chapter. A deterministic scheduling model may give rise to various stochastic counterparts, as there is a choice in the parameters that are randomized, in their distributions, and in the classes of policies that can be applied. A characteristic feature of these models is that the stochastic parameters are regarded as independent random variables with a given distribution and that their realization occurs only after the scheduling decision has been made. In the deterministic model, one has perfect information, and capitalizing on it in minimizing the realization of a performance measure may require exponential time.

Chapter 9 Sequencing and scheduling: Algorithms and complexity

The scheduling of computer and manufacturing systems has been the subject of extensive research for over forty years. In addition to computers and manufacturing, scheduling theory can be applied to many areas including agriculture, hospitals and transport. The main focus is on the efficient allocation of one or more resources to activities over time. Adopting manufacturing terminology, a job consists of one or more activities, and a machine is a resource that can perform at most one activity at a time. We concentrate on deterministic machine scheduling for which it is assumed that all data that define a problem instance are known with certainty.

A Review of Machine Scheduling: Complexity, Algorithms and Approximability

Autonomous AI systems need complex computational techniques for planning and performing actions. Planning and acting require significant deliberation because an intelligent system must coordinate and integrate these activities in order to act effectively in the real world. This book presents a comprehensive paradigm of planning and acting using the most recent and advanced automated-planning techniques. It explains the computational deliberation capabilities that allow an actor, whether physical or virtual, to reason about its actions, choose them, organize them purposefully, and act deliberately to achieve an objective. Useful for students, practitioners, and researchers, this book covers state-of-the-art planning techniques, acting techniques, and their integration which will allow readers to design intelligent systems that are able to act effectively in the real world.

Automated Planning and Acting

A survey of algorithms for the single machine total weighted tardiness scheduling problem

The problem of sequencing jobs on a single machine to minimize total cost is considered. Machine capacity constraints require that, at any time, at most one job is processed. Also, no machine idle-time between processing jobs is allowed. In contrast to most research, it is not assumed that the cost is a non-decreasing function of completion time. A dynamic programming formulation of the problem is presented. Since the number of states required by this formulation is prohibitively large, the possibilities for branch and bound algorithms are explored. It is shown that the dynamic programming formulation can be relaxed by mapping the state-space onto a smaller state-space and performing the recursion on this smaller state-space, thereby giving a lower bound. Techniques for improving this lower bound through the use of penalties and through the use of state-space modifiers are discussed. Computational results are presented for the problem in which each job has a due date, and the objective is to minimize the sum of holding costs for jobs completed before their due date and tardiness costs for jobs completed after their due date.

Dynamic Programming State-Space Relaxation for Single-Machine Scheduling

Real life scheduling problems require the decision maker to consider a number of criteria before arriving at any decision. In this paper, we consider the multi-criteria scheduling problem of n jobs on single machine to minimize a function of five criteria denoted by total completion times (∑), total tardiness (∑), total earliness (∑), maximum tardiness () and maximum earliness (). The single machine total tardiness problem and total earliness problem are already NP-hard, so the considered problem is strongly NP-hard.
We apply two local search algorithms (LSAs) descent method (DM) and simulated annealing method (SM) for the 1// (∑∑∑) problem (SP) to find near optimal solutions. The local search methods are used to speed up the process of finding a good enough solution, where an exhaustive search is impractical for the exact solution. The two heuristic (DM and SM) were compared with the branch and bound (BAB) algorithm in order to evaluate effectiveness of the solution methods.
            Some experimental results are presented to show the applicability of the (BAB) algorithm and (LSAs). With a reasonable time, (LSAs) may solve the problem (SP) up to 5000 jobs.

Local Search Algorithms for Multi-criteria Single Machine Scheduling Problem

Hybrid Bees Algorithm to Solve Aircraft Landing Problem

This paper presents an approach to schedule n jobs with processing times and due dates on a single machine based on Artificial Neural Network. The purpose of this paper to find a schedule that minimize a function of the sum of completion time and sum of tardiness (i,e to minimize the multiple objective functions (Ci,Ti)). Neural network technique was be found to be effective and used to select the best efficient and optimal schedule which minimizes the sum of completion time and sum of tardiness.

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Tariq S. Abdul-Razaq

Papers

A survey of algorithms for the single machine total weighted tardiness scheduling problem

Dynamic Programming State-Space Relaxation for Single-Machine Scheduling

Local Search Algorithms for Multi-criteria Single Machine Scheduling Problem

Hybrid Bees Algorithm to Solve Aircraft Landing Problem

Constructing of an Artificial Neural Networks to Minimize Total Completion Time and Total Tardiness