Journal ArticleDOI
Dynamic Programming State-Space Relaxation for Single-Machine Scheduling
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TLDR
The problem of sequencing jobs on a single machine to minimize total cost is considered, and 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 smallerstate-space, thereby giving a lower bound.Abstract:
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.read more
Citations
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Sequencing and scheduling: algorithms and complexity
TL;DR: This survey focuses on the area of deterministic machine scheduling, and reviews complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops.
Journal ArticleDOI
Sequencing with Earliness and Tardiness Penalties: A Review
Kenneth R. Baker,Gary D. Scudder +1 more
TL;DR: 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 is provided and such features as parallel machines, complex penalty functions and distinct due dates are added.
Book ChapterDOI
Chapter 9 Sequencing and scheduling: Algorithms and complexity
TL;DR: Different types of sequencing and scheduling problems are discussed, and different types of algorithms and the concepts of complexity theory are described.
Book ChapterDOI
A Review of Machine Scheduling: Complexity, Algorithms and Approximability
TL;DR: This work focuses on deterministic machine scheduling for which it is assumed that all data that define a problem instance are known with certainty.
Book
Automated Planning and Acting
TL;DR: This book presents a comprehensive paradigm of planning and acting using the most recent and advanced automated-planning techniques, and explains the computational deliberation capabilities that allow an actor to reason about its actions, choose them, organize them purposefully, and act deliberately to achieve an objective.
References
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Journal ArticleDOI
A Dynamic Programming Approach to Sequencing Problems
Michael Held,Richard M. Karp +1 more
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Journal ArticleDOI
State‐space relaxation procedures for the computation of bounds to routing problems
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Journal ArticleDOI
A Branch and Bound Algorithm for the Total Weighted Tardiness Problem
TL;DR: This paper presents a new branch and bound algorithm for the single machine total weighted tardiness problem that obtains lower bounds using a Lagrangian relaxation approach with subproblems that are total weighted completion time problems.
Journal ArticleDOI
A dual algorithm for the one-machine scheduling problem
TL;DR: An algorithm which solves the Lagrangian problem in a number of steps proportional to the product ofn2 and the average job processing time and an extremely sharp lower bound on the optimal objective value is presented.