In this paper we consider the problem of scheduling n non-preemptive jobs on m identical machines with availability and eligibility constraints for minimizing the maximum lateness. That is, each machine is not continuously available at all time and each job is only allows to be processed on specified machines. Each availability interval of machines has a specific service level, and each job has to be processed at availability intervals with the service level specified or higher one.
We develop a branch-and-bound algorithm to solve this scheduling problem optimally. Firstly, we propose an algorithm based on the Least Flexible Job First/ Earliest Due Date First (LFJ/EDD) rule to find the upper bound. Network flow technique is used to model the scheduling problem of the preemptive jobs into a series of base problem that is equivalent to a maximum flow problem. Then, we propose a polynomial time algorithm that combines a maximum flow algorithm and binary search procedure to solve this scheduling problem optimally and use this result as our lower bound.
Computational experiments are proposed to compare the validity with complete branching method and to test the efficiency of proposed branch and bound algorithm. According to the result of computational experiment, we find that the run time of our algorithm is acceptable.

Table of Content


Abstract i
Table of Content ii
List of Tables iv
List of Figures v

Chapter 1 Introduction 1

1.1 Background and Motivation 1
1.2 Problem Description 4
1.3 Research Objectives 5
1.4 Research Methodology and Framework 5
1.4.1 Research Methodology 5
1.4.2 Research Framework 6

Chapter 2 Literature Review 8

2.1 Machine Availability Constraint 8
2.2 Machine Eligibility Constraint 12

Chapter 3 Branch and Bound Algorithm 15

3.1 Notation 15
3.2 Bounding Scheme 17
3.2.1 Upper Bound 18
3.2.2 Lower Bound 22
3.3 Branching Scheme 42
3.3.1 Node Representation 42
3.3.2 The branching process 42
3.3.3 The Proposed Branch and Bound Algorithm for the Problem 45

Chapter 4 Computational Analysis 48

4.1 Test Generation 48
4.2 Validation of the Branch and Bound Algorithm 49
4.3 Evaluation of the Branch and Bound Algorithm 50
4.3.1 Comparing with complete branching method 51
4.3.2 The Performance of the Branch and Bound Algorithm 53

Chapter 5 Conclusion 57
5.1 Research Contribution 57
5.2 Limitation Research 58
5.3 Further Research 58

References 59

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