Author: Yeung, Wing-kwan
Title: Two-stage flow-shop scheduling with due windows to minimize earliness/tardiness penalties
Degree: Ph.D.
Year: 2004
Subject: Hong Kong Polytechnic University -- Dissertations
Production scheduling
Department: Department of Logistics
Pages: ix, 168 leaves ; 30 cm
Language: English
Abstract: The main objectives of this thesis is to investigate two-stage flow-shop machine scheduling problems involving a common due window and distinct due windows. The measures of performance under study are minimizing the earliness and tardiness, and minimizing the number of early and tardy jobs. The size of the due window is a given parameter, and the window location can either be a given parameter or a decision variable with the window location penalty in the problems. The proportionate flow-shop machine scheduling, where the processing time of each operation on the machine is the same, is also considered in this thesis. The regular measure of performance such as minimizing makespan, flowtime and total tardiness cannot meet the requirement of many practical and naturally existing problems in the real world nowadays. The just-in-time philosophy that was developed in late 80s increases the importance of non-regular performance measures involving both earliness and tardiness penalties. Incorporating due windows into such problems captures another dimension of these real world problems. Furthermore, there appear a limited number of due window single machine scheduling problems, several common due window parallel machine scheduling problems, and one common due date earliness and tardiness two-stage flow-shop machine scheduling problem in the literature. Still worse, no algorithms are available for the due window scheduling problems if the number of machines staged in series is more than one. The reason for the lack of these algorithms in the literature may be attributed to the notorious intractable hardness of the problems. Nevertheless, the two-stage flow-shop scheduling problems involving the due window has many practical applications in the real world and there is a serious need for the studies of the two-stage flow-shop machine scheduling problems involving the due window. So, five worthy study of the two-stage flow-shop scheduling problems involving the due window under different scheduling environments are proposed in Chapters 3-7 of this thesis. In Chapter 3, the proportionate flow-shop problem of minimizing the weighted earliness and tardiness is studied, where the processing time of a job at each stage is the same, and the window location is a given parameter. The new important result that the permutation schedule for the general two-stage flow-shop problem provides an optimal schedule is proved. It reduces the search space for the problem significantly, and will also attract future researchers to do investigation on the non-regular measure of performance in flow-shop scheduling problems. Moreover, an incorrect result in Weng and Ventura's (1996) pseudo-polynomial dynamic programming algorithm is shown and their algorithm is modified and improved. This revised algorithm is incorporated in a solution procedure for the problem. Based on the derived dominance properties, theorems, decomposition of the problem into subproblems, reduction and elimination rules, a novel effective and fast hybrid pseudo-polynomial dynamic programming algorithm HDP is developed, which considerably reduce the CPU time and memory requirement. In particular, the Backward Approach of HDP outperforms the Forward Approach in terms of requiring less memory space and CPU time significantly. Furthermore, the problem is proved to be NP-complete in the ordinary sense. In Chapter 4, the problem to minimize the earliness and tardiness under the environment of a common due window together with the given window location is investigated. The result proves that the problem is NP-complete in the strong sense. A heuristic and a branch and bound algorithm are developed to solve the problem. Computational experiments are then conducted to test the performances of the algorithms. A strong lower bound is derived for the branch and bound algorithm that can efficiently solve 15 jobs in about 5 minutes. The heuristic is shown to be efficient and effective, which can solve the problem of 150 jobs in about 20 seconds and provide near-optimal solution. The heuristic is justified to be an excellent solution approach for large problem instances. Four special cases are shown to be either polynomially solvable or NP-complete in the ordinary sense. In Chapter 5, the two common due window scheduling problems to minimize the weighted number of early and tardy jobs in a two-stage flow-shop are presented. The window location is either a given parameter considered in the first problem, or a decision variable along with its location penalty in the other problem. The NP-completeness proofs are derived to determine the complexities of these problems. The important dominance properties, elimination rules, and theorems including the new extended, reversed, and extended reversed Johnson's (1954) rules, are developed to successfully overcome the inherently intractable hardness of the problems. The effective and efficient Backward Approaches of the pseudo-polynomial dynamic programming algorithms are also developed to minimize not only the objective functions of the problems, but also the associated memory space and CPU time needed. In tackling the second problem, the novel elimination rules, the lower bound on the total penalty and upper bounds on the window location are incorporated in the pseudo-polynomial dynamic programming algorithm to diminish the search space. Two special cases in which the earliness is equally important as or more than the tardiness are solved in lower time complexities. The next two chapters address minimizing the weighted number of early and tardy jobs. In Chapter 6, this problem is considered in a proportionate flow-shop environment and it is proved to be NP-complete in the ordinary sense. In Chapter 7, distinct due windows are considered for this problem in a regular flow-shop environment. The due windows may overlap one another and their window locations are given parameters. The problem is shown to be NP-complete in the strong sense. Two special cases of the problem are proved to be NP-complete in the ordinary sense and polynomially solvable. The main contributions of this thesis are to (1) bring the importance and significance of the unexplored but important area of due window machine scheduling problems existing in the real world to practitioners and researchers, (2) determine the complexities, and develop new and important dominance properties and theorems, and novel effective and efficient solution methodologies for the proposed common and multiple due window two-stage flow-shop scheduling problems, and (3) provide insights serving as a basis for future research on the due window scheduling problems.
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Access: restricted access

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