Chun-Yuan Cheng

Scheduling unrelated parallel machines to minimize total weighted tardiness

This paper addresses the batch scheduling problem of unrelated parallel machines attempting to minimize the total weighted tardiness. Identical or similar jobs are typically processed in batches to decrease setup and/or processing times. Local dispatching rules such as the earliest weighted due date, the shortest weighted processing time, and the earliest weighted due date with a process utilization spread are tailored to the batch scheduling requirements. Based on the features of batch scheduling, a two-level batch scheduling framework is suggested. Existing heuristics, which show excellent performance in terms of total weighted tardiness for the single machine scheduling, such as the modified earliest due date rule and the modified cost over time rule, are extended for the problem. The simulated annealing algorithm as a meta-heuristic is also presented to obtain near optimal solutions. The proposed heuristics are compared through computational experiments with data from the dicing process of a compound semiconductor manufacturing facility

Scheduling two-machine no-wait open shops to minimize makespan

This paper examines the problem of scheduling two-machine no-wait open shops to minimize makespan. The problem is known to be strongly NP-hard. An exact algorithm, based on a branch-and-bound scheme, is developed to optimally solve medium-size problems. A number of dominance rules are proposed to improve the search efficiency of the branch-and-bound algorithm. An efficient two-phase heuristic algorithm is presented for solving large-size problems. Computational results show that the branch-and-bound algorithm can solve problems with up to 100 jobs within a reasonable amount of time. For large-size problems, the solution obtained by the heuristic algorithm has an average percentage deviation of 0.24% from a lower bound value.

The total completion time open shop scheduling problem with a given sequence of jobs on one machine

This paper addresses the open shop scheduling problem to minimize the total completion time, provided that one of the machines has to process the jobs in a given sequence. The problem is NP-hard in the strong sense even for the two-machine case. A lower bound is derived based on the optimal solution of a relaxed problem in which the operations on every machine may overlap except for the machine with a given sequence of jobs. This relaxed problem is NP-hard in the ordinary sense, however it can be quickly solved via a decomposition into subset-sum problems. Both heuristic and branch-and-bound algorithm are proposed. Experimental results show that the heuristic is efficient for solving large-scaled problems, and the branch-and-bound algorithm performs well on small-scaled problems.

The optimal periodic preventive maintenance policy with degradation rate reduction under reliability limit

Preventive maintenance (PM) can slow the deterioration process of a repairable system and restore the system to a younger age or state. Many researchers focus on studying PM models for the cases of age or failure rate reduction and developing optimal PM policies. However, the PM actions, such as cleaning, adjustment, alignment, and lubrication work, may not always reduce systems age or failure rate. Instead, it may only reduce the degradation rate of the system to a certain level. Furthermore, most of the existing optimal PM policies result in very low reliability at the time of preventive replacement (PR). In practice, however, high reliability is usually required for a system to avoid failures being occurred. This paper is to develop an optimal periodic PM policy over an infinite time span by minimizing the expected cost rate with the consideration of reliability limit (Rmin,) for Weibull-failure-time systems with degradation rate reduction after each PM. The proposed optimal periodic PM policy consists of two PM models. One model has fully periodic PM time-interval for every preventive replacement cycle; the other model has partially periodic PM time-interval where the time interval between the final PM and the PR is not a constant. For specified reliability limit, the proper model is chosen by using the algorithm provided in this paper. Examples are demonstrated and the sensitivity analysis is also presented for the proposed PM models.

A Failure-rate-reduction Periodic Preventive Maintenance Model with Delayed Initial Time in a Finite Time Period

Abstract HeA new machine will not fail easily in the early stage of its useful life. This phenomenon is consistent with the fact that the optimal sequential preventive maintenance (PM) policy which has longer PM intervals in its earlier stage of lifetime. In this paper, we propose a failure-rate-reduction periodic PM model with delayed initial time in a finite time span. Then, the optimal periodic PM policy is developed by minimizing the expected total maintenance cost, which can have smaller expected total maintenance cost than the optimal policy of the original failure-rate-reduction periodic PM model. The algorithm of finding the optimal PM policy for the proposed PM model is developed. Finally, examples are illustrated to verify the optimal policies of the proposed new PM model.

The finite-time-period preventive maintenance policies with failure rate reduction under a warranty consideration

In practice, a system or equipment has a finite useful life. When an aged system is replaced by a new system, the new system seldom has exactly the same characteristics, functions, investment cost, maintenance expenses, etc., as those of the aged system. However, the literature has shown that most researchers are devoted to studying maintenance problems in an infinite time span, which assumes that the replaced system in each replacement cycle (or period) has the same conditions and costs. Apparently, the assumption might not be practical, since the useful operating life of most systems is finite in the real world. Therefore, the purpose of this research is to develop an optimal preventive maintenance (PM) policy having failure rate reduction within a finite time span under a warranty consideration by minimizing the expected total maintenance cost. The PM cost is assumed to be a linear function of each PM effect. Two cases are studied and compared; one is with no warranty provided and the other is with a given warranty period. For the second case, we examine two policies: (1) no PM within the warranty period is assumed and (2) the PM will be performed within the warranty period. In this article, the algorithm for searching the optimal solution is presented. Examples with Weibull failure cases are given and the sensitivity analysis of the optimal solution is also provided.

THE PERIODIC MAINTENANCE POLICY FOR A WEIBULL LIFE-TIME SYSTEM WITH DEGRADATION RATE REDUCTION UNDER RELIABILITY LIMIT

From the literature, it is known that preventive maintenance (PM) can reduce the deterioration of system or equipment to a younger level. Researchers usually develop optimal PM policies based on the assumption that the PM can reduce systems age or failure rate. However, the PM actions, such as cleaning, adjustment, alignment, and lubrication work, may not always reduce systems age or failure rate. Instead, it may only reduce the degradation rate of the system to a certain level. In addition, most of the existing optimal PM policies are developed by minimizing the expected cost rate only. Yet, as demonstrated in this paper, the system will have very low reliability at the time of preventive replacement if the reliability limit is not considered.Hence, this paper is to develop an optimal periodic PM model by minimizing the expected cost rate per unit time with the consideration of reliability limit for repairable systems with degradation rate reduction after each PM. The improvement factor method is used to measure the reduction effect of the degradation rate. The algorithm for searching the optimal solutions for this PM model is developed. Examples are also presented with discussions of parameter sensitivity and special cases.

Roundness measurement using the PSO algorithm

Measuring the roundness of a circular workpiece is a crucial issue of quality control and inspection in industry. In this area, maximum inscribed circle (MIC) and Maximum circumscribing circle (MCC), Minimum zone circle (MZC) and Least Square Circle (LSC) are four commonly used methods. In particular, MIC, MCC, and MZC, which are non-linear constrained optimization problems, have not been thoroughly discussed lately. This study proposes a roundness measuring method that applies the Particle Swarm Optimization Algorithm (PSO) to compute MIC, MCC and MZC. To facilitate the PSO process, five different PSO methods are encoded using a radius (R) and circle center (x, y) and extensively evaluated using an experimental design, in which the impact of inertia weight, maximum velocity and the number of particles on the performance of the particle swarm optimizer is analyzed. The proposed method is verified with a set of testing images and benchmarked with the GA-based (Genetic Algorithm) method (Chen, 2000). The experimental results reveal that the PSO-based method effectively solved the MIC, MCC, and MZC problems and outperforms GA-based method in both accuracy and the efficiency. As a result, several industrial applications are presented to explore the effectiveness and efficiency of the proposed method.

The degradation-rate-reduction preventive maintenance policies with warranty in a finite time span

A system normally has a finite useful life. The new system in each replacement cycle seldom has exactly the same characteristics and properties. However, maintenance problems are usually defined over the infinite time span where the system is assumed to have the same conditions and costs in each replacement cycle. This assumption might not be practical. Therefore, the purpose of this research is to develop the optimal preventive maintenance (PM) policies with degradation rate reduction over a finite time span under a warranty consideration by minimizing the expected total maintenance cost. Two cases are studied and compared, one is no warranty provided and the other is with a given warranty period. For the second case, two policies, performing and not performing PM within the warranty period, are examined. In this paper, the algorithm for searching the optimal solution is presented. Examples are given and the sensitivity analysis is also provided.

Sensitivity analysis for the optimal minimal repair/replacement policies under the framework of markov decision process

For the maintenance and replacement of system subject to stochastic deterioration, flexibility is an important consideration factor. Different possible maintenance policies are discussed in this paper where the failure distribution modeled by the Weibull distribution. The total discounted cost concept is very important in decision making for the complex system such as expensive capital equipment with operating life cycle lasting for years. A modified maintenance model is proposed with incorporating the costs of operating cost, the maintenance cost of minimal repairs, failure replacements and preventive replacements. We investigate the maintenance policies by modeling the deteriorating process of a system as a Markov decision process. Under the discounted cost criterion, the optimal parameters for the control limit policy are obtained. The sensitivity analysis of these control limits is performed for the flexibility of decision making. The optimal equations of the Markov decision process are solved by using the backward recursive scheme over a set of finite planning horizons to approximate the optimal policies for the infinite planning horizons.