A constructive heuristic for total flowtime minimization in a no-wait flowshop with sequence-dependent setup times

In this paper, we addressed the problem of scheduling jobs in a no-wait flow shop with sequence-dependent setup times with the objective of minimizing the total flow time. As this problem is well-known for being NP-hard, we present a new constructive heuristic, named QUARTS, in order to obtain good approximate solutions in a short CPU time. QUARTS breaks the problem in quartets in order to minimize the total flow time. The method was tested with other literature methods: BAH and BIH by Bianco et al. (1999) [6], TRIPS, by Brown et al. (2004) [7] and the metaheuristic Iterated Greedy with Local Search proposed by Ruiz and Stützle (2007) [25]. The computational results showed that IG_LS obtained the best results and QUARTS presented the best performance regarding other constructive heuristics.     

Evaluating the effectiveness of FDM in identifying important factors in a dynamic flowshop

Dynamic events such as machine breakdown and hot jobs may induce problems on the production system such as order delay, increasing machine load, and changing inventory level. Past studies of dynamic events often use traditional design of experiments (DOE) to analyze the effects of dynamic events on system's performance. The shortcoming of this approach is that the number of experimental runs conducted would become exponentially increased as the number of factors increased. This study tries to use frequency domain methodology (FDM) instead so as to detect the higher order effects and rank important factors in a few experimental runs. Spectrum analysis is used to comprehend the effects of different location of machine breakdown and different size of hot jobs on the system's performance of flowshops with different traffic (utilization) and stability (oscillation). This study finds that the important factors identified by the FDM analysis are the same as that of DOE. However, only in some cases can the rankings of important factors be the same for both approaches. The dissimilarity between rankings of important factors found by these two methods is further measured using Kendall tau distance.     

Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.     

A remark on the subsequence problem for arc-annotated sequences with pairwise nested arcs

The Arc-Preserving Subsequence (APS) problem appears in the comparison of RNA structures in computational biology. Given two arc-annotated sequences of length n and m<n, APS asks if the shorter sequence can be obtained from the longer one by deleting certain elements along with their incident arcs. It is known that APS with pairwise nested arcs can be solved in O(mn) time. We give an algorithm running in O(m²+n) time in the worst case, actually it is even faster in particular if the shorter sequence has many arcs. The result may serve as a building block for improved APS algorithms in the general case.     

Minimizing the total completion time in a distributed two stage assembly system with setup times

In this paper, a novel distributed two stage assembly flowshop scheduling problem (DTSAFSP) is addressed. The objective is to assign jobs to several factories and schedule the jobs in each factory with the minimum total completion time (TCT). In view of the NP-hardness of the DTSAFSP, we develop heuristics method to deal with the problem and propose three hybrid meta-heuristics (HVNS, HGA-RVNS, and HDDE-RVNS). The parameters of HGA-RVNS and HDDE-RVNS are tuned by using the Taguchi method and that of HVNS is done by using the single factor ANOVA method. Computational experiments have been conducted to compare the performances of the proposed algorithms. The analyses of computational results show that, for the instances with small numbers of jobs, HDDE-RVNS obtains better performances than HGA-RVNS and HVNS; whereas for the instances with large numbers of jobs, HGA-RVNS is the best one in all the proposed algorithms. Computational results indicate that the performances of the HDDE-RVNS and HGA-RVNS are not much affected by the number of machines at the first stage and factories. The experimental results also show that the RVNS-based local search steps in both HGA-RVNS and HDDE-RVNS are efficient and effective.     

Minimizing total weighted completion time when scheduling orders in a flexible environment with uniform machines

We consider the scheduling of orders in an environment with m uniform machines in parallel. Each order requests certain amounts of k different product types. Each product type can be produced by any one of the m machines. No setup is required if a machine switches over from one product type to another. Different product types intended for the same order can be produced at the same time (concurrently) on different machines. Each order is released at time zero and has a positive weight. Preemptions are allowed. The completion time of an order is the finish time of the product type that is completed last for that order. The objective is to minimize the total weighted completion time. We propose heuristics for the non-preemptive as well as the preemptive case and obtain worst case bounds that are a function of the number of machines as well as the differences in the speeds of the machines. Even though the worst-case bounds we showed for the two heuristics are not very tight, our experimental results show that they yield solutions that are very close to optimal.