On merging sequencing and scheduling theory with genetic algorithms to solve stochastic job shops.

The stochastic job shop problem was solved using two genetic algorithms. The first was a stochastic constrained genetic algorithm to minimize total tardiness and to evaluate chromosomes using probability Gantt charting. The second was a stochastic constrained genetic algorithm to minimize total tardiness and to evaluate chromosomes using simulation. In these two algorithms, the fitness function was altered to a utility function defined as follows: Probability $\{$total tardiness of a chromosome $\le$ target total tardiness$\}.$ When comparing the two chromosome evaluation methods, the probability Gantt charting deviated from the true mean for both the makespan and the average flow time by 3% and 1.7% respectively. Also, all averages estimated for both the makespan and the average flow time fall within the 90% confidence interval. Furthermore, using probability Gantt charting reduced the CPU time needed by 554.9% when compared to the CPU time needed by simulation. When the results obtained by the two stochastic constrained genetic algorithms were compared, the second algorithm reduced the actual expected total tardiness, the actual worse case total tardiness, and the risk by 30.3%, 56%, and 18% respectively.The standard genetic algorithm has been modified to address the job shop problem by constraining the genes in the chromosomes during the genetic operators implementations to match general theoretical sequencing constraints.When comparing the deterministic constrained and unconstrained genetic algorithms to minimize makespan, the constrained algorithm improved the average percentage error by 27.44%. Also, when the deterministic constrained and unconstrained genetic algorithms to minimize total tardiness were compared, the constrained algorithm improved the average percentage errors by 248.77%

Efficient heuristics for the parallel blocking flow shop scheduling problem

We consider the NP-hard problem of scheduling n jobs in F identical parallel flow shops, each consisting of a series of m machines, and doing so with a blocking constraint. The applied criterion is to minimize the makespan, i.e., the maximum completion time of all the jobs in F flow shops (lines). The Parallel Flow Shop Scheduling Problem (PFSP) is conceptually similar to another problem known in the literature as the Distributed Permutation Flow Shop Scheduling Problem (DPFSP), which allows modeling the scheduling process in companies with more than one factory, each factory with a flow shop configuration. Therefore, the proposed methods can solve the scheduling problem under the blocking constraint in both situations, which, to the best of our knowledge, has not been studied previously. In this paper, we propose a mathematical model along with some constructive and improvement heuristics to solve the parallel blocking flow shop problem (PBFSP) and thus minimize the maximum completion time among lines. The proposed constructive procedures use two approaches that are totally different from those proposed in the literature. These methods are used as initial solution procedures of an iterated local search (ILS) and an iterated greedy algorithm (IGA), both of which are combined with a variable neighborhood search (VNS). The proposed constructive procedure and the improved methods take into account the characteristics of the problem. The computational evaluation demonstrates that both of them –especially the IGA– perform considerably better than those algorithms adapted from the DPFSP literature.Peer ReviewedPostprint (author's final draft

Heuristics for the distributed blocking Ffow shop scheduling problem

Postprint (published version

Selected heuristic algorithms for solving job shop and flow shop scheduling problems

Importance of job shop and flow shop scheduling has increased to a high extent. Nowadays, each and every industry focuses largely on how to schedule their machine working, since it is an important factor which decides the net productivity. All manufacturing systems including flexible manufacturing system follow a planned schedule of machine operation depending on the demand criterion. With the increase in number of machines and jobs to be scheduled, complexity of the problem increases which demands the need of a proper scheduling technique. Here this thesis shows some of the essential methods of solving a job shop and flow shop scheduling problems. This thesis focuses on finding the most efficient way of scheduling in a flow shop environment with the help of heuristics algorithms that include Palmer’s algorithm, CDS algorithm and NEH algorithm. Comparison was also done between the various heuristics algorithms. For getting the optimum make span for job shop scheduling we have used branch and bound algorithm and shifting bottleneck algorithm. Basis input parameters are given in the problem which are then used for computing the make span. A C programming code was generated to find the optimum results of the scheduling problem

NEH-based heuristics for the permutation flowshop scheduling problem to minimize total tardiness

Since Johnson׳s seminal paper in 1954, scheduling jobs in a permutation flowshop has been receiving the attention of hundreds of practitioners and researchers, being one of the most studied topics in the Operations Research literature. Among the different objectives that can be considered, minimising the total tardiness (i.e. the sum of the surplus of the completion time of each job over its due date) is regarded as a key objective for manufacturing companies, as it entails the fulfilment of the due dates committed to customers. Since this problem is known to be NP-hard, most research has focused on proposing approximate procedures to solve it in reasonable computation times. Particularly, several constructive heuristics have been proposed, with NEHedd being the most efficient one, serving also to provide an initial solution for more elaborate approximate procedures. In this paper, we first analyse in detail the decision problem depending on the generation of the due dates of the jobs, and discuss the similarities with different related decision problems. In addition, for the most characteristic tardiness scenario, the analysis shows that a huge number of ties appear during the construction of the solutions done by the NEHedd heuristic, and that wisely breaking the ties greatly influences the quality of the final solution. Since no tie-breaking mechanism has been designed for this heuristic up to now, we propose several mechanisms that are exhaustively tested. The results show that some of them outperform the original NEHedd by about 25% while keeping the same computational requirements.Ministerio de Ciencia e Innovación DPI2010-15573/DPIMinisterio de Ciencia e Innovación DPI2013-44461-P/DP

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Efficient constructive procedures for the distributed blocking flowshop scheduling problem

the distributed blocking flow shop scheduling problem (DBFSP) allows modeling of the scheduling process in companies with more than one factory, with productive systems configured as flow shop lines where the blocking constraint has to be considered. To the best of our knowledge, this variant of the distributed permutation flow shop scheduling problem has not been studied. In this paper, we propose some constructive heuristics that will solve the DBFSP and thus minimize the maximum completion time among the factories. The proposed procedures use two approaches that are totally different from those proposed for the distributed permutation flow shop scheduling problem (DPFSP). By taking the DPFSP procedures that we adapted to DBFSP and comparing them to the new approaches that were specifically designed for DBPFSP, we find that the latter perform considerably better.Postprint (published version

Integrated Batching and Lot Streaming with Variable Sublots and Sequence-Dependent Setups in a Two-Stage Hybrid Flow Shop

Consider a paint manufacturing firm whose customers typically place orders for two or more products simultaneously: liquid primer, top coat paint, and/or undercoat paint. Each product belongs to an associated product family that can be batched together during the manufacturing process. Meanwhile, each product can be split into several sublots so that overlapping production is possible in a two-stage hybrid flow shop. Various numbers of identical capacitated machines operate in parallel at each stage. We present a mixed-integer programming (MIP) to analyze this novel integrated batching and lot streaming problem with variable sublots, incompatible job families, and sequence-dependent setup times. The model determines the number of sublots for each product, the size of each sublot, and the production sequencing for each sublot such that the sum of weighted completion time is minimized. Several numerical example problems are presented to validate the proposed formulation and to compare results with similar problems in the literature. Furthermore, an experimental design based on real industrial data is used to evaluate the performance of proposed model. Results indicate that the computational cost of solving the model is high

Models and Strategies for Variants of the Job Shop Scheduling Problem

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia : Italy (2011