Mathematical modelling and heuristic approaches to operation scheduling problems in an FMS environment

This paper addresses an operation scheduling problem with the objective of minimizing total tardiness in a flexible manufacturing system with setup time consideration. The addressed problem is first described as a 0?1 integer programming model, and is then solved optimally. Subsequently, a heuristic is proposed to solve the problem in an acceptable running time. The heuristic begins on a schedule generator called ESCH to obtain an initial solution; then two procedures are designed to improve the solution quality. One is a sequence-improving procedure (SIP) for determining a better performance schedule from a certain routing plan; the other is a routing-exchanging procedure (REP) for selecting a good routing plan. Both procedures are achieved by simulated annealing. Computational experiments show that the proposed simulated annealing based heuristic performs well with respect to solution accuracy and efficiency.     

An algorithm for sequencing jobs to minimize total tardiness

Abstract

A theoretical framework and an efficient algorithm are presented to solve the problem of sequencing jobs on a single processor. The objective achieved is minimum total tardiness. Jobs must be independent, with deterministic processing times. A brief review of the literature concerning sequencing to achieve minimum total tardiness is presented. This review shows that Emmons’ algorithm generally results in a partial schedule, and an enumerative method, branch and bound method or dynamic programming method, was then applied to help obtain a complete sequence. Thus Emmons’ algorithm is applied as a precursor to several enumerative algorithms. Furthermore, to certain problems (i.e., LPSD: jobs which have the property of a longer processing time but a shorter due date), Emmons’ theorems would not apply before branching the problems. The algorithm presented in this paper effectively applies the partitioning method to eliminate the need for enumerative methods. A set of necessary conditions for an optimal sequence is presented with proofs in the theory section. This is followed by a statement of the algorithm. The algorithm is illustrated with an example problem taken from Ref. [7]. Computational results are then presented which show the efficiency of the algorithm relative to dynamic programming.     

An efficient hybrid evolutionary heuristic using genetic algorithm and simulated annealing algorithm to solve machine loading problem in FMS

In this paper, a machine loading problem in a flexible manufacturing system (FMS) is discussed, with bi-criterion objectives of minimising system imbalance and maximising system throughput in the occurrence of technological constraints such as available machining time and tool slots. A mathematical model is used to select machines, assign operations and the required tools in order to minimise the system's imbalance while maximising the throughput. An efficient evolutionary algorithm by hybridising the genetic algorithm (GA) and simulated annealing (SA) algorithm called GASA is proposed in this paper. The performance of the GASA is tested by using 10 sample dataset and the results are compared with the heuristics reported in the literature. The influence of genetic operators on the evolutionary search in GASA is studied and reported. Two machine selection heuristics are proposed and their influence on the quality of the solution is also studied. Extensive computational experiments have been carried out to evaluate the performance of the proposed evolutionary heuristics and the results are presented in tables and figures. The results clearly support the better performance of GASA over the algorithms reported in the literature.     

A multi-level heuristic search algorithm for production scheduling

This paper introduces a multi-level heuristic search algorithm for identifying the optimal production schedule considering different levels of manufacturing requirements and constraints. The multi-level heuristic search algorithm generates search nodes at different levels. An upper level search node is composed of lower level search nodes, and evaluated based upon the evaluation of these lower level search nodes using a heuristic function. A production scheduling system was developed based upon the multi-level heuristic search algorithm. In this scheduling system, production requirements and constraints are represented at three different levels: task level, process level, and resource level. A task describes a manufacturing requirement. A process defines a method to achieve the goal of a task. A resource, such as a machine or a person, is a facility for accomplishing a required process. The multi-level heuristic search-based scheduling system was implemented using Smalltalk, an object-oriented programming language. Discussions on scheduling quality and efficiency are addressed at the end of this paper.     

Real-time production control of an FMS in a produce-to-order environment

This paper deals with real-time control of an FMS, operating in a produce-to-order environment, with machines subject to failure. A two-level production control system (PCS) is developed and examined. The proposed PCS incorporates three principles: no need for pre-planning procedures; separation between due-date and operational considerations; and full exploitation of process flexibility. In an extensive series of simulation experiments it was demonstrated that the proposed PCS leads to good results in both criteria: maximum throughput and minimum tardiness of orders. A comparison study between this PCS and one which is not based on separation between due-date and operational considerations, indicated the advantage of the former.     

A genetic algorithm for FMS part type selection and machine loading

Part type selection (PTS) and machine loading are two major problems in the production planning of flexible manufacturing systems. In this paper, we solve these problems by the use of genetic algorithms (GAs). We exploit the problem's MIP (mixed integer programming) model to make our GA more meaningful and less computation-intensive. The GA strategy is developed in three parts: solution coding, solution generation and solution recombination. In solution coding, we replace the original binary routing variables with integer variables and thus reduce the chromosome length significantly. In solution generation, the level of feasibility is the main concern. We divide the constraints into two categories: direct and indirect. The direct constraints involve only two variables each and are easily satisfied by context-dependent genes. Since the direct constraints form the major chunk of constraints, their satisfaction controls infeasibility to a large extent. The remaining indirect constraints are handled by the penalty function approach. The solution recombination involves crossover and mutation. The crossover is performed in two steps, the PTS swap followed by the routing swap, so that the feasibility level is not disturbed. With a similar intent, the mutation is allowed to operate only on selective genes. All the steps are illustrated with examples. Our GA is able to achieve optimum or near-optimum performance on a variety of objectives. A parametric study of GA factors is also carried out, indicating population size and mutation probability as influential parameters.     

Jobs and tool sequencing in an automated manufacturing environment

A practical approach is presented for determining the sequence of jobs and tools in the magazine that would be required to process the jobs in an automated manufacturing environment. Each job has to be completed before a given due date. The magazine has a limited capacity necessitating setups which increase the lead times, Processing jobs also requires an appropriate fixture. Setting up a fixture also contributes to the setup times. A heuristic procedure is developed which determines the above sequences while minimizing the total setup and processing times. The performance of the heuristic is checked against optimal solutions for small-size problems while bounds are obtained (based on statistical lower bounding procedures) on the optimal solution for large-size problems. Computational results are provided for 155 test problems.     

A heuristic based on Vogel's approximation method for sequencing mixed-model assembly lines

Sequencing mixed-model assembly lines is a well researched topic in the literature. However, many methods that have been developed to solve this problem fail to cope with either the large size or the specific characteristics of real-life problems. In this paper, a heuristic is proposed that is derived from Vogel's approximation method for transportation planning. The heuristic is able to handle large and supposedly difficult problem instances. Sophisticated test scenarios considering real-life aspects were generated to evaluate the performance of the heuristic for realistic problem instances. It is shown that the proposed heuristic significantly outperforms priority rule-based methods and requires only reasonable computational effort.     

A genetic algorithm based heuristic for adjacent paper-reel layout problem

In this paper, we present an algorithm that solves a paper reel layout problem where the available space is divided into equal-size cells. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A genetic algorithm is used in a two-stage iterative approach to solve the problem. Computational results seem to indicate the efficiency and effectiveness of the proposed solution method.     

Scheduling jobs in an Alcan aluminium foundry using a genetic algorithm

We present a genetic algorithm for the solution of an industrial scheduling problem in an Alcan aluminium foundry situated in Québec. We seek the best processing sequence for n orders on a m parallel machines. The set-up times are sequence dependent and we must deal with multiple criteria. There are also a number of structural constraints that distinguish this situation from the classical model. The performance of the solution approach is compared with the results of the scheduling process used by the firm according to three criteria: meeting due dates, number and duration of required set-ups and metal flow.     

A two-phase heuristic algorithm for determining buffer sizes of production lines

In-process inventories are often used in many manufacturing systems to smooth and balance work flow. The buffer design problem of determining the best size of storage space between operations (or workstations) is one that has been approached in past and current research issues. Although past research attempted to apply traditional optimization methods to the buffer design problems, the applications revealed that some fundamental drawbacks were occurring due to the unique characteristics of the buffer design in the production lines. This paper addresses the unique characteristics involved in the buffer design, discusses drawbacks of traditional optimization methods applied, and finally presents an efficient two-phase heuristic method using a dimension reduction strategy and a buffer utilization-based beam search method, fn addition, numerical results show sensitivity analyses for the performance of the heuristic method with respect to parameters involved in the second phase of the method.     

A genetic algorithm for sequencing type problems in engineering design

A genetic algorithm for engineering applications that involve sequencing of operations is proposed and demonstrated. Such applications are known as travelling salesman problems in operations research literature. The proposed algorithm uses some new operators that are different from those typically used in genetic algorithms. Some enhancements for improving performance of the algorithm are also described. Treatment of two salesmen in the problem is also discussed. Results for test problems, including a vehicle A-pillar subassembly welding sequence application, show performance of the proposed algorithm to be quite robust. © 1997 John Wiley & Sons, Ltd.     

Reactive scheduling in a dynamic and stochastic FMS environment

In this paper, we study the reactive scheduling problems in a dynamic and stochastic manufacturing environment. Specifically, we develop a simulation-based scheduling system for flexible manufacturing systems. We also propose several reactive scheduling policies (i.e. when-to-schedule and how-to-schedule policies) and test their performances under various experimental conditions, processing time variations, and machine breakdowns. Moreover, we compare offline and online scheduling schemes in a dynamic manufacturing environment. The results of extensive simulation experiments indicate that the variable-time-response is better than the fixed-time-response. The full scheduling scheme generally performs better than the partial scheduling. Finally, the online scheduling is more robust to uncertainty and variations in processing times than the optimum-seeking offline scheduling. A comprehensive bibliography is also provided in the paper.     

A sequencing problem in a batch/flow environment: an alternative approach

The paper describes the surface roughness measurement of spark erosion reference standards by means of digital technique, enabling a comprehensive assessment of roughness parameters. Using digital and Fourier analysis, parameters have been evaluated in terms of density and slope distribution, Abbott curve, power spectrum, auto-correlation functions, etc. The commonly used Ra, Rms and Rt have been calculated as per the ISO standard on the mean line (M) system. The effects of standard ISO-double RC and the suggested phase-corrected filters on the roughness parameters, waviness in particular, have also been discussed.     

A new heuristic algorithm for capacity planning in a manufacturing facility under learning

In this paper, a new and efficient heuristic algorithm is presented to determine the production capacity in a new facility under the effect of learning. Different demand patterns are studied while deciding the capacity requirements. Further, the learning effects due to human-machine interaction often found in a manufacturing system are considered during the development of the model. A computer program is developed and interfaced with XMP software on a Sun 3/60 workstation. Several numerical examples are presented to illustrate the heuristic algorithm.     

A heuristic algorithm for loading new work on circuit pack assembly lines

This paper describes a scheduling algorithm used to suggest the sequence in which new products should be started on circuit pack assembly lines. For a real application many aspects, such as inaccuracy of data, incomplete information, variability and unpredictability of many events, etc., make it very difficult to have a realistic model which is analytically tractable. The scheduling approach developed here is an effort to capture the right details and to leave an allowance for the aspects not represented in the model. It shifts the emphasis from optimization with’ idealistic models to a conservative approach with more realistic models. A combination of heuristics are used to achieve the objectives of meeting weekly due dates, of keeping W1P, flow time and number of set-ups low while maintaining capacity. Due dates are given the highest priority. Within the limitations imposed by due dates, a weighted, cumulative load imbalance measure is used to balance the load on all operations. Set-up considerations determine the choice if this measure is close to (say, within 15% of) the minimum. This provides a simple, robust and reasonably sound solution to an enormously difficult problem.     

网络环境下的存储技术与设备选择

介绍了网络环境下信息的三种网络存储技术,即直接连接存储(DAS)、网络连接存储(NAS)和存储局域网络(SAN),比较了它们的差别及适用环境,在此基础上提出了高校图书馆环境下网络存储设备的选择策略.     

A constructive algorithm and a simulated annealing approach for solving flowshop problems with missing operations

In many practical cases of flowshop environments and especially in flowline manufacturing cells, some or all jobs may not require processing on all machines. Hence, this paper focuses on the flowshop scheduling problem with missing operations. A modification of the constructive NPS-set heuristic is proposed, which generates non-permutation schedules effectively. Furthermore, a two-phase simulated annealing (SA) method is presented that specifically considers missing operations in its procedure. The modified NPS-set heuristic and the two-phase SA are tested and statistically evaluated by an extensive computational study for total flow time criteria. The results show that the modified NPS-set heuristic as well as the specific consideration of missing operations can enhance the algorithms’ performance significantly.     

Provident decision making by considering dynamic and fuzzy environment for FMS evaluation

When evaluating complexity, cost and risk increase, it is difficult to make a proper decision. In such situations it is necessary to develop a model which simulates a decision maker's mind and consider both a dynamic and a fuzzy environment. In this study future oriented indices are presented which enable us to consider the effect of future changes in the index value during the decision making process. These future oriented indices are named provident indices. Also in this study to effectively integrate these multiple criteria into the decision making process, based on the analysis of the decision situation in such assessments, a suitable concept is selected. This method is based on the preference ranking organisation method for enrichment evaluations (PROMETHEE) which brings together flexibility and simplicity for the user and is therefore chosen for the enhancement towards the evaluation of fuzzy data on preferences, scores and weights. The model developed to investigate these impacts cannot perfectly reproduce all the events of the real system, but it can consider a fair number of elements of variability, which should be identified and analysed by considering present conditions and prediction about criteria values in future periods. Such a model may provide solutions with a high degree of robustness and reliability, comparable with those obtained by direct experimentation, but with a low computational cost. The uniqueness of this paper lies in two important areas: first, the incorporation of variability fuzzy and provident measures in the performance of alternatives into the decision making process; and second, is in the application of fuzzy PROMETHEE that provides the decision maker with effective alternative choices by identifying significant differences among alternatives and appropriate choices through considered future periods, and presents graphic aids for better interpretation of results. A comprehensive numerical example of a flexible manufacturing system (FMS) is provided to illustrate the results of the analysis. In a real-world manufacturing environment, the dynamics of an FMS and its stochastic characteristics require a specific approach for evaluation. This paper specifically focuses on FMSs due to the complexities involved in their proper evaluation that include factors such as high operational and managerial expertise in system implementation phases, high costs and risks. Due to these, evaluation, justification, and implementation of an FMS have been areas of major concern and importance for practitioners and researchers. In this case, various strategic, economic and operational criteria that envelop quantitative, qualitative, tangible, and intangible factors are considered.     

A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs

This paper investigates a coordinated scheduling problem in a two stage supply chain where parallel-batching machine, deteriorating jobs and transportation coordination are considered simultaneously. During the production stage, jobs are processed by suppliers and there exists one parallel-batching machine in each supplier. The actual processing time of a job depends on its starting time and normal processing time. The normal processing time of a batch is equal to the largest normal processing time among all jobs in its batch. During the transportation stage, the jobs are then delivered to the manufacturer. Since suppliers are distributed in different locations, the transportation time between each supplier and the manufacturer is different. Based on some structural properties of the studied problem, an optimal algorithm for minimising makespan on a single supplier is presented. This supply chain scheduling problem is proved to be NP-hard, and a hybrid VNS-HS algorithm combining variable neighbourhood search (VNS) with harmony search (HS) is proposed to find a good solution in reasonable time. Finally, some computational experiments are conducted and the results demonstrate the effectiveness and efficiency of the proposed VNS-HS.