Markovian queueing systems with retrials and heterogeneous servers

The asymptotic performances of a random access and an ordered entry G/M/K/Oqueueing system with a stationary counting arrival process, K heterogeneous parallel servers, no waiting room and retrials are approximated based on a two-parameter method. In a random access system, units upon arrival are randomly assigned to one of the servers. In an ordered entry system, servers are indexed from 1 to K, and units first arrive at server i and if the server is found to be busy, those units arrive at server (i + 1), for i = 1 to K − 1. In both queueing systems, if units are not processed by one of the servers, those units are not lost, instead they retry to receive service by merging with the incoming arrival units.

To approximate the asymptotic performance of the above queueing systems, a recursive algorithm is suggested, and appropriate performance measures are presented to be used as comparison criteria at the design stage. Furthermore, numerical results are provided and approximation outcomes are compared against those from a simulation study.     

Effect of reworking on defective parts in a flexible assembly cell

Consider a flexible assembly cell, consisting of a set of general-purpose machines, a finite-capacity local storage, a loading station, an unloading station and an integrated automated inspection station, where workpieces are processed according to the first-come, first-served dispatching rule, and the inspection station is capable of detecting (i) non- repairable defective, (ii) repairable defective and (iii) non-defective workpieces. This workstation is capable of processing workpieces belonging to the same family of parts, and is also capable of reprocessing the inspected defective repairable workpieces. In this paper, the performance of the workstation is modelled by anM/G/1/K queueing system with a Poisson arrival process, a buffer of sizeK, a single server, generally distributed processing time, the first-come, first-served queueing discipline and an instantaneous Bernoulli feedback mechanism. This performance model is developed to define the relationships among the loading, the processing, the inspection and the unloading operations. Finally, to be able to study the tandem behaviour of this workstation in an assembly-line manufacturing environment, the throughput process from the workstation is also identified.     

An optimal concurrent design and loading strategy for a flexible assembly line system: to control the bottleneck

In this paper, an optimal strategy is presented at the design stage for selection of the required local storages of the workstations and the transporter stations of a finite capacity flexible assembly line system, such that the throughput rate from the system is maximised while controlling the bottleneck problem. For this purpose, a mixed non-Markovian queueing network model is presented to model its performance, a stochastic optimisation model is provided to maximise its throughput rate, and a heuristic algorithm is developed for solving it. Finally, an example is presented and the approximation results are compared against those from a simulation study.     

Loading strategies for a class of just-in-time manufacturing system

In this paper, based on the group technology and the just-in-time manufacturing concepts, two loading models for optimal utilisation of the processing capabilities of an integrated manufacturing system consisting of a set of heterogeneous workstations are developed. These loading models are developed to integrate and utilise the available information from both the bill of materials and the process plans. The objective functions for these models are: the maximum tardiness and the makespan. In these models, the production quantity of each customer order for any part or product always equals its corresponding demand quantity; each part requires a finite number of aggregated stages of operation; job splitting is allowed; and the processing priorities of all the jobs during the planning time horizon are specified based on a desirable dispatching rule. The proposed mathematical programming models are fixed charge problems which are solved by compatible mixed integer programming algorithms. Finally, to provide additional decision-making capabilities, based on these models and their corresponding solution algorithms, a compatible decision support system is suggested.Notation l(1 toL) the product index - t(1 toN) the component (e.g., job type) index - i(1 toN) the job type priority index - j(1 toM) the workstation index - r(1 toR) the processing stage priority index - k(1 toK) the due date priority index - J _i,j,r,k the job with the job type priority indexi of the customer with the processing stage priority indexr and the due date priority indexk which has to be processed at the workstationj - L _i,r,k the number of units of the job with the job type priority indexi of the customer with processing stage priority indexr and the due date priority indexk (e.g. demand quantities) - t _i,j,r the required time to perform the processing stage priority indexr of each unit of the job with the job type priority indexi at the workstationj - D _i,r,k the due date of the job with the job type priority indexi of the customer with the processing stage priority indexr and the due date priority indexk - s _i,j,r the required time for setting up the workstationj for processing the job with the processing stage priority indexr, and the job type priority indexi - X _i,j,r,k the number of units of the job with job type priority indexi of the customer with the processing stage priority indexr, and the due date priority indexk to be produced at the workstationj - l _i,j,r,k the idle time at the workstationj prior to processing the job with the job type priority indexi and the processing stage priority indexr with the due date priority indexk - V the maximum tardiness - W the makespan of the operation - Y _i,j,r,k=1 ifX _i,j,r,k>0 - Y _i,j,r,k=0 ifX _i,j,r,k=0 - _i,j,r,k a sufficiently large constant (e.g. _i,j,r,kL _i,r,k)