R. Buitenhek

Capacity planning and lead time management

In this paper we discuss a framework for capacity planning and lead time management in manufacturing companies, with an emphasis on the machine shop. First we show how queueing models can be used to find approximations of the mean and the variance of manufacturing shop lead times. These quantities often serve as a basis to set a fixed planned lead time in an MRP-controlled environment. A major drawback of a fixed planned lead time is the ignorance of the correlation between actual work loads and the lead times that can be realized under a limited capacity flexibility. To overcome this problem, we develop a method that determines the earliest possible completion time of any arriving job, without sacrificing the delivery performance of any other job in the shop. This earliest completion time is then taken to be the delivery date and thereby determines a workload-dependent planned lead time. We compare this capacity planning procedure with a fixed planned lead time approach (as in MRP), with a procedure in which lead times are estimated based on the amount of work in the shop, and with a workload-oriented release procedure. Numerical experiments so far show an excellent performance of the capacity planning procedure.

Production capacity of flexible manufacturing systems with fixed production ratios

Determining the production capacity of flexible manufacturing systems is a very important issue in the design of such systems. We propose an approach for determining the production capacity (i.e., the maximum production rate) of a flexible manufacturing system with several part types, dedicated pallets, and fixed production ratios among the different part types. We show that the problem reduces to the determination of a single parameter for which we propose an iterative procedure. Simulation or approximate analytical techniques can be used as the building block performance evaluation technique in the iterative procedure.

AMVA‐based solution procedures for open queueing networks with population constraints

We propose a new method for the performance evaluation of Open Queueing Networks with a Population Constraint (represented by a set of tokens). The method is based on the application of Approximate Mean Value Analysis (AMVA) algorithms. We present procedures for single class networks and for multiple class networks, subject to either a common constraint (shared tokens) or to class‐based constraints (dedicated tokens). In fact, the new method is a unified framework into which all procedures for the different types of networks fit. We show how the new method relates to well‐known methods and present some numerical results to indicate its accuracy.

Capacity analysis of an automated kit transportation system

In this paper, we present a capacity analysis of an automated transportation system in a flexible assembly factory. The transportation system, together with the workstations, is modeled as a network of queues with multiple job classes. Due to its complex nature, the steady‐state behavior of this network is not described by a product‐form solution. Therefore, we present an approximate method to determine the capacity of the network. We first study a number of key elements of the system separately and subsequently combine the results of this analysis in an Approximate Mean Value Analysis (AMVA) algorithm. The key elements are a buffer/transfer system (the bottleneck of the system), modeled as a preemptive‐repeat priority queue with identical deterministic service times for the different job classes, a set of elevators, modeled as vacation servers, a number of work cells, modeled as multi‐server queues, and several non‐accumulating conveyor belts, modeled as ample servers. The AMVA algorithm exploits the property that the initial multi‐class queueing network can be decomposed into a sequence of single‐class queueing networks and hence is very efficient. Comparison of numerical results of the AMVA algorithm for the throughputs for the different job classes to simulation results shows that the AMVA algorithm is also accurate. For several series of instances, the maximum relative error that we found was only 4.0%.

On First-Come First-Served Versus Random Service Discipline in Multiclass Closed Queueing Networks

We consider multiclass closed queueing networks. For these networks, a lot of work has been devoted to characterizing and weakening the conditions under which a product-form solution is obtained for the steady-state distribution. From this work, it is known that, under certain conditions, all networks in which each of the stations has either the first-come first-served or the random service discipline lead to the same (product-form expressions for the) steady-state probabilities of the (aggregated) states that for each station and each job class denote the number of jobs in service and the number of jobs in the queue. As a consequence, all these situations also lead to the same throughputs for the different job classes. One of the conditions under which these equivalence results hold states that at each station all job classes must have the same exponential service time distribution. In this paper, it is shown that these equivalence results can be extended to the case with different exponential service times for jobs of different classes, if the network consists of only one single-server or multiserver station. This extension can be made despite of the fact that the network is not a product-form network anymore in that case. The proof is based on the reversibility of the Markov process that is obtained under the random service discipline. By means of a counterexample, it is shown that the extension cannot be made for closed network with two or more stations.