Design of manufacturing systems using queueing models

Optimal allocation of resources in a job shop environment

“…(This supports the traditional view that the bottleneck analysis of machines should be combined with the value of jobs¯owing through them for purpose of allocating priorities). As an example, when the resource allocations can assume only integral values then the marginal (greedy) allocation algorithm is optimal, as is discussed in Fox [24] and Appendix A of Buzacott and Shanthikumar [16]. (As a historical note, Fox credits Gross [28] for this result).…”

“…Moreover Shanthikumar and Xu showed that their allocation is strongly asymptotically optimal, that is, under heavy trac conditions (namely, utilization approaches unity) the ratio of the expected cost under their allocation to the optimal expected cost converges to unity. The method of analysis that uses bounds and approximations for the delay in the queue can be extended to networks of queues, using the Generalized Jackson Networks modeling framework, as is discussed in Buzacott and Shanthikumar [16] and Section 3.2.1 in Bitran and Morabito [17]. Buzacott and Shanthikumar in their review paper discussed the use of this approach in the solution of a number of allocation problems in manufacturing.…”

“…A number of algorithms have been proposed for this discrete optimization problem. For excellent surveys of this area of research, see Buzacott and Shanthikumar [16] and Bitran and Morabito [17]. Buzacott and Shanthikumar provide a comprehensive review on resource allocation in manufacturing systems.…”

On the Distribution of Throughput of Transfer Lines

“…The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. The second review is accomplished by Buzacott and Shanthikumar [42] in which design issues of flow lines as well as various types of manufacturing systems such as automatic transfer lines, job shops, flexible machining systems, flexible assembly systems, and multiple cell systems are addressed. Approaches to resolving the design issues of these systems using queueing models are also reviewed.…”

Availability modelling and analysis of multi-product flexible transfer lines subject to random failures

“…Production lines are among the most widely studied classes of manufacturing systems [1]. They were originally developed for a cost-efficient mass-production of standardized products, and are characterized by a product flow pattern, and very high production rates [2,3].…”