398 European Journal of Operational Research24 (1986) 398-409 North-Holland Optimal performance analysis of manufacturing systems subject to tool availability B. VINOD Operations Research, American Airlines, P.O. Box 619616, MD 2B56 Dallas/Forth Worth, TX 75261, U.S.A. M. SABBAGH Department of Computer Science SUNY College of Technology Utica, N Y 13502, U.S.A. Abstract: This paper deals with the approximate performance analysis and optimal allocation of spare tools at work stations in manufacturing systems that are subject to the availability of tools to process jobs. Keywords: Closed queueing networks, optimization, tools, spares, performance, manufacturing systems, approximation, implicit enumeration 1. Introduction The productivity of manufacturing systems can be greatly enhanced by minimizing irregularities caused by short term interruptions. A critical aspect which affects the performance of a manu- facturing system is the availability of tools at the right time to process work pieces. Tool breakage is the single most significant factor (Shaw, 1980) that decreases the productivity of a manufacturing sys- tem. A tool replacement at a work station may be required due to any one or a combination of reasons: tool breakage, tool wear and tear, raw material quality, excessive cutting temperature, chatter, poor quality finish, lack of dimensional accuracy, etc. A performance model of a manufacturing sys- tem is used to provide realistic estimates of the performance measures of the actual realization of the process. If the absence of tools at work sta- tions to process workpieces is not captured in a performance model of the system, the performance The authors would like to expresstheir gratitude to Profes- sor Joe Talavage of the School of Industrial Engineering, Purdue Universityfor his helpful suggestions. Received October 1984; revised May 1985 measures predicted by the model would exceed those observed in the real system. From the recog- nition that the availability of tools at workstations is critical to enhance the productivity of the sys- tem, an important design issue is the optimal allocation of spare tools. The organization of this paper is as follows. To analyze performance, we consider a multistage model of a manufacturing system that is subject to the availability of tools to process workpieces. Solberg (1977) observed that work flow in com- puterized manufacturing systems can be effectively modeled as a closed network of queues. In Section 2 we take a similar recourse in modeling the multistage FMS and present a load dependent approximation to capture the availability of tools in the system. When the advantages of a combina- tion of techniques can be exploited, hybrid models are frequently used (Ratcliffe, Vinod and Sparrow (1984); Vinod and John (1984); Vinod and Sol- berg (1984)). In Section 3 we present a queueing optimization model for the optimal allocation of spare tool classes. Section 4 describes the implicit enumeration algorithm used to determine the opti- mal number of spares for each tool class. We then illustrate how the optimal distribution of spare tools may be used to estimate the optimal system performance by the load dependent approxima- 0377-2217/86/$3.50 © 1986, ElsevierSciencePublishers B.V. (North-Holland)