Simultaneous determination of lot sizes and routing mix in job shops

Flexibility and versatility of batch production job shops has increased in the last 25 years through the use of multi-purpose numerically controlled NC machine tools; these computer controlled machines can perform a wide variety of different operations. In recent years, even greater flexibility has been achieved by flexible manufacturing systems, where groups of NC machines are linked by automated material handling devices and controlled by computer. In such shops, a batch of product may have several possible alternative routes that it may follow through the shop. A number of researchers have shown that determining the proper mix of routes for each product can have a significant effect on shop throughput and work-in-process inventory. Other researchers have found that the lot sizing decision also affects these performance measures. The primary thrust of this paper is to develop a model to explore the interaction between routing and lot sizing decisions in a multi-machine, multi-work center job shop. A heuristic is developed for simultaneously determining lot sizes and routing mix in problems of practical size, and numerical examples are provided in order to illustrate the solution method. The examples show that there can be considerable potential for performance improvement by simultaneous consideration of routing and lot sizing.

[1]  Hau L. Lee,et al.  A note on the convexity of performance measures of M/M/c queueing systems , 1983 .

[2]  Uday S. Karmarkar,et al.  Lot-Sizing and Lead-time Performance in a Manufacturing Cell , 1985 .

[3]  J. A. Buzacott,et al.  Open queueing network models of dynamic job shops , 1981 .

[4]  Rajan Suri,et al.  Robustness of queuing network formulas , 1983, JACM.

[5]  Kathryn E. Stecke,et al.  The Optimality of Unbalancing Both Workloads and Machine Group Sizes in Closed Queueing Networks of Multiserver Queues , 1985, Oper. Res..

[6]  David D. Yao,et al.  Reducing the congestion in a class of job shops , 1987 .

[7]  Stanley B. Gershwin,et al.  Flow optimization in flexible manufacturing systems , 1985 .

[8]  J. A. Buzacott,et al.  Models for Understanding Flexible Manufacturing Systems , 1980 .

[9]  David D. Yao,et al.  Some properties of the throughput function of closed networks of queues , 1985 .

[10]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[11]  U. Karmarkar,et al.  Lotsizing in Multi-Item Multi- Machine Job Shops , 1985 .

[12]  Uday S. Karmarkar,et al.  Lot Sizes, Lead Times and In-Process Inventories , 1987 .

[13]  Jwm Will Bertrand.  Multiproduct Optimal Batch Sizes with In-Process Inventories and Multi Work Centers , 1985 .

[14]  Didier Dubois,et al.  Heuristic methods based on mean-value analysis for flexible manufacturing systems performance evaluation , 1982, 1982 21st IEEE Conference on Decision and Control.

[15]  JoséM. Bastos.  Batching and routing: Two functions in the operational planning of flexible manufacturing systems , 1988 .

[16]  James J. Solberg,et al.  Capacity Planning with a Stochastic Workflow Model , 1981 .

[17]  N. Cook.  Computer-Managed Parts Manufacture , 1975 .

[18]  E. A. Silver,et al.  Impact of processing and queueing times on order quantities , 1985 .

[19]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[20]  W. Whitt,et al.  Open and closed models for networks of queues , 1984, AT&T Bell Laboratories Technical Journal.