Variance Effects in Cyclic Production Systems

Utilizing a cyclic queue system, this paper investigates the effect of variance on a multi-item production facility. The variance of setup time, service rate and arrival rate is shown to have a powerful and sometimes paradoxical influence. Reduction in setup time, for example, is usually presumed to reduce inventory. We demonstrate that inventory can blow up if setup time is cut. Another paradoxical effect of variance is on processing rate. Speeding up the processing rate should reduce the material waiting to be processed. Again we show that the opposite can hold. Other properties of variance are examined, such as its relationship to KAIZEN and Just-In-Time production practices, and especially its property of impairing capacity.

[1]  Ward Whitt,et al.  Approximating a Point Process by a Renewal Process, I: Two Basic Methods , 1982, Oper. Res..

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

[3]  Evan L. Porteus.  Investing in Reduced Setups in the EOQ Model , 1985 .

[4]  Paul H. Zipkin,et al.  Models for Design and Control of Stochastic, Multi-Item Batch Production Systems , 1986, Oper. Res..

[5]  J. A. Buzacott.  The production capacity of job shops with limited storage space , 1976 .

[6]  Michael J. Ferguson,et al.  Exact Results for Nonsymmetric Token Ring Systems , 1985, IEEE Trans. Commun..

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

[8]  Paul J. Schweitzer,et al.  Maximum Throughput in Finite-Capacity Open Queueing Networks with Product-Form Solutions , 1977 .

[9]  D. Sarkar,et al.  Expected waiting time for nonsymmetric cyclic queueing systems—exact results and applications , 1989 .

[10]  Ernest Koenigsberg,et al.  Twenty Five Years of Cyclic Queues and Closed Queue Networks: A Review , 1982 .

[11]  Stephen C. Graves,et al.  Production/inventory systems with a stochastic production rate under a continuous review policy , 1981, Comput. Oper. Res..

[12]  A. J. Fabens.  The Solution of Queueing and Inventory Models by Semi‐Markov Processes , 1961 .

[13]  Kathryn E. Stecke,et al.  Loading and control policies for a flexible manufacturing system , 1981 .

[14]  Hugh S. Bradlow,et al.  Mean Waiting Time Evaluation of Packet Switches for Centrally Controlled PBX's , 1987, Perform. Evaluation.

[15]  Izhak Rubin,et al.  Polling with a General-Service Order Table , 1987, IEEE Trans. Commun..

[16]  Evan L. Porteus,et al.  Setup reduction and increased effective capacity , 1987 .

[17]  Evan L. Porteus.  Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction , 1986, Oper. Res..

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