Managing Uncertainty in a Serial Production Line

This paper studies a serial production line that is uncertain. We introduce a linear model of the uncertainty that can exist in the demand for the product and in each stage's processing time, yield, rework probability, and reliability. We construct a linear discrete-time rule for controlling production, and we show that repeated application of this rule leads the system to steady-state conditions, which include closed-form formulas for the mean and variance of each buffer's stock and the mean and variance of the workload in each stage. We optimize these operating characteristics by a convex nonlinear program. For the case of identical stages with no scrap, we show that this optimal solution tends to place larger buffer stocks toward the end of the line. We adapt these discrete-time results to the short-period surrogate of the analogous continuous-time control problem.

[1]  J. G. Shanthikumar,et al.  An Algorithmic Solution to Two-Stage Transfer Lines with Possible Scrapping of Units , 1983 .

[2]  Kazuyoshi Ishii,et al.  Some ways to increase flexibility in manufacturing systems , 1985 .

[3]  D. Clay Whybark,et al.  MATERIAL REQUIREMENTS PLANNING UNDER UNCERTAINTY , 1976 .

[4]  Stephen C. Graves,et al.  A Tactical Planning Model for a Job Shop , 1986, Oper. Res..

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

[6]  Osamu Kimura,et al.  Desiǵn and analysis of Pull System, a method of multi-staǵe production control , 1981 .

[7]  Debasis Mitra,et al.  Analysis of a Kanban discipline for cell coordination in production lines , 1990 .

[8]  T. Tabe,et al.  Analysis of production ordering quantities and inventory variations in a multi-stage production ordering system , 1980 .

[9]  F. Hillier,et al.  On the Optimal Allocation of Work in Symmetrically Unbalanced Production Line Systems with Variable Operation Times , 1979 .

[10]  John B. Kidd,et al.  Toyota Production System , 1993 .

[11]  Lawrence M. Wein,et al.  Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Network with Controllable Inputs , 2011, Oper. Res..

[12]  W. Whitt,et al.  Performance of the Queueing Network Analyzer , 1983, The Bell System Technical Journal.

[13]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .

[14]  Takaya Ichimura,et al.  LOW-INVENTORY ORDERING SYSTEMS FOR THE INTERNATIONAL CO-OPERATIVE KNOCKDOWN PRODUCTION SYSTEMS , 1989 .

[15]  W. Whitt,et al.  The Queueing Network Analyzer , 1983, The Bell System Technical Journal.

[16]  Meir J. Rosenblatt,et al.  Economic Production Cycles with Imperfect Production Processes , 1986 .

[17]  Michael A. Zazanis,et al.  Push and Pull Production Systems: Issues and Comparisons , 1992, Oper. Res..

[18]  Christopher S. Tang,et al.  Linear Control of a Markov Production System , 1992, Oper. Res..

[19]  Stanley B. Gershwin,et al.  Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers , 1983, Oper. Res..

[20]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[21]  de Mbm René Koster,et al.  Capacity Oriented Analysis and Design of Production Systems , 1989 .

[22]  J. Michael Harrison,et al.  Brownian Models of Queueing Networks with Heterogeneous Customer Populations , 1988 .

[23]  Hirofumi Matsuo,et al.  Control Policy for a Manufacturing System with Random Yield and Rework , 1997 .

[24]  Richard Schonberger,et al.  World class manufacturing : the lessons of simplicity applied , 1986 .

[25]  William L. Maxwell,et al.  The Role of Work-in-Process Inventory in Serial Production Lines , 1988, Oper. Res..

[26]  Kazuyoshi Ishii,et al.  Feedback method of production ordering system in multi-stage production and inventory systems , 1987 .

[27]  J. George Shanthikumar,et al.  An Approximate Model of Multistage Automatic Transfer Lines with Possible Scrapping Of Workpieces , 1987 .

[28]  Yew Sing Lee.  Operations research models for production planning , 1991 .

[29]  David L. Woodruff,et al.  CONWIP: a pull alternative to kanban , 1990 .

[30]  Oded Berman,et al.  Analysis of transfer lines consisting of two unreliable machines with random processing times and finite storage buffers , 1981 .

[31]  Christopher S. Tang.  The impact of uncertainty on a production line , 1990 .

[32]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

[33]  Stanley B. Gershwin,et al.  An Efficient Decomposition Method for the Approximate Evaluation of Tandem Queues with Finite Storage Space and Blocking , 1987, Oper. Res..

[34]  R. E. Levitan.  The Optimum Reject Allowance Problem , 1960 .

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

[36]  Morton Klein.  Markovian Decision Models for Reject Allowance Problems , 1966 .

[37]  C. C. Holt,et al.  Planning Production, Inventories, and Work Force. , 1962 .

[38]  Emanuel Parzen,et al.  Stochastic Processes , 1962 .

[39]  Lawrence M. Wein,et al.  Scheduling Networks of Queues: Heavy Traffic Analysis of a Two-Station Closed Network , 1990, Oper. Res..