Lot streaming for quality control in two-stage batch production. (English) Zbl 1091.90013
Summary: We consider a two-stage batch manufacturing process in which the first stage shifts out-of-control at iid exponential times after starting in control. To improve quality, a production batch at Stage 1 is subjected to lot streaming: it is divided into sublots that are processed at Stage 1 and then passed one-by-one to Stage 2 for simultaneous inspection and processing. In any sublot, Stage 1 produces good items before the shift and bad items after. The state of Stage 1 is known as soon as a bad item is encountered in Stage 2, at which time Stage 1 is re-set to the in-control state. We examine both cases of continuous first-stage and continuous second-stage production. For each case we examine both LIFO and FIFO inspection and processing policies at Stage 2. We use nonlinear programming to develop lot streaming policies which minimize the expected number of defective items for LIFO and FIFO policies. We also develop simple approximately optimal policies and compare the output performance of optimal, approximately optimal and equal-lot policies (when applicable) in a numerical example.
MSC:
| 90B30 | Production models |
References:
| [1] | Avriel, M.; Diewert, W. E.; Schaible, S.; Ziemba, W. T., Introduction to concave and generalized concave functions, (Schaible, S.; Ziemba, W. T., Generalized Concavity in Optimization and Economics (1980), Academic Press: Academic Press New York) · Zbl 0539.90087 |
| [2] | Baker, K. R., Lot streaming in the two-machine flow shop with setup times, Annals of Operations Research, 57, 1-11 (1995) · Zbl 0831.90070 |
| [3] | Baker, K. R.; Jia, D., A comparative study of lot streaming procedures, Omega, 21, 561-566 (1993) |
| [4] | Çetinkaya, F. C., Lot streaming in a two-stage flow shop with set-up, processing and removal times, Journal of the Operational Research Society, 45, 1445-1455 (1994) · Zbl 0814.90045 |
| [5] | Chvátal, V., Linear Programming (1983), W.H. Freeman: W.H. Freeman New York · Zbl 0318.05002 |
| [6] | Dauzère-Pérès, S.; Lasserre, J.-B., Lot streaming in job-shop scheduling, Operations Research, 45, 584-595 (1997) · Zbl 0887.90086 |
| [7] | Egbelu, P. J., Unit load design and its impact on manufacturing systems performance, (Tanchoco, J. M.A., Material Flow Systems in Manufacturing (1994), Chapman and Hall: Chapman and Hall London) |
| [8] | Feller, W., An Introduction to Probability Theory and its Applications, vol. 2 (1966), Wiley: Wiley New York · Zbl 0138.10207 |
| [9] | Gilbert, S.; Emmons, H., Managing a deteriorating process in a batch production environment, IIE Transactions, 27, 233-243 (1995) |
| [10] | Groover, M. P., Automation, Production Systems, and Computer-Integrated Manufacturing (2001), Prentice-Hall: Prentice-Hall Upper Saddle River, NJ |
| [11] | E. Hassini, Managing Deteriorating Manufacturing Processes, MASc Thesis, Department of Management Sciences, University of Waterloo, Waterloo, Ont., 1998.; E. Hassini, Managing Deteriorating Manufacturing Processes, MASc Thesis, Department of Management Sciences, University of Waterloo, Waterloo, Ont., 1998. |
| [12] | Kalir, A. A.; Sarin, S. C., Evaluation of the potential benefits of lot streaming in flow-shop systems, International Journal of Production Economics, 66, 131-142 (2000) |
| [13] | Lee, H. L.; Rosenblatt, M. J., Simultaneous determination of production cycle and inspection schedules in a production system, Management Science, 33, 1125-1136 (1987) · Zbl 0628.90032 |
| [14] | Lee, S. D.; Rung, J. M., Production lot sizing in failure prone two-stage serial systems, European Journal of Operational Research, 123, 42-60 (2000) · Zbl 0961.90028 |
| [15] | Luenberger, D. G., Nonlinear Programming (1984), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0241.90052 |
| [16] | Mangasarian, O., Nonlinear Programming (1969), McGraw-Hill: McGraw-Hill New York · Zbl 0127.36803 |
| [17] | McClain, J. O.; Thomas, L. J.; Mazzola, J. B., Operations Management (1992), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ |
| [18] | Nurani, R. K.; Seshadri, S.; Shanthikumar, J. G., Optimal control of a single stage production system subject to random process shifts, Operations Research, 45, 713-724 (1997) · Zbl 0902.90049 |
| [19] | Porteus, E. L., Optimal lot sizing, process quality improvement and setup cost reduction, Operations Research, 43, 137-144 (1986) · Zbl 0591.90043 |
| [20] | Porteus, E. L., The impact of inspection delay on process and inspection lot sizing, Management Science, 36, 999-1007 (1990) · Zbl 0719.90029 |
| [21] | Potts, C. N.; Baker, K. R., Flow shop scheduling with lot streaming, Operations Research Letters, 8, 297-303 (1986) · Zbl 0682.90051 |
| [22] | Rosenblatt, M. J.; Lee, H., Economic production cycles with imperfect production processes, IIE Transactions, 18, 48-54 (1986) |
| [23] | Rosenblatt, M. J.; Lee, H., A comparative study of continuous and periodic inspection policies in deteriorating production systems, IIE Transactions, 18, 2-9 (1986) |
| [24] | Ross, S. M., Stochastic Processes (1983), Wiley: Wiley New York · Zbl 0555.60002 |
| [25] | Schonberger, R. J., Japanese Manufacturing Techniques: Nine Hidden Lessons in Simplicity (1982), The Free Press: The Free Press New York |
| [26] | Shingo, S., A Revolution in Manufacturing: The SMED System (1985), Productivity Press: Productivity Press Cambridge, MA |
| [27] | Trietsch, D.; Baker, K. R., Basic techniques for lot streaming, Operations Research, 41, 1065-1076 (1993) · Zbl 0791.90026 |
| [28] | Vickson, R. G.; Alfredsson, B. E., Two and three machine flow shop scheduling problems with equal sized transfer batches, International Journal of Production Research, 30, 1551-1574 (1992) · Zbl 0825.90542 |
| [29] | Vickson, R. G., Optimal lot streaming for multiple products in a two-machine flow shop, European Journal of Operational Research, 85, 556-575 (1995) · Zbl 0912.90183 |
| [30] | Vickson, R. G., Optimal inspection sublots for deteriorating batch production, IIE Transactions, 30, 1019-1024 (1998) |
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