6. Conclusion Remarks
6.2 Future Research
Future research directions might include development of efficient dynamic heuristics to solve larger scale dynamic downgrading problem, focus on estimating a demand model and generating economic scenarios to improve the discrete approximation of the probability distribution. In addition, establishing a multi-objective stochastic model for C/D wafers problem to minimize total cost can achieve multiple planning targets at one time.
61
References
[1] Azaier, M. N., Hariga, M., Al-Harkan, I., A chance-constrained multi-period model for a special multi-reservoir system. Computers & Operations Research, 32 (5), 1337-1351, 2005.
[2] Bakir, M. A. and Byrne, M. D., Stochastic linear optimization of an MPMP production planning model. International Journal of Production Economics, 55 (1), 87-96, 1998.
[3] Beale, E. M. L., On minimizing a convex function subject to linear inequalities.
Journal of the Royal Statistical Society, Series B, 17 (2), 173-184, 1955.
[4] Benavides, D. L, Duley, R., Johnson, B. E., As good as it gets: Optimal fab design and deployment. IEEE Transactions on Semiconductor Manufacturing, 12 (3), 281-287, 1999.
[5] Bhunia, A. K. and Maiti, M., Deterministic inventory models for variable production.
Journal of the Operational Research Society, 48 (2), 221-224, 1997.
[6] Bitran, G. R. and Yanasse, H. H., Deterministic approximations to stochastic production problem. Operations Research, 32 (5), 999-1018, 1984.
[7] Black, F. and Scholes, M., The pricing of options and corporate liabilities. The Journal
62
of Political Economy, 81 (3) 637-654, 1973.
[8] Blackmore, L., Li, H., and Williams, B., A probabilistic approach to optimal robust path planning with obstacles. American Control Conference, 2006.
[9] Bowman, K. O. and Shenton, L. R., Solutions to Johnson’s SB and SU
[10] Box, G. E. P. and Cox, D. R., An analysis of transformations. Journal of the Royal Statistical Society, Series B, 26 (2), 211-252, 1964.
. Communications in Statistics, Simulation and Computation, 17 (2), 343-348, 1988.
[11] Buffa, E. S., and Taubert, W. H., Production Inventory Systems: Planning and Control, Irwin, Homewood, Illinois, 1972.
[12] Bukac, J., Fitting SB curves using symmetrical percentile points. Biometrika, 59 (3), 688-690, 1972.
[13] Chang, H. J. and Dye, C. Y., An EOQ model with deteriorating items in response to a temporary sale price. Production Planning and Control, 11 (5), 464-473, 2000.
[14] Chang, H. J, Hung, C. H. and Dye, C.Y., A finite time horizon inventory model with deterioration and time-value of money under the conditions of permissible delay in payments. International Journal of Systems Science, 33 (2), 141-151, 2002.
63
[15] Charnes, A. and Cooper, A. A., Chance constrained programming. Management Science, 6 (1), 73-79, 1959.
[16] Chen, H. and Kamburowska, G., Fitting data to the Johnson system. Journal of Statistics in Computation and Simulation, 70 (1), 21-32, 2001.
[17] Chen, H. C. and Lee, C. E., Control and dummy wafers management. Journal of the Chinese Institute of Industrial Engineer, 17 (4), 437-449, 2000.
[18] Chen, H.C. and Lee, C. E., Downgrading and release rules for control and dummy wafers, International Journal of Industrial Engineering: Theory, Applications and Practice, 11 (2), 197-206, 2004.
[19] Chen, H. C. and Lee, C. E., Pull system for control and dummy wafers. The International Journal of Advanced Manufacturing, 22 (11-12), 805-818, 2003.
[20] Chou, Y. M., Polansky, A. M. and Mason, R. L., Transforming non-normal data to normality in statistical process and control. Journal of Quality Technology, 30 (2), 133-141, 1998.
[21] Christie, R. M. E. and Wu, S. D., Semiconductor capacity planning: stochastic modeling and computational studies. IIE Transactions, 34 (2), 131-143, 2002.
[22] Chung, K. J. and Tsai, S. F., Inventory systems for deteriorating items with shortages
64
and a linear trend in demand-taking account of time value. Computer and Operation Research, 28 (9), 915-934, 2001.
[23] Chung, S. H., Kang, H. Y., and Pearn, W.L., A linear programming model for the control wafers downgrading problem. The International Journal of Advanced Manufacturing, 25 (3), 377-384, 2005 a.
[24] Chung, S. H., Kang, H. Y., and Pearn, W.L., A service level model for the control wafers safety inventory problem. The International Journal of Advanced Manufacturing, 26, (5-6), 591-597, 2005 b.
[25] Covert, T. B. and Philip, G. S., An EOQ model with Weibull distribution deterioration.
IIE Transactions, 5 (4), 323-326, 1973.
[26] Dantzig G. B., Linear programming under Uncertainty. Management Science, 1 (3-4), 197-206, 1955.
[27] Das, K., Roy, T. K. and Maiti, M., Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: a geometric programming approach. Production Planning and Control, 11 (8), 781-788, 2000.
[28] Dixit, A. K. and Pindyck, R. S., Investment under Uncertainty, Princeton University
65
Press, 1994.
[29] Draper, N. R. and Cox, D. R., On distributions and their transformation to normality.
Journal of the Royal Statistical Society, Series B, 31 (4), 472-476, 1969.
[30] Duran, S., Liu, T., Simchi-levi, D., and Swann, J. L., Optimal production and inventory policies of priority and price-differentiated customers. IIE Transactions, 39 (9), 845-861, 2007.
[31] Ferguson, A. and Dantzig, G. B., The allocation of aircraft to routes: An example of linear programming under uncertain demand. Management Science, 3 (1), 45-73, 1956.
[32] Foster, B., Meyersdorf, D., Padillo, J. M., and Brenner, R., Simulation of test wafer consumption in a semiconductor facility. IEEE/SEMI Advanced Semiconductor Manufacturing Conference and Workshop, 298-302, 1998..
[33] Ghare, P. M. and Scharader, G. H., A model for exponentially decaying inventory system. International Journal of Production Research, 21 (4), 449-460, 1963.
[34] Gumus, A. T. and Guneri, A. F., Multi-echelon inventory management in supply chains with uncertain demand and lead times: literature review from an operational research perspective. Proceedings of International Mechanical Engineering, 221 (B),
66
1553-1570, 2007
[35] Gupta, A. and Maranas, C. D., A two-stage modeling and solution framework for multisite midterm planning under demand uncertainty. Industrial Engineering in Chemistry Research, 39 (10), 3799-3813, 2000.
[36] Gupta, A., Maranas, C. D., McDonald, C. M., Mid-term supply chain planning under demand uncertainty: customer demand satisfaction and inventory management.
Computers & Chemical Engineering, 24 (12), 2613-2621, 2000.
[37] Hahn, G. J. and Shapiro, S. S., Statistical Models in Engineering, Wiley, New York, 1967.
[38] Harris, F., How many parts to make at once, Factory. The magazine of management, 10 (2), 135-136, 1913.
[39] Hinkley, D. V., On power transformations to symmetry. Biometrika, 62 (1), 101-111, 1975.
[40] Hinkley, D. V., On quick choice of power transformation. Applied Statistics, 26 (1), 67-69, 1976.
[41] Hsu, A. and Bassok, Y., Random yield and random demand in a production system
67
with downward substitution. Operations Research, 47 (2), 277-290, 1999.
[42] Jana, R. K. and Biswal, M. P., Stochastic simulation-based genetic algorithm for chance constraint programming problems with continuous random variables.
International Journal of Computer Mathematics, 81 (9), 1069-1076, 2004.
[43] Jana, R. K. and Biswal, M. P., Stochastic simulation based genetic algorithm for chance constraint programming problems with some discrete random variables.
International Journal of Computer Mathematics, 81 (12), 1455-1463, 2004.
[44] Jarrow, A. R., and Rudd, A., Option Pricing, Irwin, 1983.
[45] Ji, C. L., Zhang, Y. Y., Wang, Y., and Xu, W. W., Application of chance-constrained programming to design centering, tolerance assignment, and tuning. Proceedings of IEEE International Conference on Electronics, Circuits and Systems, 2, 766-769,
2003.
[46] Johnson, N. L., Systems of frequency curves generated by methods of translation.
Biometrika, 36 (12), 149-176, 1949.
[47] Kall, P., Stochastic Linear Programming, Springer Verlag, Berlin, 1976.
[48] Kar, S., Bhunia, A. K. and Maiti, M., Deterministic inventory model with two levels of storage, a linear trend in demand and a fixed time horizon. Computer and Operation
68
Research, 28 (13), 1315-1331, 2001.
[49] King, A., Stochastic programming problems: Examples from the literature. in Ermoliev, Y., and Wets, R. T.-B. (eds.) Numerical Techniques for Stochastic Optimization, Springer Verlag, Berlin, 543-567, 1988.
[50] Kumral, M., Genetic algorithms for optimization of a mine system under uncertainty.
Production Planning & Control, 15 (1), 34-41, 2004.
[51] Leachman, R., Preliminary design and development of a corporate-level production system for the semiconductor industry. Working paper, Operations Research Center, University of California, Berkeley, CA.
[52] Leung, S. C., Wu, Y., and Lai, K. K., A stochastic programming approach for multi-site aggregate production planning. Journal of the Operational Research SocietyH, 57 (2), 123-132, 2006.
[53] Liou, C. S., Lin, T. K., Tu, B., and Chang, A., Capacity forecast model for control and dummy wafers. IEEE/ISSM International Semiconductor Manufacturing Symposium, 123-125, 2005.
[54] Mage, D. T., An explicit solution for SB parameters using four percentile points.
Technometrics, 22 (2), 247-251, 1980.
69
[55] Manandhar, S. and Tarim, A., Scenario-based stochastic constraint programming.
International Joint Conference on Artificial Intelligence, 257-262, 2003.
[56] Owen, D. B., The starship. Communication in Statistics-Simulation and Computation, 17 (2), 315-323, 1988.
[57] Özelkan, E. C., and Çakanyildirim, M., Resource downgrading. European Journal of Operational Research, 177 (1), 572-590, 2007.
[58] Pal, S., Goswami, A. and Chaudhuri, K. S., A Deterministic inventory model for deteriorating items with stock-dependent demand rate. International Journal of production Economics, 32 (3), 291-299, 1993.
[59] Petkov, S. B. and Maranas, C. D., Multi-period planning and scheduling of multiproduct batch planning under demand uncertainty. Industrial Engineering in Chemistry Research, 36 (11), 4864-4881, 1997.
[60] Platt, D. E., Robinson, L. W. and Freund, R. B., Tractable (Q, R) heuristic models for constrained service levels. Management Science, 43 (7), 951-965, 1997.
[61] Plackett, R., Reduction formula for multivariate normal integrals. Biometrika, 41, (3-4), 351-360, 1954.
[62] Popovich, S. B., Chilton, S. R., Kilgore, B., Implementation of a test wafer inventory
70
tracking system to increase efficiency in monitor wafer usage. IEEE/SEMI Advanced Semiconductor Manufacturing Conference and Workshop, 440-443, 1997.
[63] Prekopa, A., Numerical solution of probabilistic constrained programming models. in Ermoliev, Y., and Wets, R. T.-B. (editors.), Numerical Techniques for Stochastic Optimization, Springer Verlag, Berlin, 123-139, 1988.
[64] Pyzdek, T., Why normal distributions aren’t [all that normal]. Quality Engineering, 7 (4), 767-777, 1995.
[65] Rao, U. S., Swaminathan, J. M., and Zhang, J., Multi-product inventory planning with downward substitution, stochastic demand and setup costs. IIE Transactions, 36 (1), 59-71, 2004.
[66] Shapiro, S. S. and Wilk, M. B., An analysis of variance test for normality. Biometrika, 52 (3-4), 591-611, 1965.
[67] Silva Filho, O. S. and Ventura, S. D., Optimal feedback control scheme helping managers to adjust aggregate industrial resources. Control Engineering Practice, 7 (4), 555-563, 1999.
[68] Silva Filho, O. S., An aggregate production planning model with demand under uncertainty. Production Planning & Control, 10 (8), 745-756, 1999.
71
[69] Slifker, J. F. and Shapiro, S. S., The Johnson system: selection and parameter estimation. Technometrics, 22 (2), 239-246, 1980.
[70] Subrahmanyam, S., Pekny, J. F., and Reklaitis, G. V., Design of batch chemical plants under market uncertainty. Industrial Engineering Chemical Research, 33 (11), 2688, 1994.
[71] Tukey, J. W., The comparative anatomy of transformations. Annals of Mathematical Statistics, 28 (3), 602-632, 1957.
[72] Wagner, H. and Whitin, T., Dynamic version of the economic lot size model.
Management Science, 5 (1), 89-96, 1958.
[73] Watkins, D.W., McKinney, D. C., Lasdon, L.S., Nielsen, S. S., and Martin, Q. W., A scenario-based stochastic programming model for water supplies from the highland lakes. International Transaction in Operation Research, 7 (3), 211-230, 2000.
[74] Wets, R. J.-B., Solving Stochastic programs with simple recourse. Stochastic, 10 (3-4), 219-242, 1983.
[75] Wets, R. J.-B., Large-scale linear programming techniques in stochastic programming.
Numerical Techniques for Stochastic Optimization, Ermoliev Y., Wets R. T.-B. (eds.).
Springer Verlag, Berlin, 65-93, 1988.
72
[76] Wong, C. Y., and Hood, S. J., Impact of process monitoring in semiconductor manufacturing. IEEE/CPMT International Electronics Manufacturing Technology Symposium, 221-225, 1994.
[77] Wu, M. C., Chien, C. S., and K. S. Lu, Downgrading decision for control/dummy wafers in a fab, The International Journal of Advanced Manufacturing, 26 (5-6), 585-590, 2005.
[78] Wu, T. H., Huang, C. C., and Yang, Y. S., A tabu search approach for the deterministic and stochastic vehicle fleet mix and routing problem. Journal of the Chinese Institute of Industrial Engineering, 18 (2), 102-112, 2001.
[79] Yildirim, I., Tan, B., and Karaesmen, F., A multi-period stochastic production planning and sourcing problem with service level constraints. Operation Research Spectrum, 27 (2-3), 471-489, 2005.
[80] You, H. L., Jia, X. Z., Xu, L., and Cheng, G. B., Box-Cox transformation and characterization of microcircuit process equipment. Research & Progress of SSE, 25 (3), 398-402, 2005.
[81] Zhang, F., Roundy, R., Cakanyildirim, M., and Hun, W. T., Optimal capacity expansion for multi-product multi-machine manufacturing systems with stochastic
73
demand. IIE Transactions, 36 (1), 23-36, 2004.
[82] Zhu, M., Taylor, D. B., Sarin, S. C., and Kramer, R. A., Chance constrained programming models for risk-based economic and policy analysis of soil conservation.
Agricultural and Resource Economics Review, 23 (1), 58-65, 1994.