Abstract
In this paper, we develop a multi-item, multi-period, double-random inventory model and demonstrate the application of distributed-memory MIMD parallel computers to solving this model, which, like many other inventory models, provides the basis for decisions in business and manufacturing industries. The parallel algorithm we have constructed in this study, with nearly perfect speedup, can solve for our model with 2000 items simulated for 30 years with an assumption of daily re-order, by using 24 hours of CPU time on a 50-node Paragon. This suggests that modeling realistic inventory problems with several thousand items on a small parallel computer is feasible. As a consequence, an entire new range of economical processes are open to systematic study by parallel processing.
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References
Arrow, K.J., Karlin, S. and Scarf, H., 1958, Studies in the mathematical theory of inventory and production, Stanford Univ. Press, Stanford, CA.
Avriel, M., 1976, Nonlinear Programming: analysis and methods, Prentice Hall, Englewood Cliffs, NJ.
Bertsekas, D.P., 1988, The auction algorithm: a distributed relaxation method for the assignment problem’, Annals of Operations Research 14, 105–124.
Buffa, E.S. and Miller, J.G., 1979, Production Inventory Systems: Planning and Control, Sri ed., Richard D. Irwin, Homewood, Ill.
Byrd, R.H., Dert, C.L., Kan, A.H.G., and Schnabel, R.B., 1990, ‘Concurrent stochastic methods for global optimization’, Mathematical Programming 46, 1–29.
Ehrhardt, R.( 1979, ‘The power approximation for computing (s, S) inventory policies’, Management Science 25, 777–786.
Evtushenko, Y.G., Potapov, M.A. and Korotkich, V.V., 1992, ‘Numerical methods for global optimization’, in C.A. Floudas and Pardalos, P.M. (Eds.), Recent Advances in Giobal Optimization, Princeton University Press, NJ.
Freeland, J.R. and Portues, E.L., 1980, ‘Evaluating the effectiveness of a new method for computing approximately optimal (s, S) inventory policies’, Operations Research 28, 353–363.
Hadley, G. and Whitin, T., 1963, Analysis of Inventory Systems, Prentice Hall, Englewood Cliffs, NJ.
Hax, A and Candea, D., 1984, Production and Inventory Management, Prentice Hall, Englewood Cliffs, NJ.
Hillier, F.S. and Lieberman, G.J., 1990, Introduction to Operations Research, McGraw-Hill Publishing Company, NY.
Hoover, S.V. and Perry, R.F., 1990, Simulation: a problem-solving approach, Addison-Wesley Publishing Company, Inc., MA.
Kan, A.H.G. and Timmer, G.T., 1984, ‘A stochastic approach for global optimization’, American Journal of Mathematical and Management Science 4, 7–40.
Kok, A.G.D., 1987, Production-inventory Control Models: Approximations and Algorithms, Centrum Voor Wiskunde en Informatica, P.O. Box 4097, 1009 AB Amsterdam, The Netherlands.
Lindgren, B.E., 1976, Statistical Theory, MacMillan Publishing Co., NY.
Mladineo, R.H., 1992, ‘Stochastic minimization of Lipschitz function’, in C.A. Floudas and Pardalos, P.M. (Eds.), Recent Advances in Global Optimization, Princeton University. Press, NJ.
Naddor, E., 1978, ‘Sensitivity to distributions in inventory systems’, Management Science 24, 1769–1772.
Naddor, E., 1975, ‘Optimal and heuristic decisions in single-and-multi-item systems’, Management Science 21, 1234–1249.
Peterson, R. and Silver, E.A., 1979, Decision Systems for Inventory Management and Production Planning, John Wiley and Son, NY.
Roberts, D.M., 1962, ‘Approximations to optimal policies in a dynamic inventory model’, in K. Arrow, et al. (Eds.), Studies in Applied Probability and Management science, Stanford University Press, CA.
Rockefeller, R.T., 1970, Convex Analysis, Princeton University Press, Princeton, NJ.
Ross, S.M., 1989, Introduction to Probability Models, Academic Press, NY.
Ross, S.M., 1970, Applied Probability Models with Optimization Application, Holden-Day, San Francisco, CA.
Schneider, H., 1978, ‘Methods for determining the reorder point of an (s, S) ordering policy when a service level is specified’, J. Operational Res. Soc. 12, 1181–1193.
Schneider, H., 1981, ‘Effect of service-levels on order-point or order-level in inventory models’, Internat. J. Production Research 6, 615–631.
Sobel, M.J., 1970, ‘Optimal average cost policy for a queue with start-up and shut-down costs’, Operations Research 18, 145–162.
Sobel, M.J., 1982, Stochastic Models in Operations Research, McGraw-Hill Publishing Company, NY.
Solis, F.J. and Wets, R.J.E., 1981, ‘Minimization by random search techniques’, Mathematics of Operation research 6, 19–30.
Tijms, H.C., 1986, Stochastic Modeling and Analysis: A Computational Approach, John Wiley and Sons, NY.
Tijms, H.C. and Groenevelt, H., 1984, ‘Simple approximations for the re-order point in periodic and continuous review (s, S) inventory systems with service level constraints’, European Journal of Operational Research 17, 175–190.
Torn, A. and Viitanen, S., 1992, ‘Topographical global optimization’, in C.A. Floudas and Pardalos, P.M. (Eds.), Recent Advances in Global Optimization, Princeton University Press, NJ.
Yakowitz, S.J., 1977, Computational Probability and Simulation, Addison-Wesley Publishing Company, Inc., MA.
Zenios, S.A., 1989, ‘Parallel numerical optimization: current status and an annotated bibliography’, ORSA Journal on Computing 1, 20–43.
Zielinski, R., 1981, ‘A stochastic estimate of the structure of multi-external problems’, Mathematical Programming 22, 104–116.
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Wang, Y., Deng, Y. (1996). Multi-Item Stochastic Inventory Models with Constraints and Their Parallel Computation. In: Gilli, M. (eds) Computational Economic Systems. Advances in Computational Economics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8743-3_5
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DOI: https://doi.org/10.1007/978-94-015-8743-3_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4655-0
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