Abstract
In this paper, a multi-machine replacement problem is studied. T(1) represents an existing technology currently in operation; and machine T(2) represents a new technological breakthrough of which introduction time is uncertain. Economies of scale yield age-group based optimal replacement policies. This, in return, provides substantial reduction in the complexity of the problem. Sufficient conditions limit the amount of information needed to determine regenerative type optimal solutions to the infinite horizon problem.
Similar content being viewed by others
References
BEAN, J.C. & R.L. SMITH. 1985. Optimal capacity expansion over an infinite horizon. Management Science, 31, 1523–1532.
CHAND S. & S.P. SETHI. 1982. Planning horizons procedures for machines replacement models with several possible replacement alternatives. Naval Research Logistics Quarterly, 29, 483–493.
GOLDSTEIN, Z., S.P. LADANY & A. MEHREZ. 1986. A note on planning horizon procedure for machine replacements with several possible alternatives. Operations Research, 34, 938–941.
GOLDSTEIN, Z., S.P. LADANY & A. MEHREZ. 1988. A discounted machine replacement model with an expected future technological breakthrough. Naval Research Logistics Quarterly, 35, 209–220.
LUNDIN, R.E. & T.E. MORTON. 1975. Planning horizon for dynamic lot size model: Zabel vs. protective procedure and computational results. Operations Research, 23, 711–734.
MEHREZ, A. & N. BERMAN. 1994. Maintenance optimal control three-machine replacement model under technological breakthrough expectations. Journal of Optimization Theory and Applications, 81, 591–618.
SETHI, S.P. & G.L. THOMPSON. 1977. Christmas toy manufacturer’s problem: An application of the stochastic maximum principle. Opsearch, 14, 161–173.
SILVER, E.A. 1976. A simple method of determining order quantities in joint-replenishment under deterministic demand. Management Science, 22, 1351–1361.
UTTERBUCK, J.M. & W.J. ABERNATHY. 1975. A dynamic model of process and product innovation. OMEGA, 3, 639–655.
ZANGWILL, W.I. 1968. Minimum concave cost flow in certain networks. Management Science, 14, 429–450.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Goldstein, Z., Mehrez, A. A Concave Cost Multimachine Replacement Problem With an Expected Breakthrough. OPSEARCH 36, 307–324 (1999). https://doi.org/10.1007/BF03398585
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03398585