Hybrid approach to the rational management of machine replacement

The paper analyzes a nonlinear integer-valued optimization problem that describes the optimal machine replacement under improving technology. The problem is extended into the classes of real-valued discrete-time optimization problems and continuous-time optimal control. The results include some qualitative properties of optimal management policies and the construction of an efficient numeric algorithm.

[1]  Donald R. Plane,et al.  Discrete optimization : integer programming and network analysis for management decisions , 1971 .

[2]  Suresh Chand,et al.  Planning Horizon Procedures for Machine Replacement Models , 1979 .

[3]  Raouf Boucekkine,et al.  Replacement Echoes in the Vintage Capital Growth Model , 1997 .

[4]  Suresh Chand,et al.  A parallel machine replacement model , 2002 .

[5]  Thomas L. Magnanti,et al.  Applied Mathematical Programming , 1977 .

[6]  James M. Malcomson,et al.  Replacement and the rental value of capital equipment subject to obsolescence , 1975 .

[7]  Natali Hritonenko,et al.  Turnpike and Optimal Trajectories in Integral Dynamic Models with Endogenous Delay , 2005 .

[8]  Natali Hritonenko,et al.  Optimization of the lifetime of capital equipment using integral models , 2005 .

[9]  Suresh K. Nair,et al.  A model for equipment replacement due to technological obsolescence , 1992 .

[10]  James E. Ward,et al.  A model for parallel machine replacement with capacity expansion , 2000, Eur. J. Oper. Res..

[11]  Natali Hritonenko,et al.  Structure of optimal trajectories in a nonlinear dynamic model with endogenous delay , 2004 .

[12]  Natali Hritonenko,et al.  Integral-functional equations for optimal renovation problems , 1996 .

[13]  C. E. Love,et al.  Utilizing Weibull Failure Rates in Repair Limit Analysis for Equipment Replacement/Preventive Maintenance Decisions , 1996 .

[14]  Suresh P. Sethi,et al.  Minimal Forecast Horizons in Equipment Replacement Models with Multiple Technologies and General Switching Costs , 1992 .

[15]  W. D. Northup,et al.  USING DUALITY TO SOLVE DISCRETE OPTIMIZATION PROBLEMS: THEORY AND COMPUTATIONAL EXPERIENCE* , 1975 .

[16]  Robert L. Smith,et al.  A paradox in equipment replacement under technological improvement , 2003, Oper. Res. Lett..

[17]  Natali Hritonenko,et al.  Optimal equipment replacement without paradoxes: A continuous analysis , 2007, Oper. Res. Lett..

[18]  Onno van Hilten.  The optimal lifetime of capital equipment , 1991 .

[19]  Harvey M. Salkin,et al.  Integer Programming , 2019, Engineering Optimization Theory and Practice.

[20]  Suresh P. Sethi,et al.  Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography , 2001, Manuf. Serv. Oper. Manag..

[21]  Natali Hritonenko,et al.  Modeling and Optimization of the Lifetime of Technologies , 1996 .