Optimal selection of obsolescence mitigation strategies using a restless bandit model

Obsolescence of embedded parts is a serious concern for managers of complex systems where the design life of the system typically exceeds 20Â years. Capital asset management teams have been exploring several strategies to mitigate risks associated with Diminishing Manufacturing Sources (DMS) and repeated life extensions of complex systems. Asset management cost and the performance of a system depend heavily on the obsolescence mitigation strategy chosen by the decision maker. We have developed mathematical models that can be used to calculate the impact of various obsolescence mitigation strategies on the Total Cost of Ownership (TCO) of a system. We have used classical multi-arm bandit (MAB) and restless bandit models to identify the best strategy for managing obsolescence in such instances wherein organizations have to deal with continuous technological evolution under uncertainty. The results of dynamic programming and greedy heuristic are compared with Gittins index solution.

[1]  K..  A model for equipment replacement due to technological obsolescence * , 2003 .

[2]  Christopher M. Anderson.  Behavioral models of strategies in multi-armed bandit problems , 2001 .

[3]  Jack R. Lohmann,et al.  A Dynamic Replacement Economy Decision Model , 1984 .

[4]  Paul A. Grout,et al.  Competitive Planned Obsolescence , 2003 .

[5]  In Ho Lee,et al.  A Theory of Economic Obsolescence , 2003 .

[6]  Y. Asiedu,et al.  Product life cycle cost analysis: State of the art review , 1998 .

[7]  W. R. Thompson.  ON THE LIKELIHOOD THAT ONE UNKNOWN PROBABILITY EXCEEDS ANOTHER IN VIEW OF THE EVIDENCE OF TWO SAMPLES , 1933 .

[8]  Mark A. Olson,et al.  An experimental analysis of the bandit problem , 1997 .

[9]  P. Whittle.  Restless bandits: activity allocation in a changing world , 1988, Journal of Applied Probability.

[10]  R. Meyer,et al.  Sequential Choice Under Ambiguity: Intuitive Solutions to the Armed-Bandit Problem , 1995 .

[11]  Warrren B Powell,et al.  Index policies for discounted bandit problems with availability constraints , 2008, Advances in Applied Probability.

[12]  U. Dinesh Kumar,et al.  Reliability and maintainability allocation to minimize total cost of ownership in a series-parallel system , 2007 .

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

[14]  W. J. Tomczykowski.  A study on component obsolescence mitigation strategies and their impact on R&M , 2003, Annual Reliability and Maintainability Symposium, 2003..

[15]  M. Keane,et al.  Decision-Making Under Uncertainty: Capturing Dynamic Brand Choice Processes in Turbulent Consumer Goods Markets , 1996 .

[16]  John N. Tsitsiklis,et al.  The Complexity of Optimal Queuing Network Control , 1999, Math. Oper. Res..

[17]  Donald A. Berry,et al.  Bandit Problems: Sequential Allocation of Experiments. , 1986 .

[18]  P. Sandborn,et al.  Forecasting technology insertion concurrent with design refresh planning for COTS-based electronic systems , 2005, Annual Reliability and Maintainability Symposium, 2005. Proceedings..

[19]  Kin Keung Lai,et al.  A sequential method for preventive maintenance and replacement of a repairable single-unit system , 2001, J. Oper. Res. Soc..

[20]  Jeremy I. Bulow.  An Economic Theory of Planned Obsolescence , 1986 .

[21]  J. Bather,et al.  Multi‐Armed Bandit Allocation Indices , 1990 .

[22]  P. K. Banerjee,et al.  On Optimal Replacement Policies - Random Horizon , 1994, Oper. Res..

[23]  L. Pretorius,et al.  A model using an obsolescence mitigation timeline for managing component obsolescence of complex or long life systems , 2004, 2004 IEEE International Engineering Management Conference (IEEE Cat. No.04CH37574).

[24]  Michael Pecht,et al.  Electronic part life cycle concepts and obsolescence forecasting , 2000 .

[25]  K. Glazebrook,et al.  Some indexable families of restless bandit problems , 2006, Advances in Applied Probability.

[26]  James M. Hulbert,et al.  Profiles of Product Innovators Among Large U.S. Manufacturers , 1992 .

[27]  Kevin D. Glazebrook,et al.  Procedures for the evaluation of strategies for resource allocation in a stochastic environment , 1990, Journal of Applied Probability.

[28]  J. Niño-Mora.  RESTLESS BANDITS, PARTIAL CONSERVATION LAWS AND INDEXABILITY , 2001 .

[29]  Wendy K. Smith,et al.  A Structural Approach to Assessing Innovation: Construct Development of Innovation Locus, Type, and Characteristics , 2002, Manag. Sci..

[30]  C. Tovey,et al.  Replacement under ongoing technological progress , 2004 .

[31]  John N. Tsitsiklis,et al.  The complexity of optimal queueing network control , 1994, Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory.

[32]  Kevin D. Glazebrook,et al.  Reflections on a New Approach to Gittins Indexation , 1996 .

[33]  Joseph C. Hartman.  An Economic Replacement Model with Probabilistic Asset Utilization , 2001 .

[34]  Kevin D. Glazebrook,et al.  Index policies for the maintenance of a collection of machines by a set of repairmen , 2005, Eur. J. Oper. Res..

[35]  Kevin D. Glazebrook,et al.  Sensitivity Analysis for Stochastic Scheduling Problems , 1987, Math. Oper. Res..

[36]  C. D. Wilkinson,et al.  Strategic alliance to address safety system obsolescence and maintainability , 1994, Proceedings of 1994 IEEE Nuclear Science Symposium - NSS'94.

[37]  A. S. Harding.  Markovian decision processes , 1970 .

[38]  P. Whittle.  Arm-Acquiring Bandits , 1981 .

[39]  Pameet Singh,et al.  Obsolescence Driven Design Refresh Planning for Sustainment-Dominated Systems , 2006 .

[40]  Shaul P. Ladany,et al.  A discounted machine-replacement model with an expected future technological breakthrough , 1988 .