This paper deals
with the production-dependent failure rates for a hybrid manufacturing/remanufacturing
system subject to random failures and repairs. The failure rate of the manufacturing
machine depends on its production rate, while the failure rate of the
remanufacturing machine is constant. In the proposed model, the manufacturing
machine is characterized by a higher production rate. The machines produce one
type of final product and unmet demand is backlogged. At the expected end of
their usage, products are collected from the market and kept in recoverable
inventory for future remanufacturing, or disposed of. The objective of the
system is to find the production rates of the manufacturing and the
remanufacturing machines that would minimize a discounted overall cost
consisting of serviceable inventory cost, backlog cost and holding cost for
returns. A computational algorithm, based on numerical methods, is used for
solving the optimality conditions obtained from the application of the
stochastic dynamic programming approach. Finally, a numerical example and
sensitivity analyses are presented to illustrate the usefulness of the proposed
approach. Our results clearly show that the optimal control policy of the
system is obtained when the failure rates of the machine depend on its production
Kiesmuller, G.P. (2003) A New Approach for Controlling a Hybrid Stochastic Manufac-turing/Remanufacturing System with Inventories and Different Leadtimes. European Journal of Operational Research, 147, 62-71.
Kumar, S. and Putnam, V. (2008) Cradle to Cradle: Reverse Logistics Strategies and Opportunities across Three Industry Sectors. International Journal of Production Economics, 115, 305-315.
Esterman, M., Gerst, P., DeBartolo, E. and Haselkorn, M. (2006) Reliability Pre-diction of a Remanufactured Product: A Welding Repair Process Case Study. 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006, 5-10 November 2006, Chicago,
Min, H. and Ko, H.-J. (2008) The Dynamic Design of a Reverse Logistics Network from the Perspective of Third-Party Logistics Service Providers. International Journal of Production Economics, 113, 176-192.
Berthaut, F., Pellerin, R. and Gharbi, A. (2009) Control of a Repair and Overhaul System with Probabilistic Parts Availability. Production Planning and Control, 20, 57-67. http://dx.doi.org/10.1016/j.ijpe.2007.11.015
Zhang, T.Z., Wang, X.P., Chu, J.W. and Cui, P.F. (2010) Remanufacturing Mode and Its Reliability for the Design of Automotive Products. 5th International Conference on Responsive Manufacturing—Green Man-ufacturing (ICRM 2010), Ningbo, 11-13 January 2010, 25-31.
Kenne, J.-P., Dejax, P. and Gharbi, A. (2012) Production Planning of a Hybrid Manufacturing-Remanufacturing System under Uncertainty within a Closed-Loop Supply Chain. International Journal of Production Economics, 135, 81-93. http://dx.doi.org/10.1016/j.ijpe.2010.10.026
Ouaret, S., Polotski, V., Kenné, J.-P. and Gharbi, A. (2013) Optimal Production Control of Hybrid Manufacturing/Remanufacturing Failure-Prone Systems under Diffusion-Type Demand. Applied Mathematics, 4, 550-559.
Hu, J.-Q., Valiki, P. and Yu, G.-X. (1994) Optimality of Hedging Point Policicies in the Production Control of Failure Prone Manufacturing Systems. IEEE Transactions on Automatic Control, 39, 1875-1880.
Martinelli, F. (2007) Optimality of a Two-Threshold Feedback Control for a Manufacturing System with a Production Dependent Failure Rate. IEEE Transactions on Automatic Control, 52, 1937-1942.
Martinelli, F. (2010) Manufacturing Systems with a Production Dependent Failure Rate: Structure of Optimality. IEEE Transactions on Automatic Control, 55, 2401-2406. http://dx.doi.org/10.1109/TAC.2010.2054790
Gharbi, A., Hajji, A. and Dhouib, K. (2011) Production Rate Control of an Unreliable Manufacturing Cell with Adjustable Capacity. International Journal of Production Research, 49, 6539-6557.
Dehayem, N.F.I., Kenne, J.P. and Gharbi, A. (2011) Production Planning and Repair/Remplacement Switching Policy for Deteriorating Manufacturing Systems. International Journal of Advanced Manufacturing Technology, 57, 827-840.