Abstract
For high-value added products, machining tools’ lifespan significantly influences the quantity of procurement in machining process. Preemption of tools from the workpiece while processing is continuing is sometime beneficial to safeguard the product from the damage due to tool failure or its malfunction. Also an early discard of a tool is costly for the manufacturing operation. Therefore an optimal strategy for the tool life is sought here to determine the maximum allowable tool lifespan to preempt from the workpiece and to have an appropriate amount of tool stock in the crib to ascertain the proper running of the production schedule and tool inventory. Therefore, an impact of the machining tool lifespan on the production-inventory policy of the system is investigated in this paper. An integrated lifespan related inventory model for machining tools is developed to meet the responding accurate requirement of procurement and inventory. Two numerical examples are presented to illustrate the integrated model. The results show that the practical lifespan adoption of machining tools has significant impact on the whole quantity of procurement, and eventually influences the coordinating economic decision making.
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This research is supported by the National Natural Science Fund of China (NSFC.51375357).
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Appendix
Appendix
Results from ∂TC/∂T m =0.
In order to find the stationary point of the objective function in Equation (13), ∂TC/∂T m =0 leads to
from which we can write
Since 
and 
Equation (A.3) can be transformed to
which simplifies to
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Li, C., Chen, X., Sarker, B. et al. Determining the optimal procurement policy and maximum allowable lifespan for machining tools with stochastically distributed toollife. J Oper Res Soc 66, 2050–2060 (2015). https://doi.org/10.1057/jors.2015.30
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DOI: https://doi.org/10.1057/jors.2015.30