Abstract
We consider the production control problem of a production-inventory system with correlated demand inter-arrival and processing times that are modeled as Markovian Arrival Processes. The control problem is minimizing the expected average cost of the system in the steady-state by controlling when to produce an available part. We prove that the optimal control policy is the state-dependent threshold policy. We evaluate the performance of the system controlled by the state-dependent threshold policy by using the Matrix Geometric method. We determine the optimal threshold levels of the system by using policy iteration. We then investigate how the autocorrelation of the arrival and service processes impact the performance of the system. Finally, we compare the performance of the optimal policy with 3 benchmark policies: a state-dependent policy that uses the distribution of the inter-event times but assumes i.i.d.inter-event times, a single-threshold policy that uses both the distribution and also the autocorrelation, and a single-threshold policy that uses the distribution of the inter-event times but assumes they are not correlated. Our analysis demonstrates that ignoring autocorrelation in setting the parameters of the production policy causes significant errors in the expected inventory and backlog costs. A single-threshold policy that sets the threshold based on the distribution and also the autocorrelation performs satisfactorily for systems with negative autocorrelation. However, ignoring positive correlation yields high errors for the total cost. Our study shows that an effective production control policy must take correlations in service and demand processes into account.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.