Hello everyone,
I am looking to model an inventory-production process as a G/G/1 queue. The problem statement is as follows:
Customer demand for any particular part is fulfilled from the inventory system. Each unit of customer demand triggers one unit for replenishment through a production process. These replenishment units are grouped together and once an optimum size of the group/batch is reached, a production order is instituted and the batch is manufactured and stored in the inventory system.
When the production order is instituted, there are already a few other orders in the factor-floor due to which the batch under consideration cannot be fulfilled immediately, but needs to wait for its turn.There is no underlying pattern in production order fulfilment, rather it happens according to an arbitrary distribution pattern with a lot of ad-hoc decision making.
I am trying to arrive at a reliable estimation of the inventory in the system, taking into account the batch size per order and the probability distribution function.
Back-orders are not important for this problem and we are not taking into account lost sales.
This means,
I need to estimate E(Inventory), which, from my understanding is coded as given in the picture attached.
I am not sure of the probability model I should adopt, as there is no underlying probability distribution on the data-set I am working on. I am also not able to find a reliable estimate of the probability for the inventory replenishment system, while there have been estimates for stochastic modeling of production systems, on the basis of the G/G/1 model, taking into account the shop-floor utilization rate ( From the book stochastic modeling of manufacturing systems- a very detailed seminal text : Buzacott, J.A. and J.G. Shanthikumar. (1993). Stochastic Models of Manufacturing Systems. Prentice-Hall )
Any leads in this regard would be useful.
Looking forward to hearing from you all !
Thanks in advance,
Akhil Ramesh
Hi.
You'd better model your problem as a stochastic process instead of queueing system. Also, You can approximate G/G/1 by an M/M/1. Moreover, the following paper will be useful.
A hybrid method for performance analysis of G/G/m queueing networks
finally, you should study section 7.2 from the following book:
Shortle, J.F., Thompson, J.M., Gross, D. and Harris, C.M., 2018. Fundamentals of queueing theory.
Regards
Take a look at make to stock queues literature for ideas. In general, it would be easier for your analysis of the demand process is a Poisson process because results for M/G/1 queues are readily available.
Please see section 9.4 on Batching Laws of Hopp and Spearman Factory Physics book
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