A joint replenishment production-inventory model as an MMAP[K]/PH[K]/1 queue

In this paper we analyze a continuous review finite capacity production-inventory system with two products in inventory. With stochastic order quantities and time between orders, the model reflects supply chain that operates an environment high levels of volatility. The inventory is replenished using independent order-up-to (s, S) policy or can-order c, joint replenishment which endogenously determined lead times drive parameters policy. production facility modeled as multi-type MMAP[K]/PH[K]/1 queue there are K possible positions when placed age process busy has matrix-exponential distribution. We characterize determine steady state distribution matrix analytic methods. Using numerical methods obtain minimize total ordering related costs. present comparisons policies varying times, quantities, cost reductions. further demonstrate interplay terms