Replacement of failed items in a two commodity retrial queueing-inventory system with multi-component demand and vacation interruption.

This study investigates a crucial aspect of inventory management, which is the process of replacing failed items. In dynamic commercial environments, it is essential to efficiently and strategically replace failed items to maintain operational efficiency and ensure profitability. We consider a two-commodity retrial queueing-inventory system with vacation interruption. Upon purchasing the first commodity, the second commodity is provided as a complimentary item. In contrast, no item is given as a complimentary for the purchase of the second item. Only the first commodity is stored in a dedicated pooled storage for replacement when it fails. The policy governs replenishing the first commodity while the second is replenished through instantaneous ordering. The model considers the multi-component demand rate for customer arrivals. Server vacations are initiated during customer absence in waiting hall or when the first commodity is unavailable. We formulate a level-dependent quasi-birth-and-death process, and its steady-state probability vector is computed using Neuts and Rao's truncation method. The stability condition for the system is derived, and various system performance measures, including expected total cost, number of replaceable items, and customers in the waiting hall and orbit, are established. The comparative analysis between the system with replacement is done with the regular model without replacement, which revealed the efficiency of replacement. The analysis of multi-component demand towards homogeneous arrival highlights the impact of multi-component demand on boosting customer arrival. Also, parametric sensitivity analysis has been conducted numerically over total cost, mean number of failed items for replacement, and mean number of customers in the waiting hall and orbit.