Analysis of Switching the Purchase Option in a Two‐Commodity Perishable Inventory System

This research examines a queueing‐inventory model that includes two perishable commodities, each having a distinct lifetime, service duration, lead time, and individual ( s , Q ) ordering policy. The system consists of two finite‐capacity waiting zones for two distinct types of clients, with arrivals governed by independent Poisson processes. A single server is assigned to serve both types of clients. To enhance client satisfaction, the system allows clients in the queue to switch their purchase option from one commodity to another before their service is completed. In this system, inventory depletion occurs either through client consumption or perishability. The service duration for both client types and the time required to switch the purchase option, as well as the lifespan and lead time of both commodities, follow independent exponential distributions. In this model, the joint probability distribution of a five‐dimensional stochastic process, system performance metrics, and the matrix geometric method is employed to derive the optimal total cost. The waiting time for both client types is analyzed through the Laplace–Stieltjes transform (LST). Numerical results are presented to demonstrate the proposed model. MSC2020 Classification: 60K25, 90B05