An Optimization of Home Delivery Services in a Stochastic Modeling with Self and Compulsory Vacation Interruption

Abstract

This study presents and discusses the home delivery services in stochastic queuing-inventory modeling (SQIM). This system consists of two servers: one server manages the inventory sales processes, and the other server provides home delivery services at the doorstep of customers. Based on the Bernoulli schedule, a customer served by the first server may opt for a home delivery service. If any customer chooses the home delivery option, he hands over the purchased item for home delivery and leaves the system immediately. Otherwise, he carries the purchased item and leaves the system. When the delivery server returns to the system after the last home delivery service and finds that there are no items available for delivery, he goes on vacation. Such a vacation of a delivery server is to be interrupted compulsorily or voluntarily, according to the prefixed threshold level. The replenishment process is executed due to the (s,Q) reordering policy. The unique solution of the stationary probability vector to the finite generator matrix is found using recursive substitution and the normalizing condition. The necessary and sufficient system performance measures and the expected total cost of the system are computed. The optimal expected total cost is obtained numerically for all the parameters and shown graphically. The influence of parameters on the expected number of items that need to be delivered, the probability that the delivery server is busy, and the expected rate at which the delivery server’s self and compulsory vacation interruptions are also discussed.

Modeling of Junior Servers Approaching a Senior Server in the Retrial Queueing-Inventory System

“…Aghsami et al [23] proposed a multi-server queuing-inventory model based on the hospital blood bank, considering the request for blood as arrival and blood as inventory. Selvakumar et al [24] analyzed the home delivery service facility in the QIS considering two distinct servers. The first server was always available in the system in order to maintain the sales of items, and the second server was used for the delivery process of purchased items who is offered the vacation facility.…”