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

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