Time dependent partial backordering rate under FCFS & LCFS policy

Abstract

In the traditional literature for production and inventory models, the backlogging phenomenon is often modeled using backordering and lost sale costs. But it has been recognized that backorder and lost sale costs are not easy to estimate throughout the inventory literature. Thus, different approaches are required to quantify the lost sales or backordering rate. Under the assumption that one major factor affecting the customer behavior under a stock out occasion is the waiting time, backordering rate should be modeled as a function of waiting time. But none of the existing research examined the time dependency of the backordering rate under both of Last-Come-First-Service (LCFS) and First-Come-First-Service (FCFS) policies. In this paper, it is assumed that the demand is partially backordered when a stock-out situation occurs and the rate of the backlogging follows an exponentially decreasing function of the waiting time. The waiting time is defined as the length of time customers have to wait until their backorders are satisfied, i.e. time between the moment of demand occurrence and the moment of the satisfaction of the demand. Then we develop mathematical models for backordering rate under LCFS and FCFS policies utilizing differential equations. Through numerical examples, the validity of the developed models is illustrated.