A single period model where the lost sales recapture is a function of (r/p)

Abstract

We consider a lost sale recapture model in a newsvendor framework. In this paper we analyse how to recapture lost customers in which easier to win back old customers than it is to acquire new customers. We consider a single-period decision of a retailer facing uncertain and price dependent demand. The typical modeling of the problem in a newsvendor framework assumes the unfulfilled demand to be lost once and for all. However, in reality, there may be an opportunity to backlog the lost sales, by offering some incentive for waiting. Nevertheless, the retailer's procurement price may be higher, due to the likely cost increase of the emergency purchase. Further, not all the customers that could not buy in the first instance may avail the rebate offer and buy. The backlog fill rate is modeled as a function of the proportion of the rebate to the price. Then the retailer has to decide ahead of the realization of the demand the quantity to be ordered, the price and the rebate to be offered for backlogged sales that will maximize its expected profit. Numerical examples are presented to highlight model sensitivities to parametric changes. The back log fill rate is modelled as a log function of adding one to the proportion of rebate relative to the price. Sensitivities of optimal rebate to demand errors are carried out with uniform distribution.