Compound Poisson demand with price-dependent intensity for fast moving items: price optimisation and parameters estimation

Abstract

We consider a single-period single-item inventory system. The demand is a compound Poisson process with price-dependent intensity and continuous batch size distribution. The intensity of the customers’ arrivals is sufficiently high to use a diffusion approximation of the demand process. Equations for retail price maximising of an expected profit with the optimal order quantity are obtained and an approximate solution is proposed. Numerical results illustrating the percentage of the increase in profit for linear price-intensity dependence are given. An approximate distribution of the selling time of a large order is obtained. Demand parameters estimation procedures based on two censored samples – the observed selling durations and demands – are discussed.