Analytical characterisations of a seasonal compound Poisson demand process with growth trend

The seasonal compound distribution is of interest for the study of operations management, since it is widespread in reality. However, due to the difficulties involved in obtaining the analytical results for the seasonal compound distribution, studies are usually limited to employing stationary compound Poisson process. In the paper, the demand occurring in seasonal random environments with trend is discussed. We present a demand model in which demand occurs according to a homogeneous Poisson process and demand sizes varying seasonally. As the main results, the general closed‐form formulae for calculating demand, cumulative demand up to any time, and their Laplace transforms are developed, respectively. The analytical results of the seasonal demand model provide the operations management studies such as production/inventory control, service capacity planning and supply chain management under seasonal demand environment with a corner stone, which can be directly used to describe the demand of various operations management studies.