Iterative Approach to Calculating the Order Fill Rate Under Purchase Dependence

Abstract

For the business environment under purchase dependence that characterizes customer purchase patterns observed in such areas as marketing, manufacturing systems, and distribution systems, this paper proposes a new approximate approach to calculate the order fill rate, probability of filling an entire customer order immediately from the shelf. The new approximate approach divides customer orders into item orders and calculates fill rates of all order types to approximate the order fill rate. In order to avoid the curse of dimensionality and prevent the solution from diverging for the large instances, we develop the greed iterative search algorithm (GISA) based on the Gauss-Seidel method. Through the computational analysis that compares the GISA with the simulation, we demonstrate that the GISA is a dependable algorithm to derive the stationary joint distribution of on-hand inventories in the type-K pure system. In addition, we present some managerial insights.