Modeling and Solving the Joint Replenishment Problem with Cross-Selling Effects Considering One Shared Minor Item

Abstract

In this paper, we provide a model to handle multiple replenishment cycles and the cross-selling of multiple major items with one minor item, while allowing partial late delivery. The optimization analytic expression of the model is finally obtained by utilizing the convexity of cost function for F and using the first-order conditions in optimization theory. Numerical examples and sensitivity analysis demonstrate the effectiveness of the model and algorithm, which offers a competent solution for practical applications.