An Economic Order Quantity Model for Bundling Items with Probabilistic Demand

Abstract

The purpose of this study is to investigate the extension of the classical Economic Order Quantity (EOQ) model to the problem of bundling two or more products. In particular, we examine the case whereby a wholesaler sells bundled items consist-ing of multiple products. The wholesaler is concerned with determining the order size from each supplier and the time of placing the order. The products are received in lots at the beginning of each inventory cycle and combined into bundles con-taining one item of each type. It is assumed that the wholesaler adopts a pure bun-dling strategy whereby only bundled items are sold to retailers. Several inventory scenarios are considered in this thesis. For each scenarios, a mathematical model is formulated and used to derive the optimal order quantity. An explicit expression for the optimal quantity is obtained. First, bundling two types of products of per-fect quality is considered while assuming that the lead times are zero. Then, the model is generalized to the case of bundling more than two types of products. The effect of nonzero constant lead times is incorporated into each of the previously examined models. In each case, the wholesaler’s optimal ordering policy consist-ing of the optimal ordering quantity along with the reordering points is obtained. Finally, the underlying assumption of a constant demand rate is relaxed whereby the demand during lead time is considered as a random variable with a known probability distribution. In this case, the wholesaler’s optimal ordering policy is obtained by calculating the optimal ordering quantity, the reordering points, and the safety stock of each type of product needed to attain a required service level. Numerical examples illustrating the computations of the optimal solution are provided.