A note on generalized single-vendor multi-buyer integrated inventory supply chain models with better synchronization

Abstract

In a recent paper, Hoque (2011) developed two single-vendor multi-buyer models with synchronization by transferring the vendor′s lot with equal and/or unequal sized batches. He reported that his proposed models lead to significant cost reductions when compared to the existing related ones in the literature. In this note, we show that the comparison of Hoque′s model with Zavanella and Zanoni′s (2009) model is not appropriate as they are based on different treatments of the total ordering costs. Furthermore, in case of zero transportation cost, we show that Hoque′s models lead to impractical solutions. Even when we adjust the total ordering costs to be similar to the one in Zavanella and Zanoni′ model, Hoque′s models do not generate promising results as reported with the original form of the ordering costs.

Introduction

A high level of coordination and cooperation among supply chain members is essential for survival in a very competitive market. Such collaboration is vital to efficiently manage inventory, deliver products to the final customer, mitigate the bullwhip effect, and respond quickly to sudden change in demand. In particular, the integrated vendor–buyers production and inventory decisions have received a lot of attention in recent years as it represents the building block for the wider supply chain. Typically, the retailers (buyers) observe a deterministic demand and order lots from the manufacturer (vendor). The vendor satisfies this downstream demand through manufacturing the requested product in lots, where each produced lot is shipped to the buyer in batches. The problem is to find the number of shipments, timing, and size of each batch such that the joint manufacturer and retailers cost is minimized.

There are several papers dealing with the integrated single-vendor multi-buyer problem. In general, the integrated solution results in a better solution than when the vender and buyers operate independently. However, the different parties will not benefit equally from the coordination. In addition to synchronizing shipments to the buyers, researchers proposed incentives in the form of discounts and various pricing schemes to make the coordinated solution attractive for both parties. Works in this line of research include Viswanathan and Piplani (2001), Bernstein et al. (2006), Li and Zhang (2008), Karabati and Sayin (2008), and among others. Authors who focused on the coordination and synchronization issues include Kim et al. (2006), Gurbuz et al. (2007), Sarmah and Goyal (2008), Hoque, 2008, Hoque, 2009, and Zavanella and Zanoni′s (2009). Among other issues addressed in the context of single-vendor multi-buyer include demand uncertainty (Bernstein and Federgruen, 2005), information sharing (Li and Zhang, 2008), and replenishment routing (Li et al., 2008).

Recently, Hoque (2011) proposed two single-vendor multi-buyer models with synchronization by transferring the vendor′s lot with equal and/or unequal sized batches to the buyers. He reported significant cost reductions compared to the existing related models in the literature.

In this note, we show that the comparison of Hoque′s model with Zavanella and Zanoni′s (2009) model is not appropriate as the two models are based on different functional forms of the total ordering costs. Furthermore, in the case of negelible transportation cost, we show that Hoque′s (2011) model leads to an unrealistic solution. When adjusting the total ordering costs to be similar to the ones in Zavanella and Zanoni′s model, Hoque′s model does not generate promising results as claimed in Hoque (2011) with original form of the ordering costs.

The remainder of this paper contains an analysis of Hoque′s models I and II (2011) in Section 2, modifications of some of Hoque′s models in Section 3, and some concluding remarks in Section 4.