موجودی مدیریت فروشنده (VMI) همراه با محموله با نظر گرفتن یادگیری و فراموشی اثرات

The paper considers two research issues that usually interact in practice, which are the ‘VMI with consignment’ inventory policy and the ‘Learning Curve’. Under a VMI with consignment agreement, the vendor is the one who manages the buyer's inventory, and he holds the property of the inventory until the withdrawal of the buyer: this practice also offers to the vendor the possibility of revising its production plans and shipments according to alternative policy also exploiting the opportunity offered by learning in production. The paper, which considers a two-level supply chain system with a single-vendor and a single-buyer at each level, investigates and compares different policies that the vendor may adopt to exploit the advantages offered by the VMI with consignment agreement when the vendor's production process is subject to learning effects. The main result of the study is to show how learning in production can give flexibility to the supply chain stake holders in assigning the size and the time of each shipment.

This study is concerned with a special inventory management practice in supply chains known as VMI with consignment according to the classification of inventory systems proposed by Lee and Whang, 2008. Although consignment stock policy has been noted in the literature some time ago, an analytical model for the VMI with consignment policy was first proposed by Braglia and Zavanella (2003). The application of this policy (in practice) over different industrial sectors increased considerably in the past few years, confirming its economic benefits. In manufacturing environments, the ideal candidates for starting the implementation of a VMI with consignment policy are those firms whose items already provisioned according to an “open order” scheme. These codes (items) are generally inexpensive (e.g., nuts, screws, some raw materials) and their stock levels are frequently assessed by the vendor (Valentini and Zavanella, 2003). However, recently, the VMI with consignment business practice has been applied to manage the inventories of critical and strategic items that are usually associated with high financial costs (e.g., an interesting application may be found in spare part management of complex oil refineries, as in Zanoni et al. (2005)). In such a case, the vendor (producer of service parts) benefits by exploiting the economies of scale through larger batch sizes (where additionally the learning effects in production may be exploited), while the buyer (oil refiner) benefits by experiencing an higher service level of spare parts for his plant. Moreover, the vendor may also benefit from the situation when multi-buyers are considered (Zavanella and Zanoni, 2009). Furthermore, several VMIs with consignment applications involve items that are co-designed and/or produced under a co-makership agreement, thanks to the natural development of partnerships for manufacturing and provisioning complex and critical parts (e.g., frame and chassis in the automotive field, groups of preassembled codes for valves or appliances production). Such a partnership is very relevant when satisfying the demand for newly launched products, a period during which learning benefits are particularly perceived and observed by the vendor. Strong relationship of the VMI with consignment agreement usually establishes between the partners (e.g., vendor−buyer) evolves naturally from inexpensive codes to including critical and expensive ones. In the authors’ opinion, these considerations show how the present study may contribute to practice and to the understanding of the managerial implications when VMI with consignment policy is implemented as a partnership/coordination mechanism in firms. In particular, the VMI with consignment policy developed here is analysed in a setting where the vendor experiences learning in production. The effects of learning in different industrial settings have been investigated in several studies, e.g., lot sizing (Jaber and Bonney, 1999), dual resource constrained systems (Jaber et al., 2003), quality (Jaber and Guiffrida, 2004), supplier quality (Jaber et al., 2008), and supply chain coordination (Jaber et al., 2010). Although learning improves systems productivity and reduces its cost, it may be impeded by its opposite phenomenon-forgetting. Forgetting has usually been associated with production breaks during which the facility is idle, producing (performing) different products (activities), or due to labour turnover. These breaks result in some of the knowledge acquired (usually measured in units) to be lost; so relearning is experienced when the same production activities resume, which is costly to firms. The longer the break, the more costly the forgetting; so a production manager has to find the right trade-off between the different costs, including learning and relearning. The effects of learning and forgetting on the lot sizing problem were first investigated by Keachie and Fontana (1966), with a reasonably comprehensive review of the literature (1966–2011) appearing in Jaber and Bonney (2011). Recent studies on the topic are found in Jaber and Guiffrida (2007), Jaber and Bonney (2007), and Jaber et al. (2009). Although the applications of learning and forgetting to inventory problems have been of interest and relevance, very few researchers have investigated them in the context of a supply chain coordination. The first reported work is that of Nanda and Nam (1992), which investigates a joint replenishment policy in a two-level (manufacturer-retailer) supply chain with a single buyer, further extended to a multiple buyer case (Nanda and Nam, 1993). In these works, they considered lot-for-lot (LFL) policy and a quantity discount schedule. Forgetting effects were considered as a percentage of accumulated experience. Jaber et al. (2010) investigated a three-level supply chain (supplier−manufacturer−retailer) where the manufacturing operations undergo a learning-based continuous improvement process by encountering learning and forgetting effects in setups, production, and product quality. These articles demonstrate the paucity of the research that investigates learning and forgetting effects on joint replenishment policies in supply chains. Investigating learning and forgetting in a supply chain that adopts VMI with consignment as a business practice will make an original contribution to the literature, which this paper provides. The paper is organised as follows. Section 2 provides a brief description of the learning and forgetting process. The problem description and the notations used are presented in Section 3. Section 4 describes the model structure, hypotheses, and features for the different inventory strategies that have been identified. Section 5 provides numerical examples, and discussion of results where some managerial insights are drawn. Finally, in Section 6, some concluding remarks are presented and future extensions are outlined.

In this paper a VMI with consignment agreement between a vendor and a buyer is studied, considering the situation with vendor that experiences a learning effect in its production process. Moreover, we have taken into account a partial forgetting phenomenon between each production cycle to consider partial transfer learning (forgetting) between the production cycles. According to this scenario, five different policies to arrange shipments between a vendor and a buyer have been investigated: these policies have been analytically modelled. The approach followed for the comparison of different policies is a centralised one; thus the optimisation of the total system costs requires the knowledge of both parties parameters: this can represent the benchmark results from the total chain point of view. An explicit analytical comparison between the strategies was not possible; therefore a numerical analysis was carried out to get some insights about the different policies. The main result of the study is to show how it is more convenient to adjust shipments, depending on the main problem parameter values, under VMI with consignment agreement between a vendor and a buyer when learning effect is considered. In the numerical analysis we have shown the sensitivity of the different policies to the main parameters influencing the learning phenomenon, which are the learning rate (LR) and the length of the interruption period over which total forgetting occurs (B). Both the parameters exhibit a significant impact on total costs, with a different repartition on vendor and retailer components. Results over different policies exhibit different utilisations of the buyer's warehouse (that it is assumed with infinite capacity in the model presented) compared with the situation without learning: significantly larger in the first shipment and then decreasing to significantly smaller in the last shipments. Moreover, one of the policies proposed, i.e. policy I.3, showed a better performance of all settings investigated based on the numerical example given. Finally, by modelling the learning curve effects, management may then use these established learning models to better utilise capacity, improve the management of inventories, and coordinate production and distribution throughout the supply chain under a VMI with consignment business practice. Further developments of this study may consider the situation of multi-buyer (as in Zavanella and Zanoni, 2009) so as to investigate how the vendor may also benefit from this situation or situations with stochastic demand at the buyer. Additionally a limited capacity for the buyer's warehouse could be considered as a limiting parameter while choosing among different policies. Moreover, learning may occur in set-ups and product quality (Jaber et al., 2010) and also this issue may be investigated in future works. Additional attention should be finally devoted to enhance the model proposed, considering some kind of profit sharing mechanism to guarantee benefits to the vendor and to the buyer while adopting one of the proposed VMIs with consignment policy considering learning and forgetting effects.