تخصیص فضای خرده فروشی و مدل های تعیین اندازه دسته تولید یکپارچه شده تحت فروش مدیریت شده موجودی و محموله ترتیبات سهام

In this paper, we develop integrated retail shelf space allocation and inventory models for a single item with a stock dependent demand. The integrated models are developed for a supply chain operating under vendor-managed inventory (VMI) and consignment stock (CS) agreement. More precisely, the supplier is responsible for initiating orders on behalf of the retailer and decides about the size of each order, the quantity to be displayed on the shelves, and the reorder point. In addition, the supplier owns the stock at the retailer’s premises until it is sold. We develop mathematical models to assess the benefits accrued by both parties as a result of the adoption of VMI–CS partnership. Results from the numerical experimental study show that such partnership is more attractive to all supply chain members when the retailer provides a flexible display capacity. Moreover, the supplier can use his/her selling price and the maximum allocated shelf space as negotiation means to benefit from the partnership.

Several programs of collaboration and coordination between supply chain (SC) partners have been successfully implemented in practice. Such programs help the different parties involved in the SC to collaborate, through the sharing of demand and inventory data, and to coordinate their decision making process in order to manage their inventory systems more efficiently and to improve their services. Vendor managed inventory (VMI) and consignment stock (CS) are collaborative initiatives which have been theoretically and empirically shown to improve SC efficiency and responsiveness. Under VMI partnership, the supplier is responsible for managing inventory levels at the retail store by determining the right timing and size of the orders. In return, the supplier gets a better visibility about the final customer demand. Historically, VMI originated in the retail industry to overcome some of the problems regarding the amount of required retail shelf space, the amount of inventory to be kept on hand, inventory obsolescence, and the logistics of returned products (Blatherwick, 1998 and Cachon and Fisher, 1997). Blatherwick (1998) stated that VMI practices can be very helpful because the suppliers with greater familiarity of a smaller number of products should be able to forecast and manage the flow of those products through the end of customers. The benefits of VMI are well recognized by successful retail businesses such as Wal-Mart, JC Penney, and Dillard Department Stores (Dong & Xu, 2002). Successful VMI implementations in retailing are more observed in the apparel industry (Kaipia & Tanskanen, 2003). For example, VF Corporation was able to increase the sales of its men’s jeans by 20% through the adoption of a replenishment system based on point-of-sales data and VMI principles. According to APICS Dictionary (Blackstone & Cox, 2004), consignment stock is defined as “The process of supplier placing goods at a customer location without receiving payment until after the goods are used or sold.” In other words, under CS partnership, the stock of items belongs to the supplier until it is used by the retailer. Therefore, the retailer is not charged for the cost of capital (financing cost) resulting from tying up capital in inventory. However, it is the retailer who decides about the timing and size of the orders. Although, it seems that only the retailer gains from CS partnership, Battini, Grassi, Persona, and Sgarbossa (2010) reported several benefits for the vendor as well. Indeed, through the adoption of CS partnership, the vendor reduces transportation and inventory holding costs, saves storage space as items are stored at the retailer’s location, and has access to real-time demand information. Moreover, CS initiatives are attractive for consumer items, such as metallic and plastic fasteners, small parts, tools, packaging parts, and personal protection equipment (Battini et al., 2010). The implementation of both VMI and CS initiatives leads to a change in the costs structure for both parties involved in the partnership. VMI and CS require a transfer of certain inventory cost components from one party to another as a result of the changes in decision making responsibility and inventory ownership. Table 1 compares these two SC partnerships against the combined VMI and CS initiative in terms of inventory decisions and costs responsibilities (Gümüş, Jewkes, & Bookbinder, 2008).Under VMI and VMI&CS programs, the supplier assumes the responsibility for setting the quantity and timing of the orders. Consequently, the cost of initiating an order shifts from the retailer to the vendor. However, under CS it is the retailer who decides about the ordering policy and is charged for any resulting costs. The holding cost is incurred by the retailer under VMI but it is shared under both CS and VMI&CS. Given the well-recognized benefits achieved by the implementation of VMI and CS programs, we consider a distributor/supplier who is investigating the economic feasibility of offering a combined VMI and CS partnership to a single retailer. We assume that the distributor is authorized to manage the stocks of a single item at the retail location. More precisely, the supplier decides about the ordering quantity, the quantity of the product to be displayed on the shelves, and the reorder point. In this framework, we develop an integrated model for the shelf space allocation and replenishment problems for a single item with a shelf space dependent demand. In order to assess the cost benefits of the VMI–CS partnership for both parties, we also determine optimal ordering policies for the supplier and retailer when they act independently (their decisions are not coordinated). To the best of our knowledge, this paper is the first to study the combined benefits of VMI and CS partnerships within the retailing context. The remainder of this paper is organized as follows. The following section presents relevant literature related to the problem addressed in this paper. Section 3 states the problem and outlines the modeling assumptions and notation. Section 4 presents the developed inventory model for the case of no partnership, while Section 5 provides the integrated space allocation and inventory model under VMI–CS partnership from the supplier’s perspective. Section 6 discusses the numerical analysis of the benefits realized by both parties when operating under VMI and CS partnership. Finally, the last section concludes the paper and suggests further research avenues.

In this paper, we considered the case where a supplier is authorized to manage the stock of a single retail product facing a stock dependent demand. More specifically, the supplier decides on behalf of the retailer about the sizing of each order, the maximum shelf space to be reserved for the item, and the reorder point. We developed profit-maximization models to study the advantages of the VMI–CS partnership. We also carried out an extensive sensitivity analysis to investigate the impact of key parameters on the problem decision variables and on both parties’ net profits. It was observed that when the retailer does not restrict the shelf space capacity, it is more economical for the supplier to display directly the ordering quantity on the shelves without temporarily storing it in the retailer backroom facility. Moreover, the partnership was beneficial to the retailer in all cases except for low inventory capital cost and low demand. This confirms that the retailer is more likely to generate more profit under VMI–CS as he/she is not charged for the capital cost of the stored items and the order initiation cost. The numerical experimental study also revealed that VMI–CS is more beneficial to all supply chain members when the retailer provides a flexible display capacity. A possible extension to this research work is to consider the case of a manufacturer with a finite rate of production. Another avenue for future research is to extend the current work to the case of multiple retailers each facing stock dependent demand.