مدل طراحی شبکه لجستیک با مدیریت موجودی توسط فروشنده

In this paper, we study a logistics network design problem with vendor managed inventory in which the company is in charge of managing inventory for its downstream warehouses and retailers, and can choose whether to satisfy each retailer's demand. The problem incorporates the location, transportation, pricing, and warehouse-retailer echelon inventory replenishment decisions. Traditionally, these decisions are made separately. We formulate the problem as a set-packing model and solve it using branch-and-price. The pricing problem that arises from each iteration of the column generation procedure is an interesting nonlinear IP problem. We show the pricing problem can be solved in time for each warehouse, where n is the number of retailers. The computational results shed insights on the benefits that the integrated approach can achieve significant profit improvement. The computational results also highlight the efficiency of the solution algorithm.

Vendor managed inventory (VMI) is an effective supply chain planning technique that aims at reducing logistics cost and improving service by coordinating the operations of different logistical entities across the supply chain. Traditionally, each logistical entity involved in the supply chain manages its own inventory independently. By centralizing the inventory control and coordinating the multi-echelon inventory replenishment under VMI, the system-wide logistics cost can be significantly reduced and the service level can be improved. As shown by Simchi-Levi et al. (2003), Ballou (2004), and Yang et al. (2010), a unified systems approach is required to successfully implement VMI, which can help effectively integrate the supplier, its downstream warehouses and retailers so that the product is produced and distributed at the right quantities, to the right locations, and at the right time. Motivated by this recent popular supply chain initiative — vendor managed inventory, in this paper, we study a logistics network design problem integrating multi-echelon inventory management under the VMI framework in which the supplier manages the inventory of a single product for its downstream warehouses and retailers. Under this VMI framework, the system-wide inventory, including the inventory maintained at both warehouses and retailers, is owned by the supplier. The supplier is the sole decision maker who is in charge of the warehouse-retailer echelon inventory replenishment, the transportation of the product from it to the warehouses and from the warehouses to the retailers, and the price of the product. The warehouse-retailer echelon inventory is owned by the supplier until it is sold. The goal of the supplier is to maximize the total profit. A supply chain distribution network's physical structure can substantially affect its performance and profit margin. Most existing research on supply chain network design pursues a cost-minimization objective and tries to satisfy all the demands. However, the additional revenue generated from serving some retailers could be much lower than the cost associated with serving them. Thus, trying to satisfy all the retailers' demands might not give us the highest profit. As shown by Shen (2006), it could be more profitable for a company to lose some potential demands to competitors. It is difficult to determine whether it is profitable to serve each individual retailer a priori. Thus, we intend to propose a logistics network design model that can help simultaneously determine the location, warehouse-retailer assignment, warehouse-retailer echelon inventory replenishment, sale price, and which set of retailers to serve. The problem can be described as follows. We consider a company that produces a single product in a production site. We are given a set of retailers each of which faces a deterministic demand at a constant rate. We are also given a set of potential warehouse locations and each warehouse is assumed to be uncapacitated. The product will be shipped from the production site to certain retailers via some selected warehouses. The company wants to determine (i) the number and locations of the warehouses to open and the retailers to serve, (ii) the retailer assignments, (iii) the warehouse-retailer echelon inventory replenishment policy, and (iv) the sale price of the product associated with each warehouse located, so as to maximize the total profit which equals to the total revenue minus the total cost. The cost components include the warehouse establishing and operating cost, the warehouse-retailer echelon inventory related cost, and the shipment cost from the production site to the warehouses open and from each open warehouse to respective retailers served. The cost of establishing and operating a warehouse is fixed, which is assumed to be independent of the number of retailers assigned to that warehouse. Comparing with other logistics network design models in the literature, the novelties of our model lie in the following three aspects. First, it brings the VMI concept into logistics distribution network design with a profit-maximizing objective. Second, it allows the supplier to decide whether to serve each retailer, i.e., the supplier can choose the set of retailers to serve within the multi-echelon inventory management context. This gives rise to a set-packing profit-maximizing model. It is unlike other traditional multi-echelon logistics network design models which pursue a cost-minimizing objective and try to satisfy all the demands. Third, we use extensive computational experiments to demonstrate the potential practical impact of integrated decision-making by comparing the solutions obtained from our model with the traditional sequential decision-making process. The average benefit ranges from 10.4% to 21.7% in terms of the total profit. The computational results also shed insights on the benefits of our model with the supplier having retailer-serving flexibility over the traditional model that requires all the demands should be served. The rest of this paper is organized as follows. In Section 2, we review the related literature. In Section 3, we present a set-packing model with a profit-maximizing objective for our network design problem. In Section 4, we study the solution procedure which includes the solution to the pricing problem and a speed up heuristic for column generation. In Section 5, we present a traditional sequential decision-making approach for the problem. In Section 6, we report and discuss the computational results. Finally, we outline a few generalizations of our model and conclude the paper in 7 and 8, respectively.

In this paper, we study a logistics network design problem with vendor managed inventory in which the company is in charge of managing inventory for its downstream warehouses and retailers, and can choose whether to fulfill each retailer's demand. We formulate the problem as a set-packing model and solve it using branch-and-price. The pricing problem that arises from each iteration of the column generation procedure is an interesting nonlinear IP problem. We propose an efficient algorithm which runs in View the MathML sourceO(n2logn) time to tackle it. Furthermore, we propose a heuristic to speed up the column generation procedure. We use extensive computational experiments to compare the solution of our integrated decision-making model with the one of the traditional sequential decision-making model. The average benefit ranges from 10.4% to 21.7% in terms of the total profit. The computational results also shed insights on the benefits of our model with the supplier having retailer-serving flexibility over the traditional model that requires all the demands should be served. In the literature, most of the integrated supply chain network design models assume one level of warehouses. Practically, we might have two or even more level of facilities. Also currently, we can only deal with medium size problem instances. Therefore, we want to explore the possibility of designing efficient approximation algorithms for it and its variants (cf. Du et al., 2010; Du et al., this issue; Xu and Du, 2006, Xu and Yang, 2009, Xu and Zhang, 2008 and Zhang, 2006), and being able to solve large-scale instances of the problem. Each of these could be an interesting topic for further investigation in future research.