مدل محل موجودی برای زنجیره های تامین بزرگ سه سطحی

We study the location-inventory problem in three-level supply networks. Our model integrates three decisions: the distribution centers location, flows allocation, and shipment sizes. We propose a nonlinear continuous formulation, including transportation, fixed, handling and holding costs, which decomposes into a closed-form equation and a linear program when the DC flows are fixed. We thus develop an iterative heuristic that estimates the DC flows a priori, solves the linear program, and then improves the DC flow estimations. Extensive numerical experiments show that the approach can design large supply networks both effectively and efficiently, and a case study is discussed.

In the last decades, supply chain management has proved to be a primary lever for companies to lower their costs and improve their overall competitiveness. In particular, the strategic design of the supply network is of crucial importance. It deeply impacts the supply chain planning and eventually the performance of the company. Thus, the facility location problem and its variants have been the focus of much attention from the scientific community. However, the problem is less often approached from a supply chain management perspective (Melo et al., 2009). In particular, while inventory costs may have a significant effect on the cost balance and the positioning of facilities, inventory management considerations are often neglected. Furthermore, the problem remains difficult to solve for large supply chains in reality. Our research was inspired by the real-life case of a leading European glass manufacturer, mainly producing glass panes for the automotive and construction industries. Its supply chain includes 10 factories and around 500 customers (which can be retailers) throughout Europe. The case presented by the company concerns its reverse logistics network, and more precisely the return flow of reusable items (empty trestles) from the points of consumption to the factories. Currently, empty trestles are directly shipped back to the factories in the same truck that delivered the glass panes to the customer, whereas empty trestles can be folded and are thus less voluminous. The glass producer wishes to assess the advisability of an alternative strategy for the return flow: accumulating empty trestles in regional depots, to return them to factories in trucks that are better utilized. Consequently, inventory management decisions, such as the shipment size, play a central role, and have to be integrated with the location-allocation decisions within a single framework. We are therefore confronted with a fairly classic and difficult problem: the network design and inventory management of a three-level supply chain. In fact, this problem in the reverse logistics context bears a strong resemblance to that in a forward network. Solution methodologies can be applied equally well in both contexts, as indicated by Melo et al. (2009). We thus present our methodology in a general fashion, without distinguishing between the forward and reverse cases. Both will subsequently be discussed and exemplified. Inspired by this real-life case, we study the location of intermediary facilities in a three-level network where factories and customers have fixed locations, and fixed constant production and demand rates. We also want to consider the impact of inventory decisions, and of shipment size in particular. Our approach assists with the making of location-allocation decisions as well as inventory management decisions in an integrated fashion. In other words, the cost function covers transportation and facility fixed costs as well as inventory holding and handling costs, and thus underlines the important trade-off between these costs. The targeted decision level is strategic. We consider a single-period planning horizon and a single product. Furthermore, we allow for direct flows between factories and customers and consider capacitated vehicles. In order to be able to analyze large real-life problems, we develop a continuous optimization formulation (and avoid using integer variables). The latter is shown to decompose when the flows through the DCs are fixed. In this case, the inventory decisions can be computed from a closed-form equation and the location-allocation decisions follow from solving a linear program. Based on this, we then propose an iterative heuristic which, at each iteration, estimates the DC flows, solves a linear program, and then improves the DC flow estimations. The remainder of the paper is structured as follows. In the next section, we review the related literature. In Section 3, we present the problem and our mathematical modeling. A heuristic method is then proposed to solve it in Section 4. In order to assess the efficiency of the solution procedure, the heuristic is then tested on many different configurations in Section 5. In Section 6, we illustrate the application of the methodology in reverse logistics, to the case of the glass producer, and we discuss the application to forward supply networks. Finally, we conclude in Section 7.

In this paper, we present a new approach to design supply networks while integrating inventory decisions. Assumptions regarding inventory control (EOQ logic and perfect coordination) are made to integrate tactical/operational information at an appropriate level of detail in this strategic problem. They allow us to formulate a model that is both realistic and tractable. An iterative heuristic is proposed to solve the model and is shown to be both effective and efficient using extensive numerical experiments. Finally, its applicability to real-life problems is illustrated by means of a case study. The contribution of the paper to the literature lies mainly in the size and features of the supply networks that can be designed using our approach. First, a new location-inventory model is proposed and includes features that are generally applicable and common in practice, but rarely considered in the literature: capacitated transportation, multiple sourcing, direct shipments and inventory in every layer. Second, an iterative heuristic is devised to solve our continuous non-convex formulation. This heuristic solves one linear program at each iteration and is thus able to design large networks (1000 customers). To our knowledge, there is no other approach in the literature able to design three-level supply networks of such sizes. Furthermore, we show that the sizes of shipments between factories and customers, and between DCs and customers, can be computed a priori, independently of the location-allocation decisions. The heuristic we propose is intended to be simple and to directly take advantage of the specificities of our problem formulation. However, in the future, more evolved solution procedures could be devised, based on non-convex optimization techniques. Moreover, our approach could quite easily be extended to take intra-layer flows into account. Future research could also aim to analyze vehicle tours, another way to locally consolidate shipments.