【正文】 graphical or other considerations, the stops have been partitioned into sectors. Each sector is served by a single vehicle. Beullens et al. provide an excellent survey of sector design models in reverse logistics. The problem is considered within a multiperiod planning horizon. This raises the question of whether to use a different stop routing sequence each period or to use the same stop sequence. For ease of implementation, some dispatchers prefer a fixed daily stop routing sequence. Fixed routing has the advantage of enhancing regularity of service and increasing driver performance through familiarity. Unless stated otherwise, the sequence of visited stops by a vehicle, once determined, is assumed to be the same each period. Also in a given period, one may choose not to visit a stop when there is no delivery volume even if there are some materials to be returned. This additional decision adds another level of plexity to an already difficult problem. To keep the problem tractable, it is assumed that each stop is visited 4 every period. Moreover, in the motivating example (ARC), all hospitals have a positive demand on most days. Hence for making the strategic policy, it is believed that not much is lost with this assumption. Operationally, one can simply skip a stop that has no demand. For a given vehicle route, the reverse logistics strategy will depend on the cost of leaving returning materials at stops. Obvious examples of explicit factors are the direct charge at a stop for holding returning materials and the extra materials (for example, packing materials such as boxes, containers, and pallets) needed for delivery due to delays in their return. Background Only recently, reverse logistics has bee a topic of research concern. Much of the previous work has been exploratory, emphasizing the need and importance of reverse logistics issues. General frameworks have been provided. Only recently, researchers have considered the use of quantitative techniques to various issues related to reverse logistics. Fleischmann et al. offer a survey focused on distribution planning, inventory management, and production planning. BloemhofRuward et al. examined distribution issues such as location of collection points in a reverse logistic system. Jayaraman et al. developed a 0–1 mixed integer singleperiod deterministic model for determining the distribution/remanufacturing locations to open, the quantities to stock, the quantities of product to ship from an open facility to customers, and the quantities of recovered materials to ship from customers to open facilities. Designing vehicle routes was not recent book by Dekker et al. provides a pilation of recent research that considers issues like collection and distribution, work design, inventory control, and routing in a reverse logistics (closedloop) systems context. Imbedded in reverse logistics system design is the problem of routing vehicles to serve a set of locations for both delivery and backhaul of products. Beullens et al. discuss the collection and vehicle routing issues in a reverse logistics systems. They list various features of reverse logistic systems that make the existing normative vehicle routing models generally inapplicable. For example, the classical capacitated vehicle routing problem (CVRP) considers only deliveries or only backhauls but not the bination of inbound and outbound flow, The models of the vehicle routing problem with backhauling (VRPB) bining deliveries and pickups assume that the backhaul points are visited only after all deliveries are made, A few researchers consider mixed loads (vehicle routing problem with mixed deliveries and collection (VRPM), and vehicle routing problem with pickup and delivery (VRPPD)) where pickups can be made before all deliveries. for a survey of these and related problems. However, there are two key features of the proposed problem that distinguishes it from these models。 1 附件：外文翻譯原文 Reverse logistics: simultaneous design of delivery routes and returns strategies 1． Abstract A reverse logistics problem, motivated by blood distribution of the American Red Cross, is examined where containers in which products are delivered from a central processing point to customers (stops) in one period are available for return to the central point in the following period. Any container not picked up in the period following its delivery incurs a penalty cost resulting primarily from operating costs and customer dissatisfaction. The result is a dynamic logistics planning problem where in each delivery period the vehicle dispatcher needs to design a multistop vehicle route while determining the container quantities to be picked up at each stop. This research is unique in that route design and pickup strategies are developed simultaneously, where stop volumes are known only probabilistically over a planning horizon. A heuristic procedure is developed for treating the route designpickup strategy planning problem. 2． Introduction There are many motivations for planning the reverse logistics channel. Some are economic and others are environmental. With continuing pressures to reduce operating costs while often incurring additional costs brought about by environmental restrictions, firms must be concerned with the costs of returning materials associated with the products that they deliver. Examples of returning materials are products in their original form returned for repair or direct reuse (defective products and reusable containers such as boxes and pallets)； portions of a product after disassembly that may have value for inclusion in subsequent products (precious metals and valuable ponents)； and materials associated with a product that may be recycled (glass, paper, plastics, and metals). This research concerns returni