We suppose that a vehicle visits N ordered customers in order to collect from them two similar but not identical materials. The actual quantity and the actual type of material that each customer possesses become known only when the vehicle arrives at the customer’s location. It is assumed that the vehicle has two compartments. We name these compartments, Compartment 1 and Compartment 2. It is assumed that Compartment 1 is suitable for loading Material 1 and Compartment 2 is suitable for loading Material 2. However it is permitted to load items of Material 1 into Compartment 2 and items of Material 2 into Compartment 1. These actions cause extra costs that are due to extra labor. It is permissible for the vehicle to interrupt its route and go to the depot to unload the items of both materials. The costs for travelling from each customer to the next one and the costs for travelling from each customer to the depot are known. The objective is to find the routing strategy that minimizes the total expected cost among all possible strategies for servicing all customers. A dynamic programming algorithm is designed for the determination of the routing strategy that minimizes the total expected cost among all possible strategies. The structure of optimal routing strategy is characterized by a set of critical numbers for each customer.

我们假设车辆访问了N下令客户以从他们那里收集两种相似但不完全相同的材料。每个客户拥有的材料的实际数量和实际类型仅在车辆到达客户所在地时才知道。假定车辆具有两个车厢。我们将这些隔室分别命名为隔室1和隔室2。假定隔室1适合装入物料1，隔室2适合装入物料2。但是，允许将物料1的物料装入隔室2和物料的物料。 2进入隔室1。这些操作会由于额外的人工而导致额外的费用。允许车辆中断其行驶路线并前往仓库卸下两种物料。从每个客户到下一个客户的运输费用以及从每个客户到仓库的运输费用是已知的。目的是在为所有客户提供服务的所有可能策略中找到使总预期成本最小化的路由策略。设计了一种动态编程算法来确定路由策略，从而将所有可能策略中的总预期成本降至最低。最佳路由策略的结构以每个客户的一组关键数字为特征。设计了一种动态编程算法来确定路由策略，从而将所有可能策略中的总预期成本降至最低。最佳路由策略的结构以每个客户的一组关键数字为特征。设计了一种动态编程算法来确定路由策略，从而将所有可能策略中的总预期成本降至最低。最佳路由策略的结构以每个客户的一组关键数字为特征。