This paper investigates the selection of third-party logistics providers (3PLs) based on the best prices offered by them. The focus is on outbound logistics where 3PLs must have their own distribution centres for storage and picking activities. They must also have suitable trucks for distribution to different small-scale customers. The motivation for this paper is a case study from Germany in which a furniture company with hundreds of small customers in ten zones is seeking one or more 3PLs to do the distribution. A mathematical programming model was built based on integer programming where demand per order can be expressed using exponential distribution in each customer zone. The main contribution of this paper is that it finds the best 3PLs based on the different pricing methods of the various providers; this means including the location problem indirectly using the new integer programming model. The model takes into consideration three different methods of pricing based on the offers of five 3PLs. These different methods make it difficult for the decision makers to choose the best solution, especially if specific trends in demand are expected in the future for some customer zones. The results show that future increases in demand in terms of the number of orders or order size could affect the optimal solution. The best pricing method with the lowest variability in cost over time is selected.

本文根据第三方提供的最佳价格调查了第三方物流提供者（3PL）的选择。重点是出库物流，其中3PL必须拥有自己的配送中心以进行存储和拣配活动。他们还必须拥有合适的卡车，以分配给不同的小规模客户。本文的动机是来自德国的一个案例研究，在该案例中，一家家具公司在十个区域拥有数百个小客户，他们正在寻求一个或多个3PL来进行分配。基于整数规划建立了数学规划模型，其中可以使用每个客户区域中的指数分布来表示每个订单的需求。本文的主要贡献在于，它根据各种提供商的不同定价方法找到了最佳的3PL。这意味着使用新的整数编程模型间接包括位置问题。该模型基于五个3PL的报价考虑了三种不同的定价方法。这些不同的方法使决策者难以选择最佳解决方案，尤其是如果将来某些客户区域的需求趋势会有所变化时，尤其如此。结果表明，未来订单数量或订单大小方面的需求增长可能会影响最佳解决方案。选择成本随时间变化最小的最佳定价方法。特别是如果将来某些客户区域的需求有特定趋势的话。结果表明，未来订单数量或订单大小方面的需求增长可能会影响最佳解决方案。选择成本随时间变化最小的最佳定价方法。尤其是如果将来某些客户区域的需求有特定趋势的话。结果表明，未来订单数量或订单大小方面的需求增长可能会影响最佳解决方案。选择成本随时间变化最小的最佳定价方法。