Optimal selection of third-party logistics providers using integer programming: a case study of a furniture company storage and distribution

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.