Locating a single facility considering uncertain transportation time

It is discussed how to determine the location of a supplier's facility from which trucks pick up products and deliver them to customers. A major assumption is that customers impose penalties on the supplier for the earlier or later arrivals of products at the customers' facilities beyond the time windows pre-specified by customers. The objective is to minimize the expected total cost that consists of the transportation cost between customers and the supplier and costs resulting from the violation of time window constraints. A numerical example is provided and results of the sensitivity analysis for some parameters are also provided. And, model suggested in this paper is compared with the conventional center-of-gravity model.