Competitive service network design when demand is sensitive to congestion

In this paper we present a market-oriented service network design model where the seller’s problem is to determine the number of facilities, their locations, their service capacity, and their service level such that overall profit is maximized. Our model explicitly takes into account customer choice of a facility as a function of typical choice determinants, such as travel distance and congestion delays (endogenously impacted by the seller’s decision), as well as other exogenous factors such as price level and product variety. We relax the assumption of many related works that the service provider has discretion about the assignment of customers to facilities; rather, we allow customers to self-select based on their preference for facility attributes according to an attraction-based choice model. Furthermore, we do not only capture the effect that congestion has on demand but also the reciprocal impact of demand on congestion and service level, respectively, by modeling each facility as an M/G/1 queue where service capacity is a decision variable. The resulting model is a nonlinear mixed-integer problem; however, we show that problem can be linearized and solved exactly by introducing several new continuous variables and "big M"constraints. We test the performance of our approach in an extensive computational experiment. A case study of locating new convenience stores in Heidelberg, Germany illustrates real-world applicability of the model using empirical market research data. The problem arises in a number of other applications, in particular in service shop industries such as restaurants, retailers, etc. but surprisingly, profit maximization under customer choice behavior has been hardly considered as an objective in the literature