Market-oriented service network design when demand is sensitive to congestion

In this paper, we present a market-oriented service network design model in which the seller’s problem is to determine how many facilities to open, where to locate them, and which service capacities and service levels they should have to maximize overall profit. Our model explicitly considers the customers’ facility choice as a function of typical choice determinants, such as travel distance and congestion delays (which are endogenously impacted by the seller’s decisions) as well as other, exogenous factors such as price level and product variety. We relax the assumption adopted in many related works that the service provider has discretion as to the assignment of customers to facilities; instead, we allow customers to self-select based on their preferences for facility attributes according to an attraction-based choice model. Furthermore, we capture not only the effect of congestion on demand but also the reciprocal impacts of demand on congestion and service level by modeling each facility as an M/G/1 queue with service capacity as a decision variable. The resulting model represents a non-linear mixed-integer problem (MIP); however, we show that this problem can be linearized introducing several new continuous variables and constraints. To solve the linearized MIP to proven optimality or approximately, we develop an exact decomposition approach and heuristics. We report the performance testing of our approach with regard to run times and solution quality in an extensive computational experiment. A case study of the selection of locations for new convenience stores in Heidelberg, Germany illustrates the real-world applicability of the model using empirical market research data. An equivalent problem arises in a number of other applications, particularly in service shop industries such as restaurants and retailers. Surprisingly, profit maximization under customer-choice-driven behavior has rarely been considered as an objective in the related literature