On the optimality of the sequential approach for network design problems of service operations

We consider the problem of service network design: choosing the optimal number, locations, and service capacities of facilities, taking into account that facilities may have a finite or an infinite waiting room. Accordingly, our service measure is either the percentage of blocked customers or the percentage of customers who need to wait in line. The goal is to minimize the total cost, which consists of costs associated with traveling, blocking or queueing delay, service capacities, and operating (fixed) costs. We derive structural results when facilities are on a two-node network, and then use them to study the problem for a general network. We prove that the cost of service capacity and the cost of blocking or queueing delay are independent of the number of opened facilities as long as all facilities are identical in terms of their design parameters c and K (or only c in the case of an infinite waiting room). We use our results to develop an efficient algorithm that solves the problem for general networks. Finally, to demonstrate the applicability of our results and tractability of our algorithm, we discuss as an example an industrial-size problem, which considers the drive-through operations of McDonald's in the Toronto metropolitan area.