Socially optimal location of facilities with fixed servers, stochastic demand and congestion (ABSTRACT)
Castillo, I., A. Ingolfsson, and T. Sim
published: 2009 | Research publication | Refereed Journals - ODS
Castillo, I., A. Ingolfsson, and T. Sim (2008). "Socially optimal location of facilities with fixed servers, stochastic demand and congestion", Production & Operations Management, 18(6):721-736.
ABSTRACT: We consider two capacity choice scenarios for the optimal location of facilities with fixed servers, stochastic demand and congestion. Virtual call centers, consisting of geographically dispersed centers, walk-in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems are motivating examples of such facilities. The choice of location for such facilities influences the travel cost for users as well as their waiting times. In contrast to most previous research, we explicitly embed both customer travel/connection and delay costs in the objective function and solve the location-allocation problem as well as choose service capacities for each open facility simultaneously. The choice of capacity for a facility that is viewed as a queueing system with Poisson arrivals and exponential service times could mean choosing a service rate for the servers (scenario 1) or choosing the number of servers (scenario 2). We express the optimal service rate in closed form in scenario 1 and the (asymptotically) optimal number of servers in closed form in scenario 2. This allows us to eliminate both the number of servers and the service rates from the optimization problems, leading to tractable mixed-integer nonlinear programs. Our computational results show that both problems can be solved efficiently using a Lagrangian relaxation optimization procedure.
revised Oct 19/09
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