Allocating servers to facilities, when demand is elastic to travel and waiting times

Public inoculation centers are examples of facilities providing service to customers whose demand is elastic to travel and waiting time. That is, people will not travel too far, or stay in line for too long to obtain the service. The goal, when planning such services, is to maximize the demand they attract, by locating centers and staffing them so as to reduce customers' travel time and time spent in queue. In the case of inoculation centers, the goal is to maximize the people that travel to the centers and stay in line until inoculated. We propose a procedure for the allocation of multiple servers to centers, so that this goal is achieved. An integer programming model is formulated. Since demand is elastic, a supply-demand equilibrium equation must be explicitly included in the optimization model, which then becomes nonlinear. As there are no exact procedures to solve such problems, we propose a heuristic procedure, based on Heuristic Concentration, which finds a good solution to this problem. Numerical examples are presented.

[1]  M. John Hodgson,et al.  Heuristic concentration for the p-median: an example demonstrating how and why it works , 2002, Comput. Oper. Res..

[2]  Oded Berman,et al.  Approximating performance measures for public services , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[3]  Oded Berman,et al.  Facility Location Problems with Stochastic Demands and Congestion , 2002 .

[4]  C. Revelle,et al.  The Standard Response Fire Protection Siting Problem , 1991 .

[5]  Vladimir Marianov,et al.  Location of Multiple-Server Congestible Facilities for Maximizing Expected Demand, when Services are Non-Essential , 2003, Ann. Oper. Res..

[6]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[7]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[8]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[9]  Vladimir Marianov,et al.  Location of multiple server common service centers or public facilities for minimizing general congestion an travel cost functions , 2011 .

[10]  Oded Berman,et al.  Optimal 2-Facility Network Districting in the Presence of Queuing , 1985, Transp. Sci..

[11]  J Malczewski.  Central Facility Location and Environmental Health , 1991 .

[12]  Mark S. Daskin,et al.  Network and Discrete Location , 1995 .

[13]  Vladimir Marianov,et al.  Location models for airline hubs behaving as M/D/c queues , 2003, Comput. Oper. Res..

[14]  K. Rosing.  Heuristic Concentration: A Study of Stage One , 2000 .

[15]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[16]  Oded Berman,et al.  Location-allocation on congested networks , 1986 .

[17]  Said Salhi,et al.  Facility Location: A Survey of Applications and Methods , 1996 .

[18]  Oded Berman,et al.  The Stochastic Queue p-Median Problem , 1987, Transp. Sci..

[19]  Charles S. Revelle,et al.  A gamma heuristic for the p-median problem , 1999, Eur. J. Oper. Res..

[20]  C. Revelle,et al.  Heuristic concentration: Two stage solution construction , 1997 .

[21]  Vladimir Marianov,et al.  Location Problems in the Public Sector , 2002 .

[22]  S. L. HAKIMIt.  AN ALGORITHMIC APPROACH TO NETWORK LOCATION PROBLEMS. , 1979 .

[23]  Vladimir Marianov,et al.  The capacitated standard response fire protection siting problem: Deterministic and probabilistic models , 1993, Ann. Oper. Res..

[24]  Polly Bart,et al.  Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph , 1968, Oper. Res..

[25]  Gilbert Laporte,et al.  Exact Solution to a Location Problem with Stochastic Demands , 1994, Transp. Sci..

[26]  Baoding Liu,et al.  New stochastic models for capacitated location-allocation problem , 2003, Comput. Ind. Eng..

[27]  Vladimir Marianov,et al.  Location–Allocation of Multiple-Server Service Centers with Constrained Queues or Waiting Times , 2002, Ann. Oper. Res..

[28]  Thomas A. Grossman,et al.  Location with Market Externalities , 1995 .