Selecting hierarchical facilities in a service-operations environment

Abstract This paper presents and solves a hierarchical model for the location of service facilities and further looks at the operational issues associated with managing such facilities. By the very nature of the demand they serve, service systems require that timely service be readily available to those who need it. We argue that the location–allocation of such facilities often involves several layers of service. When all of a facility’s resources are needed to meet each demand for service, and demand cannot be queued, the need for a backup unit may be required. Effective siting decisions must address both the need for a backup response facility for each demand point and a reasonable limit on each facility’s workload. The paper develops an integer linear programming model for locating facilities offering several layers of service. A Lagrangian relaxation methodology coupled with a heuristic is employed. Results of extensive computational experiments are presented to demonstrate the viability of the approach.

[1]  Marvin B. Mandell,et al.  Covering models for two-tiered emergency medical services systems , 1998 .

[2]  Peter B. Keenan.  Spatial decision support systems for vehicle routing , 1998, Decis. Support Syst..

[3]  Ralph H. Sprague,et al.  Building Effective Decision Support Systems , 1982 .

[4]  Hasan Pirkul,et al.  Production, Transportation, and Distribution Planning in a Multi-Commodity Tri-Echelon System , 1996, Transp. Sci..

[5]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[6]  Marshall L. Fisher,et al.  An Applications Oriented Guide to Lagrangian Relaxation , 1985 .

[7]  Ulrich Faigle,et al.  A Lagrangian relaxation approach to the edge-weighted clique problem , 2001, Eur. J. Oper. Res..

[8]  Vladimir Marianov,et al.  Hierarchical location-allocation models for congested systems , 2001, Eur. J. Oper. Res..

[9]  Mark S. Daskin,et al.  APPLICATION OF AN EXPECTED COVERING MODEL TO EMERGENCY MEDICAL SERVICE SYSTEM DESIGN , 1982 .

[10]  R L Church,et al.  A hybrid FLEET model for emergency medical service system design. , 1988, Social science & medicine.

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  Hasan Pirkul,et al.  Capacitated emergency facility siting with multiple levels of backup , 1993, Ann. Oper. Res..

[13]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[14]  Erik Rolland,et al.  VisOpt: a visual interactive optimization tool for P-median problems , 1999, Decis. Support Syst..

[15]  Subhash C. Narula.  Hierarchical location-allocation problems: A classification scheme , 1984 .

[16]  Moshe Dror,et al.  Interactive graphical computer application for large-scale cattle feed distribution management , 1997, Decis. Support Syst..

[17]  Sridhar Narasimhan.  The Concentrator Location Problem With Variable Coverage , 1990, Comput. Networks ISDN Syst..

[18]  Sheng-Roan Kai,et al.  NETCAP—An Interactive Optimization System for GTE Telephone Network Planning , 1992 .

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

[20]  James M. Tien,et al.  Improved formulations to the hierarchical health facility location-allocation problem , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  Ellis L. Johnson,et al.  A note of the knapsack problem with special ordered sets , 1981, Oper. Res. Lett..

[22]  Daniel Serra,et al.  The Coherent Covering Location Problem , 1996 .

[23]  M. Brandeau,et al.  An overview of representative problems in location research , 1989 .

[24]  Rajan Batta,et al.  Covering-Location Models for Emergency Situations That Require Multiple Response Units , 1990 .

[25]  Richard L. Church,et al.  A Bicriterion Maximal Covering Location Formulation Which Considers the Satisfaction of Uncovered Demand , 1991 .

[26]  Vijay V. Vazirani,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001, JACM.

[27]  Di Yuan,et al.  A Lagrangian Heuristic Based Branch-and-Bound Approach for the Capacitated Network Design Problem , 2000, Oper. Res..

[28]  C. Robert Kenley,et al.  Gaussian influence diagrams , 1989 .

[29]  David J. Eaton,et al.  Determining Emergency Medical Service Vehicle Deployment in Austin, Texas , 1985 .

[30]  J. Current,et al.  Capacitated Covering Models , 1988 .

[31]  H. Pirkul,et al.  The Maximal Covering Location Problem with Capacities on Total Workload , 1991 .

[32]  S. Selcuk Erenguc,et al.  Modeling the order picking function in supply chain systems: formulation, experimentation, and insights , 2001 .