Ensuring feasibility in location problems with stochastic demands and congestion

被引:12
作者
Baron, Opher [1 ]
Berman, Oded [1 ]
Kim, Seokjin [2 ]
Krass, Dmitry [1 ]
机构
[1] Univ Toronto, Rotman Sch Management, Toronto, ON M5S 3E6, Canada
[2] Suffolk Univ, Sawyer Business Sch, Dept Informat Syst & Operat Management, Boston, MA 02108 USA
关键词
Location; network; queueing; congestion; MODEL;
D O I
10.1080/07408170802382758
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A location problem with stochastic demand and congestion where mobile servers respond to service calls originating from nodes is considered. The problem is of the set-covering type: only servers within the coverage radius of the demand-generating node may respond to a call. The service level constraint requires that at least one server must be available to respond to an arriving call, with some prespecified probability. The objective is to minimize the total number of servers. It is shown that earlier models quite often overestimate servers' availability and thus may lead to infeasible solutions (i.e., solutions that fail to satisfy the service level constraint). System stability conditions and lower bounds on system availability are developed by analyzing the underlying partially accessible queueing system. These lead to the development of two new models for which feasibility is guaranteed. Simulation-based computational experiments show that the proposed models achieve feasibility without significantly increasing the total number of servers. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix of Tables of Computational Results for Section 7.].
引用
收藏
页码:467 / 481
页数:15
相关论文
共 22 条
[1]   A RELIABILITY MODEL APPLIED TO EMERGENCY SERVICE VEHICLE LOCATION [J].
BALL, MO ;
LIN, FL .
OPERATIONS RESEARCH, 1993, 41 (01) :18-36
[2]   BOUNDING A PROBABILITY MEASURE OVER A POLYMATROID WITH AN APPLICATION TO TRANSPORTATION PROBLEMS [J].
BALL, MO ;
SHANTHIKUMAR, JG .
MATHEMATICS OF OPERATIONS RESEARCH, 1994, 19 (01) :112-120
[3]   THE MAXIMAL EXPECTED COVERING LOCATION PROBLEM - REVISITED [J].
BATTA, R ;
DOLAN, JM ;
KRISHNAMURTHY, NN .
TRANSPORTATION SCIENCE, 1989, 23 (04) :277-287
[4]   OPTIMAL SERVER LOCATION ON A NETWORK OPERATING AS AN M/G/1 QUEUE [J].
BERMAN, O ;
LARSON, RC ;
CHIU, SS .
OPERATIONS RESEARCH, 1985, 33 (04) :746-771
[5]  
Berman O, 2002, FACILITY LOCATION APPLICATIONS AND THEORY, P329
[6]  
BERTSIMAS D, 2007, INTRO QUEUEING UNPUB
[7]   The ex-post evaluation of the minimum local reliability level:: An enhanced probabilistic Location Set Covering Model [J].
Borrás, F ;
Pastor, JT .
ANNALS OF OPERATIONS RESEARCH, 2002, 111 (1-4) :51-74
[8]  
CALDENTEY R, 2007, OM20074 NEW YORK U S
[9]   ON POSITIVE HARRIS RECURRENCE OF MULTICLASS QUEUEING NETWORKS: A UNIFIED APPROACH VIA FLUID LIMIT MODELS [J].
Dai, J. G. .
ANNALS OF APPLIED PROBABILITY, 1995, 5 (01) :49-77
[10]   A MAXIMUM EXPECTED COVERING LOCATION MODEL - FORMULATION, PROPERTIES AND HEURISTIC SOLUTION [J].
DASKIN, MS .
TRANSPORTATION SCIENCE, 1983, 17 (01) :48-70