extension of the maximal covering location-allocation...
TRANSCRIPT
Extension of the Maximal Covering Location-Allocation
Model for Congested System in the Competitive and User-
Choice Environment
N. Zarrinpoor, H. Shavandi*, J. Bagherinejad
Naeme Zarrinpoor, Student of MS Industrial Eng- Alzahra University Hassan Shavandi, Assistance professor of Industrial Eng- Sharif University of Technology
Jafar Bagherinejad, Assistance professor of Industrial Eng- Alzahra University
Keywords 1ABSTRACT
The main objective of facilities location and service system design is
covering of potential customers’ demand. Many location models are
extended with the covering objective and considered constraints,
details of problem and its different aspects. In this paper the maximal
covering location-allocation model for congested system is extended
in the competitive environment. In the proposed model, several
important characteristics such as spatial interaction model,
congestion, the competitive user-choice environment and probabilistic
demand are considered. The objective of the model is maximization of
the demand captured by each facility in the competitive environment.
The optimization software of lingo 8 and the genetic algorithm are
used for solving the small-size problems. Due to the complexity of
problem and its nonlinear nature, the software of lingo 8 cant solved
the large-size problems and the genetic algorithm is applied to solve
the larger size problems. Numerical results verify the effectiveness of
proposed algorithm for solving the model and show that the use of
queuing theory in service system design can improve different service
strategies, promote organization’s business process and increase
customer’s satisfaction.
© 2012 IUST Publication, IJIEPM. Vol. 22, No. 4, All Rights Reserved
**
Corresponding author. Hassan Shavandi Email: [email protected]
MMaarrcchh 22001122,, VVoolluummee 2222,, NNuummbbeerr 44
pppp.. 339933--440044
hhttttpp::////IIJJIIEEPPMM..iiuusstt..aacc..iirr//
IInntteerrnnaattiioonnaall JJoouurrnnaall ooff IInndduussttrriiaall EEnnggiinneeeerriinngg && PPrroodduuccttiioonn MMaannaaggeemmeenntt ((22001122))
Facility location,
Competitive environment,
Congestion,
User-choice environment,
Genetic algorithm
٭
-
*
[email protected] .Maximal Covering Location Problem
3.Congestion 4. Emergency Medical Service (EMS)
hhttttpp::////IIJJIIEEPPMM..iiuusstt..aacc..iirr//
ISSN: 2008-4870
[1]
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Mobile server.3
Maximum Availability Location Problem.4
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. [17]
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NP-complete
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[20]
1 .Queuing Maximal Covering Location-Allocation Model 2 .Maximum Expected Covering Location Model
[21]
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3 .clustering search 4 .user-choice
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Our
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0 2 2 2,4 8,9 8.159267 2.139917 0.7922 1,5 7.42910 3.041147 0.7095 0.1044
2 3 4,7,8 1,2 5.732489 3.568021 0.6164 2,3 4.21217 3.05702 0.5795 0.0599
3 2 2,4 7,8,9 9.717945 1.723232 0.8494 1,5,6 8.08272 1.96514 0.8044 0.0530
3 3 4,8,9 1,2,5 7.132690 2.992325 0.7045 1,2,3 5.36251 2.29469 0.7003 0.0060
12 2 2 2,4 8,10 10.52336 2.145364 0.8307 5,6 8.49182 3.64928 0.6994 0.1581
2 3 1,3,6 8,10 7.634409 3.736332 0.6714 7,10 5.27378 4.05808 0.5651 0.1583
3 2 10,11 1,2,8 12.12807 1.791802 0.8713 4,7,9 9.37492 3.32281 0.7383 0.1526
3 3 8,10,11 1,2,5 9.233452 3.390546 0.7314 1,5,7 6.37033 2.77489 0.6966 0.0476
2,5.0,4.0,2.0 b
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Number
of node p R
Competitor’s
location
Lingo Genetic algorithm
Our
location
Our
market
share
Our
location
Our
market
share
Gap
10 2 2 1,3 2,5 10.2572 5.45933 0.6526 -
2 3 6,7,8 1,2 8.731786 5.548723 0.6114 1,2 6.96158 4.45793 0.6096 0.0034
3 2 8,9 1,2,3 14.79692 2.701132 0.8456 1,2,7 11.2733 3.30435 0.7733 0.0855
3 3 6,8,9 1,2,3 12.83834 4.678136 0.7329 1,2,5 8.60633 3.33387 0.7208 0.0165
12 2 2 1,4 - - - - 2,6 13.5007 5.47663 0.7114 -
2 3 4,9,11 - - - - 2,3 7.05733 5.66078 0.5549 -
3 2 3,4 - - - - 1,2,11 16.3291 3.85507 0.8090 -
3 3 1,3,6 8,10,11 14.05441 4.841408 0.7438 7,9,10 9.54576 3.91114 0.7094 0.0462
2,5.0,4.0,2.0 b4ih
competitor's
market share
Our market
shareCometitor locationour locationr p
0.36300.637010.890120.34923,5,9,12,142,11,13,17,195
5 0.40450.595511.790917.50811,2,4,6,8,183,9,10,11,146
0.41300.587010.540515.57031,6,7,12,16,17,192,3,9,11,187
0.31790.682111.699821.40492,6,7,16,198,10,11,12,17,18 56
0.33970.660311.086919.82445,6,9,14,17,191,3,10,11,13,186
0.38090.61919.5566116.18121,3,4,11,12,14,172,6,9,10,18,197
0.24870.751310.014423.24791,5,6,14,182,8,9,11,12,17,195
7 0.28390.71619.3723120.44201,2,4,6,8,189,10,11,12,13,14,196
0.30920.69088.4230617.19793,5,8,9,12,14,181,2,11,13,16,17,197
2,5.0,4.0,2.0 b4ih
competitor's
market share
Our market
shareCometitor locationOur locationr p
0.4551 0.544919.216126.60353,13,16,20,271,10,11,21,23 5
0.46630.533720.839423.47095,8,12,22,23,272,6,13,15,166
0.47420.525820.079721.240714,16,17,21,22,23,255,6,8,10,187
0.38920.610817.799228.31543,7,11,15,2112,14,23,25,26,28
6 0.41030.589717.120225.75853,6,9,15,27,282,5,7,10,13,256
0.42810.571916.315722.06275,13,16,17,21,27,282,8,10,11,12,187
0.31880.681214.378430.57075,8,14,19,226,11,12,13,23,25,265
7 0.33500.665013.310826.37835,6,11,20,23,252,9,10,19,26,27,286
0.37900.621015.195623.01412,6,16,17,19,24,273,10,12,18,21,22,297
2,5.0,4.0,2.0 b4ih
competitor's
market share
Our market
share Cometitor
location Our location r p
0.5293 0.4707 28.1119 26.5403 6,22,23,32,34 14,15,18,24,37 5 5
0.5364 0.4636 25.2868 24.0506 1,7,20,28,28,36,38 21,23,30,33,39 6
0.5444 0.4556 26.7028 22.7321 6,22,23,31,32,34,38 8,15,16,18,35 7
0.4011 0.5989 21.9167 33.6160 6,23,24,35,39 2,16,21,25,29,33 5 6
0.4319 0.5681 21.2328 28.2315 6,22,23,31,32,34 11,15,16,25,28,35 6
0.4532 0.5468 21.3109 25.8281 2,4,6,8,14,29,31 1,12,16,23,33,38 7
0.3684 0.6316 21.0822 37.8657 7,18,25,34,35 1,5,6,10,11,15,36 5 7
0.4125 0.5875 22.3377 28.9991 4,11,13,15,27,38 2,3,5,16,19,22,25 6
0.4311 0.5689 18.3387 26.3276 2,6,18,24,25,28,34 12,13,17,22,26,32,36 7
30
10
100
50
6
.
1
1 30
2,5.0,4.0 b
8
-
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