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Competitive facility location
and design problem

 

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Two players, a leader and a follower, open facilities and compete to attract clients from a given market. Each player has a budget and maximizes own market share. Each client splits own demand probabilistically over all opened facilities by the gravity rule. The goal is to find the location and design of the leader facilities to maximize his market share.

Mathematical model

 

References:

1. Aboolian R., Berman O., Krass D. Competitive facility location and design problem. European J. Oper. Res. 2007.  Vol. 182. P. 40-62.

2. E. Alekseeva, Yu. Kochetov, N. Kochetova, and A. Plyasunov. Heuristic and exact methods for the discrete (r|p)centroid problem. LNCS. 2010. Vol. 6022. P. 1122. (pdf.file)

3. Yu. Kochetov, N. Kochetova, and A. Plyasunov. A matheuristic for the leader-follower facility location and design problem. 10th international Metaheuristics Conference(MIC 2013). Singapure 5-8 August, 2013. (pdf-file)

 

Test Instances

| I | = | J | = 50. | R | = 3.  BL , BF = 10,20,..., 100.   The matrix dij is the Euclidean distance matrix. 

The instance data are in different formats: (111.xls111.xlsx, 111.txt, 111.zip)

 

Follower
budget

Leader
budget

10

20

30

40

50

60

70

80

90

100

10

127,00

93,17

70,29

53,36

43,50

35,93

30,78

 

 

 

20

160,83

127,00

99,13

78,92

63,81

56,49

50,03

 

 

 

30

183,71

154,87

127,00

108,82

91,59

78,62

69,88

63,90

57,56

 

40

200,64

174,90

148,08

127,00

109,99

98,30

88,37

80,79

75,03

 

50

210,50

190,19

162,41

143,70

127,00

114,15

104,03

95,94

88,76

 

60

218,07

197,51

173,42

155,70

139,85

127,00

116,21

107,63

100,63

95,30

70

223,22

203,97

183,81

165,63

149,97

137,79

127,00

118,07

111,22

105,00

80

 

 

190,10

172,96

158,06

146,37

135,93

127,00

119,94

113,73

90

 

 

195,03

178,45

165,24

153,37

142,78

134,06

127,00

120,78

100

 

 

 

 

 

158,70

149,00

140,27

133,22

127,00

 

Numbers in green cells indicate the cases where we have no Nash equilibrium.