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Table 4 Descriptive statistics for the total cost of policies considering two types of overbooking, two levels of overtime resources, and three cost levels, with IP and EP arrival probabilities at the low level

From: Dynamic capacity allocation in a radiology service considering different types of patients, individual no-show probabilities, and overbooking

Type of overbooking

# overtime resources

Cost levels(2)

Arrival probabilities \( {\boldsymbol{p}}_{\boldsymbol{i}}^{\mathbf{IP}}=\mathbf{0.40} \) e \( {\boldsymbol{p}}_{\boldsymbol{i}}^{\mathbf{EP}} \) = 0.10

Optimal

P1

P2(1)

P3

P4

P5

Double overbooking

1 resource

  Baseline level ($)

112.25

(77.45)

165.03

(110.69)

114.96*

(89.18)

179.42

(115.82)

150.68

(114.73)

139.50

(94.95)

  Low level ($)

55.03

(37.45)

82.52

(54.28)

55.85

(43.87)

82.68

(54.85)

73.57

(56.65)

71.09

(48.15)

  High level ($)

161.53

(114.41)

222.40

(156.82)

166.57*

(131.12)

258.82

(169.23)

223.99

(174.05)

212.16

(145.72)

2 resources

  Baseline level ($)

90.92

(63.62)

152.79

(99.96)

101.44*

(62.99)

161.55

(101.63)

127.83

(91.51)

140.21

(89.69)

  Low level ($)

46.75

(32.27)

80.96

(51.52)

48.60*

(31.32)

82.66

(51.98)

64.37

(45.68)

66.53

(43.46)

  High level ($)

143.99

(93.77)

230.29

(151.72)

146.50*

(98.73)

248.54

(156.36)

196.58

(138.51)

203.99

(131.22)

Flight overbooking

1 resource

  Baseline level ($)

169.43

(85.57)

252.00

(134.24)

170.55

(102.37)

238.96

(133.80)

240.45

(137.52)

207.82

(114.96)

  Low level ($)

84.34

(44.76)

116.28

(64.76)

84.48

(50.13)

123.63

(66.59)

119.13

(68.31)

103.82

(58.20)

  High level ($)

249.22

(129.76)

369.74

(199.12)

255.11*

(146.80)

383.96

(203.73)

357.37

(205.57)

302.48

(171.79)

2 resources

  Baseline level ($)

153.10

(74.07)

240.35

(126.87)

156.41*

(79.62)

246.59

(128.17)

216.77

(113.97)

206.45

(107.87)

  Low level ($)

78.23

(37.65)

117.70

(61.94)

78.23

(39.90)

118.99

(63.56)

111.28

(57.93)

99.76

(52.41)

  High level ($)

233.99

(114.59)

349.00

(187.17)

240.04*

(119.92)

369.78

(190.75)

325.58

(170.51)

313.09

(164.14)

  1. (1)Policy with total cost closest to optimal policy; (2)Waiting, overtime, and penalty costs set at the same level; *Value differs from the optimal policy at 5% significance level