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Frontiers of Engineering Management

Front. Eng    2020, Vol. 7 Issue (2) : 259-274     https://doi.org/10.1007/s42524-019-0080-x
RESEARCH ARTICLE
Efficiency measurement for mixed two-stage nonhomogeneous network processes with shared extra intermediate resources
Qingxian AN, Xuyang LIU, Shijie DING()
School of Business, Central South University, Changsha 410083, China
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Abstract

Unreasonable allocation of shared resources reduces the system efficiency and is a considerable operational risk. Sub-processes with insufficient portion of shared resources could not help accomplish complicated tasks, and overstaffing and idle resources will occur in the sub-processes assigned with redundant shared resources. This unfair portion distribution may cause internal contradictions among sub-processes and even lead to the collapsing of the entire system. This study proposes a data-driven, mixed two-stage network data envelopment analysis model. This method aims to reasonably define the allocation portion of shared extra intermediate resources among several nonhomogeneous subsystems and measure the overall system performance. A data set of 58 international hotels is used to test the features of the proposed model.

Keywords shared resource allocation      mixed two-stage system      data envelopment analysis      efficiency     
Corresponding Author(s): Shijie DING   
Just Accepted Date: 27 December 2019   Online First Date: 27 February 2020    Issue Date: 27 May 2020
 Cite this article:   
Qingxian AN,Xuyang LIU,Shijie DING. Efficiency measurement for mixed two-stage nonhomogeneous network processes with shared extra intermediate resources[J]. Front. Eng, 2020, 7(2): 259-274.
 URL:  
http://journal.hep.com.cn/fem/EN/10.1007/s42524-019-0080-x
http://journal.hep.com.cn/fem/EN/Y2020/V7/I2/259
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Fig.1  Mixed two-stage nonhomogeneous network processes.
Fig.2  Work of our method.
Fig.3  Mixed two-stage structure of hotel’s production.
Mean SD Maximum Minimum
Original input:
Operating expenses (´106 NT$) 543.3 488 2227.1 45.4
Rooms 298.9 148.6 865 50
Catering space (ft2) 4495.4 7094.8 52966.00 210
Employees 315.9 207.4 868 53
Intermediate output:
Occupancy service capacity 72.8 42 213.1 7.8
Catering service capacity 1038.6 2773.7 20286.00 4.1
Intermediate input:
Marketing expense (´106 NT$) 7 9.4 61.3 0.1
Final output of the occupancy division:
Occupancy revenue (´106 NT$) 245 224.8 1243.7 26.1
Final output of the catering division:
Catering revenue (´106 NT$) 270.3 269.8 1127.9 8.5
Tab.1  Descriptive statistics for 58 Taiwan international tourist hotels
No. Hotel Ranking Eo* Eo(1)* Eo(2)** Eo(1)** Eo(2)* f(1)* f(2)*
1 Grand Hotel 18 0.6877 0.8853 0.4915 0.8743 0.5025 0.4941 0.5059
2 Ambassador 26 0.6449 0.9353 0.3573 0.8300 0.4617 0.4970 0.5030
3 Imperial Hotel 29 0.6228 0.7926 0.5177 0.7551 0.5409 0.5546 0.4454
4 Gloria Prince 24 0.6477 0.8625 0.4106 0.8536 0.4205 0.5228 0.4772
5 Emperor Hotel 10 0.7835 0.9105 0.7817 0.8740 0.7822 0.4638 0.5362
6 Hotel Riverview 28 0.6242 1.0000 0.2783 0.9998 0.2785 0.4792 0.5208
7 Caesar Park 13 0.7346 1.0000 0.4926 1.0000 0.4926 0.4745 0.5255
8 Golden China 7 0.8047 0.8900 0.7386 0.8831 0.7440 0.4273 0.5727
9 San Want Hotel 17 0.7063 0.8922 0.5139 0.8891 0.5171 0.5060 0.4940
10 Brother Hotel 30 0.6186 0.8084 0.4047 0.7834 0.4329 0.5289 0.4711
11 Santos Hotel 5 0.8612 1.0000 0.7639 0.9999 0.7639 0.4035 0.5965
12 Lands Hotel 25 0.6456 0.7703 0.4851 0.7668 0.4897 0.5624 0.4376
13 United Hotel 1 0.9443 0.9039 0.9776 0.9035 0.9779 0.4439 0.5561
14 Sheraton 14 0.7294 1.0000 0.4768 0.7836 0.6788 0.4829 0.5171
15 Hotel Royal 15 0.7231 0.9057 0.5569 0.9026 0.5597 0.4726 0.5274
16 Howard Hotel 19 0.6842 0.9912 0.3463 0.7841 0.5743 0.5120 0.4880
17 Grand Hyatt 57 0.4444 0.7586 0.0297 0.3791 0.5306 0.5689 0.4311
18 Formosa 11 0.7793 0.9535 0.5796 0.7519 0.8107 0.5322 0.4678
19 Sherwood Hotel 16 0.7105 0.8630 0.5153 0.7606 0.6463 0.5614 0.4386
20 Far Eastern Plaza 8 0.7999 0.9299 0.6409 0.7807 0.8234 0.5494 0.4506
21 Westin 4 0.8671 0.7433 0.9243 0.6742 0.9562 0.5620 0.4380
22 Miramar Garden 20 0.6798 1.0000 0.3831 1.0000 0.3831 0.4788 0.5212
23 Hotel Kingdom 27 0.6359 1.0000 0.3241 0.9997 0.3243 0.4614 0.5386
24 Holiday Garden 47 0.5615 0.8104 0.2540 0.7808 0.2906 0.5527 0.4473
25 Ambassador 45 0.5726 0.8456 0.2629 0.8355 0.2743 0.5302 0.4698
26 Grand Hi-Lai 21 0.6700 1.0000 0.3465 0.9772 0.3688 0.4943 0.5057
27 Howard Hotel 39 0.5904 0.9362 0.2100 0.8683 0.2847 0.5238 0.4762
28 Splendor 44 0.5779 0.7915 0.3253 0.7421 0.3837 0.5418 0.4582
29 Han-Hsien Intl 34 0.6097 0.9331 0.2732 0.9190 0.2879 0.5098 0.4902
30 Lees Hotel 48 0.5536 0.7317 0.3355 0.7276 0.3405 0.5489 0.4511
31 Hotel National 53 0.5053 0.6666 0.2779 0.6642 0.2813 0.5851 0.4149
32 Plaza Intl 40 0.5893 0.9250 0.2283 0.8708 0.2866 0.5181 0.4819
33 Evergreen Laurel 43 0.5796 0.7702 0.3430 0.7086 0.4194 0.5528 0.4472
34 Howard Hotel 37 0.5967 0.7992 0.3806 0.7739 0.4076 0.5355 0.4645
35 Splendor 56 0.4595 0.5385 0.3124 0.5284 0.3312 0.6501 0.3499
36 Marshal Hotel 52 0.5160 0.7051 0.2534 0.6888 0.2760 0.5813 0.4187
37 Chinatrust Hotel 49 0.5465 0.7711 0.2763 0.7630 0.2861 0.5440 0.4560
38 Parkview Hotel 31 0.6150 0.8916 0.3463 0.8783 0.3592 0.5299 0.4701
39 Farglory Hotel 33 0.6130 0.6976 0.5054 0.5976 0.6325 0.5557 0.4443
40 Lands Resort 46 0.5693 0.4815 0.7175 0.4634 0.7480 0.6279 0.3721
41 The Lalu Hotel 3 0.8981 0.8246 0.9640 0.7882 0.9967 0.5434 0.4566
42 Fleur De Chine 35 0.6070 0.5522 0.7055 0.5451 0.7184 0.6423 0.3577
43 Hibiscus Resort 6 0.8556 0.4611 0.8616 0.3535 0.8632 0.0149 0.9851
44 Grand 38 0.5956 0.3976 0.6085 0.1353 0.6255 0.0610 0.9390
45 Caesar Park 12 0.7628 0.8808 0.6516 0.8760 0.6562 0.4792 0.5208
46 Howard Hotel 22 0.6569 0.8728 0.4174 0.8382 0.4558 0.5257 0.4743
47 Chihpen 23 0.6493 0.7662 0.4967 0.7576 0.5079 0.5663 0.4337
48 Silks Place 55 0.4721 0.4575 0.5003 0.4565 0.5022 0.6564 0.3436
49 CHIAO-HIS 9 0.7989 0.7657 0.8415 0.7539 0.8567 0.5614 0.4386
50 Taoyuan Hotel 36 0.6064 1.0000 0.2334 0.9999 0.2335 0.4866 0.5134
51 Ta Shee Resort 58 0.3235 0.3027 0.3458 0.2906 0.3587 0.7583 0.2417
52 Hotel Royal 42 0.5837 0.6773 0.4731 0.6749 0.4760 0.5631 0.4369
53 Ambassador 41 0.5868 0.7033 0.4205 0.6411 0.5092 0.5878 0.4122
54 Nice Prince 54 0.5011 0.6329 0.2915 0.6204 0.3114 0.6139 0.3861
55 Hotel Tainan 2 0.9431 0.6546 0.9487 0.4656 0.9523 0.0190 0.9810
56 Evergreen Plaza 32 0.6148 0.7454 0.4484 0.7098 0.4937 0.5601 0.4399
57 Tayih Landis 51 0.5258 0.7029 0.2746 0.6699 0.3214 0.5858 0.4142
58 Naruwan 50 0.5291 0.6289 0.4005 0.6242 0.4065 0.6145 0.3855
Tab.2  Efficiency analysis
Fig.4  Decomposition efficiency when the first stage is given pre-emptive priority.
Fig.5  Decomposition efficiency when the second stage is given pre-emptive priority.
No. Hotel Ltk = 0.2, Utk = 0.8 Ltk = 0.1, Utk = 0.9 Ltk = 0, Utk = 1
Eo* a(1)* a(2)* Eo* a(1)* a(2)* Eo* a(1)* a(2)*
1 Grand Hotel 0.6824 0.8 0.2 0.6877 0.9 0.1 0.6886 0.9283 0.0717
2 Ambassador 0.6447 0.8 0.2 0.6449 0.8126 0.1874 0.6449 0.8126 0.1874
3 Imperial Hotel 0.6097 0.8 0.2 0.6228 0.9 0.1 0.6383 0.9937 0.0063
4 Gloria Prince 0.6458 0.8 0.2 0.6477 0.9 0.1 0.6486 0.9606 0.0394
5 Emperor Hotel 0.7561 0.8 0.2 0.7835 0.9 0.1 0.8550 1 0
6 Hotel Riverview 0.6242 0.6568 0.3432 0.6242 0.6568 0.3432 0.6242 0.6568 0.3432
7 Caesar Park 0.7311 0.8 0.2 0.7346 0.9 0.1 0.7358 0.9442 0.0558
8 Golden China 0.7942 0.8 0.2 0.8047 0.9 0.1 0.8131 0.9945 0.0055
9 San Want Hotel 0.7034 0.8 0.2 0.7063 0.9 0.1 0.7076 0.9503 0.0497
10 Brother Hotel 0.6176 0.8 0.2 0.6186 0.8360 0.1640 0.6186 0.8360 0.1640
11 Santos Hotel 0.8459 0.8 0.2 0.8612 0.9 0.1 0.8647 0.9987 0.0013
12 Lands Hotel 0.6455 0.2 0.8 0.6456 0.1 0.9 0.6457 0.0220 0.9780
13 United Hotel 0.9305 0.8 0.2 0.9443 0.9 0.1 0.9942 0.9999 0.0001
14 Sheraton 0.7294 0.7445 0.2555 0.7294 0.7445 0.2555 0.7294 0.7445 0.2555
15 Hotel Royal 0.7176 0.8 0.2 0.7231 0.9 0.1 0.7262 0.9660 0.0340
16 Howard Hotel 0.6837 0.8 0.2 0.6842 0.8837 0.1163 0.6842 0.8837 0.1163
17 Grand Hyatt 0.4425 0.2 0.8 0.4444 0.1 0.9 0.4456 0.0234 0.9766
18 Formosa 0.7769 0.8 0.2 0.7793 0.8672 0.1328 0.7793 0.8672 0.1328
19 Sherwood Hotel 0.7105 0.5 0.5 0.7105 0.5 0.5 0.7105 0.5 0.5
20 Far Eastern Plaza 0.7997 0.2 0.8 0.7999 0.1 0.9 0.8001 0.0221 0.9779
21 Westin 0.8411 0.8 0.2 0.8671 0.9 0.1 0.8973 0.9972 0.0028
22 Miramar Garden 0.6786 0.8 0.2 0.6798 0.9 0.1 0.6806 0.9992 0.0008
23 Hotel Kingdom 0.6359 0.2447 0.7553 0.6359 0.2447 0.7553 0.6359 0.2447 0.7553
24 Holiday Garden 0.5615 0.8 0.2 0.5615 0.9 0.1 0.5626 0.9993 0.0007
25 Ambassador 0.5725 0.2 0.8 0.5726 0.1 0.9 0.5727 0.0065 0.9935
26 Grand Hi-Lai 0.6697 0.2 0.8 0.6700 0.1 0.9 0.6701 0.0229 0.9771
27 Howard Hotel 0.5904 0.5 0.5 0.5904 0.5 0.5 0.5904 0.5 0.5
28 Splendor 0.5779 0.7979 0.2021 0.5779 0.7979 0.2021 0.5779 0.7979 0.2021
29 Han-Hsien Intl 0.6096 0.8 0.2 0.6097 0.8247 0.1753 0.6097 0.8247 0.1753
30 Lees Hotel 0.5527 0.8 0.2 0.5536 0.8502 0.1498 0.5536 0.8502 0.1498
31 Hotel National 0.5053 0.7890 0.2110 0.5053 0.7890 0.2110 0.5053 0.7890 0.2110
32 Plaza Intl 0.5892 0.8 0.2 0.5893 0.8135 0.1865 0.5893 0.8135 0.1865
33 Evergreen Laurel 0.5791 0.8 0.2 0.5796 0.8397 0.1603 0.5796 0.8397 0.1603
34 Howard Hotel 0.5955 0.8 0.2 0.5967 0.8899 0.1101 0.5967 0.8899 0.1101
35 Splendor 0.4594 0.2 0.8 0.4595 0.1 0.9 0.4595 0.0220 0.9780
36 Marshal Hotel 0.5159 0.8 0.2 0.5160 0.8155 0.1845 0.5160 0.8155 0.1845
37 Chinatrust Hotel 0.5449 0.8 0.2 0.5465 0.8764 0.1236 0.5465 0.8764 0.1236
38 Parkview Hotel 0.6132 0.8 0.2 0.6150 0.9 0.1 0.6170 0.9905 0.0095
39 Farglory Hotel 0.6104 0.8 0.2 0.6130 0.9 0.1 0.6146 0.9818 0.0182
40 Lands Resort 0.5693 0.3922 0.6078 0.5693 0.3922 0.6078 0.5693 0.3922 0.6078
41 The Lalu Hotel 0.8964 0.8 0.2 0.8981 0.9 0.1 0.9072 0.9798 0.0202
42 Fleur De Chine 0.6070 0.2 0.8 0.6070 0.1 0.9 0.6070 0.0220 0.9780
43 Hibiscus Resort 0.8041 0.8 0.2 0.8556 0.9 0.1 0.9071 0.9999 0.0001
44 Grand 0.5612 0.2 0.8 0.5956 0.1 0.9 0.6293 0.0020 0.9980
45 Caesar Park 0.7569 0.8 0.2 0.7628 0.9 0.1 0.7668 0.9990 0.0010
46 Howard Hotel 0.6567 0.8 0.2 0.6569 0.8108 0.1892 0.6569 0.8108 0.1892
47 Chihpen 0.6493 0.5 0.5 0.6493 0.5 0.5 0.6493 0.5 0.5
48 Silks Place 0.4711 0.8 0.2 0.4721 0.8566 0.1434 0.4721 0.8566 0.1434
49 CHIAO-HIS 0.7984 0.2 0.8 0.7989 0.1 0.9 0.7992 0.0220 0.9780
50 Taoyuan Hotel 0.6064 0.4300 0.5700 0.6064 0.4300 0.5700 0.6064 0.4300 0.5700
51 Ta Shee Resort 0.3192 0.8 0.2 0.3235 0.9 0.1 0.3309 0.9950 0.0050
52 Hotel Royal 0.5814 0.8 0.2 0.5837 0.9 0.1 0.5852 0.9950 0.0050
53 Ambassador 0.5866 0.2 0.8 0.5868 0.1 0.9 0.5868 0.0494 0.9506
54 Nice Prince 0.5011 0.5 0.5 0.5011 0.5 0.5 0.5011 0.5 0.5
55 Hotel Tainan 0.8981 0.2 0.8 0.9431 0.1 0.9 0.9870 0.0024 0.9976
56 Evergreen Plaza 0.6144 0.8 0.2 0.6148 0.8262 0.1738 0.6148 0.8262 0.1738
57 Tayih Landis 0.5256 0.2 0.8 0.5258 0.1 0.9 0.5260 0.0060 0.9940
58 Naruwan 0.5290 0.8 0.2 0.5291 0.9 0.1 0.5317 0.9992 0.0008
Tab.3  Interval corresponds to efficiency
No. Hotel Efficiency change rate b1 Efficiency change rate b2 Average efficiency change rate b0
1 Grand Hotel 0.777% 0.131% 0.454%
2 Ambassador 0.031% 0 0.016%
3 Imperial Hotel 2.149% 2.489% 2.319%
4 Gloria Prince 0.294% 0.139% 0.217%
5 Emperor Hotel 3.624% 9.126% 6.375%
6 Hotel Riverview 0 0 0
7 Caesar Park 0.479% 0.163% 0.321%
8 Golden China 1.322% 1.044% 1.183%
9 San Want Hotel 0.412% 0.184% 0.298%
10 Brother Hotel 0.162% 0 0.081%
11 Santos Hotel 1.809% 0.406% 1.108%
12 Lands Hotel 0.015% 0.015% 0.015%
13 United Hotel 1.483% 5.284% 3.384%
14 Sheraton 0 0 0
15 Hotel Royal 0.766% 0.429% 0.598%
16 Howard Hotel 0.073% 0 0.037%
17 Grand Hyatt 0.429% 0.270% 0.350%
18 Formosa 0.309% 0 0.154%
19 Sherwood Hotel 0 0 0
20 Far Eastern Plaza 0.025% 0.025% 0.025%
21 Westin 3.091% 3.483% 3.287%
22 Miramar Garden 0.177% 0.118% 0.147%
23 Hotel Kingdom 0 0 0
24 Holiday Garden 0 0.196% 0.098%
25 Ambassador 0.017% 0.017% 0.017%
26 Grand Hi-Lai 0.045% 0.015% 0.030%
27 Howard Hotel 0 0 0
28 Splendor 0 0 0
29 Han-Hsien Intl 0.016% 0 0.008%
30 Lees Hotel 0.163% 0 0.081%
31 Hotel National 0 0 0
32 Plaza Intl 0.017% 0 0.009%
33 Evergreen Laurel 0.086% 0 0.043%
34 Howard Hotel 0.202% 0 0.101%
35 Splendor 0.022% 0 0.011%
36 Marshal Hotel 0.019% 0 0.010%
37 Chinatrust Hotel 0.294% 0 0.147%
38 Parkview Hotel 0.294% 0.325% 0.309%
39 Farglory Hotel 0.426% 0.261% 0.343%
40 Lands Resort 0 0 0
41 The Lalu Hotel 0.190% 1.013% 0.601%
42 Fleur De Chine 0 0 0
43 Hibiscus Resort 6.405% 6.019% 6.212%
44 Grand 6.130% 5.658% 5.894%
45 Caesar Park 0.779% 0.524% 0.652%
46 Howard Hotel 0.030% 0 0.015%
47 Chihpen 0 0 0
48 Silks Place 0.212% 0 0.106%
49 CHIAO-HIS 0.063% 0.038% 0.050%
50 Taoyuan Hotel 0 0 0
51 Ta Shee Resort 1.347% 2.287% 1.817%
52 Hotel Royal 0.396% 0.257% 0.326%
53 Ambassador 0.034% 0 0.017%
54 Nice Prince 0 0 0
55 Hotel Tainan 5.011% 4.655% 4.833%
56 Evergreen Plaza 0.065% 0 0.033%
57 Tayih Landis 0.038% 0.038% 0.038%
58 Naruwan 0.019% 0.491% 0.255%
Tab.4  Efficiency change rate
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