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A new method for ranking decision making units using common set of weights: A developed criterion

  • * Corresponding author: Gholam Hassan Shirdel

    * Corresponding author: Gholam Hassan Shirdel 
Abstract Full Text(HTML) Figure(6) / Table(6) Related Papers Cited by
  • In this paper we have developed a new model by altering Liu and Peng's approach [20] toward ranking method using CSW. In fact, we have adopted a new criterion which is stronger in terms of maximizing efficiencies. After showing advantages of our model theoretically and illustrating it geometrically, two examples demonstrated how the proposed method is practically more capable.

    Mathematics Subject Classification: Primary: 90C05, 90C29; Secondary: 90B50.

    Citation:

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  • Figure 1.  $0<y_P<x_P, \Delta_P = x_p-y_p ,m_p = {y_p \over x_p} , o<m_{p_1}<m_P<m_{p_2}$

    Figure 2.  The interior points of the area $OQ_1P$, $R_1$, have less amount of $\Delta$ than $P$ while slopes of crossing lines from the origin and these points are less than $m_P$

    Figure 3.  Slopes of crossing lines from the origin and the points located in the areas $R_1$ and $R_2$ are less than $m_P$

    Figure 4.  Range of slopes of the lines crossing the origin and the points located in $R_3$ is the same as that for the the points located in the area enclosed by the segments $OP$, $OQ_6$ and $Q_6P$.

    Figure 5.  Slope of the line crossing the origin and $P^{(U_1,V_1)}_o$ is maximum.

    Figure 6.  Two pairs of DMUs with the same efficiency scores.

    Table 1.  Input and Output data of DMUs

    $DMU_j$ $x_{1j}$ $x_{2j}$ $x_{3j} $ $x_{4j}$ $y_{1j}$ $y_{2j} $
    $DMU_1$99562051375262941271678
    $DMU_2$91758981379204737211277
    $DMU_3$3178100493615351127062051
    $DMU_4$81358331124173021761538
    $DMU_5$123686392486499052202042
    $DMU_6 $114676101600358935171856
    $DMU_7$70556001557362323522060
    $DMU_8$2871115242880245217551664
    $DMU_9$109889981730282344122334
    $DMU_{10}$203293832421445453862080
    $DMU_{11}$1414104682140364957352691
    $DMU_{12}$1967112602759317860792804
    $DMU_{13}$185198802335457058932495
    $DMU_{14}$3100156495487294052483692
    $DMU_{15}$5016180104008356778004852
    $DMU_{16}$1924126822490297560403396
     | Show Table
    DownLoad: CSV

    Table 2.  The generated common set of weights

    $v^*_1$ $v^*_2$ $v^*_3 $ $v^*_4$ $u^*_1$ $u^*_2 $
    Our method0.0000010.1810810.0000010.1243920.1164660.578059
    Liu and Peng's method [20]0.0000010.0000010.0000017.50E-078.70E- 070.000004
     | Show Table
    DownLoad: CSV

    Table 3.  The efficiencies

    $DMU_j$ $E^*_j$CWA-EfficiencyCCR-Efficiency
    $DMU_1$111
    $DMU_2$0.8857610.8770071
    $DMU_3$0.6651010.557160.690363
    $DMU_4$0.898570.9114881
    $DMU_5$0.8184360.8077231
    $DMU_6$0.8125570.8239970.881091
    $DMU_7$111
    $DMU_8$0.487620.4404690.555791
    $DMU_9$0.9406760.9689861
    $DMU_{10}$0.8120470.7748540.863042
    $DMU_{11}$0.946380.9632530.996068
    $DMU_{12}$0.9566930.9205911
    $DMU_{13}$0.902880.8842990.915511
    $DMU_{14}$0.8580840.751161
    $DMU_{15}$0.9600840.8674781
    $DMU_{16}$111
     | Show Table
    DownLoad: CSV

    Table 4.  The average of the efficiencies in each method and their ratio

    Our methodLiu and Peng's method [20]The ratio
    0.8715560.8467791.02926
     | Show Table
    DownLoad: CSV

    Table 5.  The ranking scores

    $DMU_j$Our method: Input-oriented approachOur method: Output-oriented approachCWA-rankingCCR
    $DMU_1$1321
    $DMU_2$101091
    $DMU_3$1515156
    $DMU_4$9971
    $DMU_5$1212121
    $DMU_6$1313114
    $DMU_7$2231
    $DMU_8$1616167
    $DMU_9$7741
    $DMU_{10}$1414135
    $DMU_{11}$6652
    $DMU_{12}$5561
    $DMU_{13}$8883
    $DMU_{14}$1111141
    $DMU_{15}$44101
    $DMU_{16}$3111
     | Show Table
    DownLoad: CSV

    Table 6.  The averages of the obtained efficiencies and their ratio in each case

    Size of the sampleOur methodCWA-EfficienciesThe ratio
    60.9161280.9069611.010107
    120.5390860.5390821.000006
    250.6899370.1481764.656189
    500.5507240.5533200.995309
    1000.6392430.4716781.355254
    2000.5823100.5807111.002753
     | Show Table
    DownLoad: CSV
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