Labour/Labor :: Mix/Gang-Composition Variance

... From Page L:9
A Problem  
 
200 hrs of Skilled Labour/Labor @ Rs. 20 per hr, 400 hrs of Semi-Skilled Labour/Labor @ Rs. 15/hr and 150 hrs of Unskilled Labour/Labor @ Rs. 10 per hr were planned to be utlised for manufacturing 7,500 units of a product. 240 hrs of skilled labour/labor @ Rs. 22 per hr, 500 hrs of Semi-skilled labour/labor @ Rs. 14/hr and 220 hrs of Unskilled labour/labor @ Rs. 12 per hr were actually used for manufacturing 7,125 units of the product. 16 hrs of Skilled Labour/Labor time, 50 hrs of Semi-Skilled Labour/Labor time and 22 hrs of Unskilled Labour/Labor time were lost due to break down which is abnormal.
The proportion in which the labour/labor types are to be mixed
Standard Proportion :: 200 hrs : 400 hrs : 150 hrs i.e. 4 : 8 : 3
Actual Proportion :: 216 hrs : 450 hrs : 198 hrs i.e. 12 : 25 : 11

What is the variation in total cost on account of variation in the proportion in which the labour/labor types are engaged?
This information is provided by the labour/labor mix or Gang Composition variance.

The problem data arranged in a working table:

Standard
[Production: 7,500 units]
Actual
[Production: 7,125 units]
Time
(hrs)
Rate
(Rs/hr)
Cost
(Rs)
Rate
(Rs/hr)
Gross/Total Net Abnromal
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Skilled 200 20 4,000 22 240 5,280 216 4,752 24 528
Semi Skilled 400 15 6,000 14 500 7,000 450 6,300 50 700
Un Skilled 150 10 1,500 12 220 2,640 198 2,376 22 264
Total 750   11,500   960 14,920 864 13,428 96 1,492

The Formulae » Labor/Labour Mix/Gang-Composition Variance (LMV/GCV)  
 
That part of the variance in the total cost of labour/labor on account of a variation between the standard mix (standard proportion in which labour/labor time of various labour/labor types are to be employed) and the proportion of actual mix (proportion in which they are actually used). It is a part of the Labour/Labor Usage/Efficiency Variance or a Sub-Part of the Labour/Labor Cost Variance.

It is the difference between the Standard Cost of Standard Time for Actual Input (Actual Quantity of Mix) and the Standard Cost of Actual Net Time.
⇒ Labour/Labor Mix Variance = Standard Cost of Standard Time for Actual MixStandard Cost of Actual Time

  • For each Labour/Labor type Separately

    LMV/GCV = SC of ST for AM − SC of AT
    =
    ({
    AT(N)Mix
    STMix
    × STLab} × SRLab)(AT(N)Lab × SRLab)
    =
    ({
    AT(N)Mix
    STMix
    × STLab} − AT(N)Lab) × SRLab)
  • For all Labour/Labor types together
    [Total Labour/Labor Mix/Gang-Composition Variance :: TLMV/TGCV]

    When two or more types of labour/labor are used for the manufacture of a product, the total Labour/Labor Mix/Gang-Composition Variance is the sum of the variances measured for each labour/labor type separately.

    ⇒ TLMV/TGCV = LMV/GCVSk + LMV/GCVSe + ....

    Direct Formula

    There is no direct formula for calculating the total mix variance

LMV/GCV » Formula interpretation  
 
The above formulae for Labour/Labor Mix/Gang-Composition Variance, can be used in all cases i.e. both when ATMix = STMix as well as when ATMix ≠ STMix. When ATMix ≠ STMix, the ratio ATMix/STMix works as a correction factor to readjust the ST to ST for AI and thereby the SC to SC for AI.

  • Actual Time ⇒ Net Time

    Wherever you find the presence of actual time in the formula, you should interpret it as Actual (Net) Time. Where there abnormal loss of time, the actual time is segregated into two as abnormal loss time and net time. Even in such cases, for the purpose of calculating the Mix/Gang-Composition Variance, the (Net) time should be considered for actual time.
  • Where ATMix = STMix

    ATMix/STMix becomes 1 thus nullifying its effect, in which case the formula would read as:

    For each labour/labor type separately
    LMV/GCV = (ST × SR) − (AT × SR)
    = (ST − AT) × SR

    Caution:

    The formula for Labour/Labor Efficiency/Usage Variance also reads the same
    [LEV/LUV = (ST × SR) − (AT × SR)] when AO = SO.
    In case of Mix Variance the condition to be satisfied is ATMix = STMix.
  • LMV/GCV = 0

    Labour/Labor mix or Gang Composition variance for each labour/labor type would be zero, when the proportion of the actual time of labour/labor types to the total time of actual mix (AT/AT(AM)) is the same as the proportion of the standard time of the labour/labor types to the total time of standard mix (ST/ST(SM)).

    LMV/GCV for each labour/labor type would be zero, when the proportion of the labour/labor time of each labour/labor type to the time of mix is the
    same both in the standards as well as actuals. i.e. when
    STLab
    STMix
    =
    AT(N)Lab
    ATMix

    Where there is only one labour/labor type being used, there is no meaning in thinking of the Labour/Labor Mix/Gang-Composition Variance. Where LMV/GCV = 0, the total efficiency/usage variance is nothing but Yield Variance.
    LEV/LUV = LMV/GCV + LYV/LSUV/LSEV
    = 0 + LYV/LSUV/LSEV
    = LYV/LSUV/LSEV

  • TLMV/TGCV = 0

    When more than one type of labour/labor is used, the total LMV/GCV may become zero
    1. when the LMV/GCV on account of each labour/labor type is zero, or
    2. when the proportion of labour/labor times inter-se between them both as per the standard and the actual is the same. ST1 : ST2 : ... = AT(N)1 : AT(N)2 : ...
    3. when the unfavourable variance due to one or more labour/labor types is set off by the favourable variance due to one or more other labour/labor types.

    Therefore, it would not be appropriate to conclude that there is no variance on account of any labour/labor type just because the total LMV/GCV is zero.

Solution [Using the data as it is]  
 
For working out problems with the data considered as it has been given without having to do any recalculations, use the above formulae (which are capable of being used in all cases)

Consider the working table above:

Standard
[Production: 7,500 units]
Actual
[Production: 7,125 units]
Time
(hrs)
Rate
(Rs/hr)
Cost
(Rs)
Rate
(Rs/hr)
Total Normal Abnromal
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Skilled 200 20 4,000 22 240 5,280 216 4,752 24 528
Semi Skilled 400 15 6,000 14 500 7,000 450 6,300 50 700
Un Skilled 150 10 1,500 12 220 2,640 198 2,376 22 264
Total 750   11,500   960 14,920 864 13,428 96 1,492

Using,
LMV/GCV =
({
AT(N)Mix
STMix
× STLab} − AT(N)Lab) × SRLab
Labour/Labor Mix or Gang Composition Variance due to labourers/laborers who are

Skilled =
({
864 hrs
750 hrs
× 200 hrs} − 216 hrs) × Rs. 20/hr
= ({1.152 × 200 hrs) − 216 hrs) × Rs. 20/hr
= (230.4 hrs − 216 hrs) × Rs. 20/hr
= (+ 14.4 hrs) × Rs. 20/hr
= + Rs. 288 ⇒ LMV/GCVSk = + Rs. 288 [Fav]
Semi-skilled =
({
864 hrs
750 hrs
× 400 hrs} − 450 hrs) × Rs. 15/hr
= ({1.152 × 400 hrs) − 450 hrs) × Rs. 15/hr
= (460.8 hrs − 450 hrs) × Rs. 15/hr
= (+ 10.8 hrs) × Rs. 15/hr
= + Rs. 162 ⇒ LMV/GCVSe = + Rs. 162 [Fav]
Unskilled =
({
864 hrs
750 hrs
× 150 hrs} − 198 hrs) × Rs. 10/hr
= ({1.152 × 150 hrs) − 198 hrs) × Rs. 10/hr
= (172.8 hrs − 198 hrs) × Rs. 10/hr
= (− 25.2 hrs) × Rs. 10/hr
= − Rs. 252 ⇒ LMV/GCVUn = − Rs. 252 [Adv]
Total Labour Mix/Gang-Composition Variance + Rs. 198 [Fav]

Solution [Using recalculated data]  
 
Where you find that the STMix ≠ AT(N)Mix, you may alternatively recalculate the standard to make the STMix = AT(N)Mix and use the figures relating to the recalculated standard in the working table. In such a case, the formulae that you use would look simpler (without the adjustment factor AT(N)Mix/STMix).

From the data relating to the problem, it is evident that STMix ≠ AT(N)Mix. Thus we recalculate the standard data for Actual Input [Refer to the calculations].

Consider the recalculated standard data and the actual data arranged in a working table.

Standard
[Production: 8,640 units]
Actual
[Production: 7,125 units]
Time
(hrs)
Rate
(Rs/hr)
Cost
(Rs)
Rate
(Rs/hr)
Total Normal Abnromal
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Time
(hrs)
Cost
(Rs)
Skilled 230.4 20 4,608 22 240 5,280 216 4,752 24 528
Semi Skilled 460.8 15 6,912 14 500 7,000 450 6,300 50 700
Un Skilled 172.80 10 1,728 12 220 2,640 198 2,376 22 264
Total 864   13,248   960 14,920 864 13,428 96 1,492

Using LMV/GCV = (ST − AT) SR [Since AT(AM) = ST(SM)]

Labour/Labor Mix or Gang Composition Variance due to labour/labor type which are
Skilled = (230.4 hrs − 216 hrs) × Rs. 20/hr
= (+ 14.4 hrs) × Rs. 20/hr
= + Rs. 288 ⇒ LMV/GCVSk = + Rs. 288 [Fav]
Semi-skilled = (460.8 hrs − 450 hrs) × Rs. 15/hr
= (+ 10.8 hrs) × Rs. 15/hr
= − Rs. 162 ⇒ LMV/GCVSe = − Rs. 162 [Adv]
Unskilled = (172.8 hrs − 198 hrs) × Rs. 10/hr
= (− 25.2 hrs) × Rs. 10/hr
= − Rs. 252 ⇒ LMV/GCVUn = − Rs. 252 [Adv]
Total Labour Mix/Gang-Composition Variance + Rs. 198 [Fav]

Note:

This formula can be used only when AT(N)Mix = STMix

You don't need to recalculate the standard

The formula with the adjustment factor AT(N)Mix/STMix can be used in all cases i.e. both when AT(N)Mix = STMix and AT(N)Mix ≠ STMix. Therefore, you don't need to rebuild the working table by recalculating the standards for the purpose of finding the variances.

Check:

The same problem was solved in both the cases above. The only difference being that in the second case, the data was considered by recalculating the Standard for Actual Input to make AT(N)Mix = STMix.

Formulae using Inter-relationships among Variances  
 
These formulae can be used both for each labour/labor type separately as well as for all the labour/labor types together
  1. LEV/LUVN = LMV/GCV + LYV/LSUV   ⇒ (1)
    • For each Labour/Labor Type Separately

      LMV/GCVLab = LEV/LUV(N)Lab − LYV/LSUVLab
    • For All Labour/Labor Types Together

      TLMV/TGCV = TLEV/TLUVN − TLYV/TLSUV
  2. LCV = LRPV + LMV/GCV + LYV/LSUVN + LITV   ⇒ (2)
    • For each Labour/Labor Type Separately

      LMV/GCVLab = LCVLab − LRPVLab − LYV/LSUV(N)Lab − LITVLab
    • For All Labour/Labor Types Together

      TLMV/TGCV = TMCV − TMPV − TLYV/LSUV(N) − TLITV

Who is held responsible for the Variance?  
 
Since this variance is on account of the variation in the ratio in which the constituent labour/labor types are mixed i.e. the gang composition being different from the standard ratio, the people or department responsible for authorising the work time usage and mixing of component labourers/laborers for production can be held responsible for this variance.
Author Credit : The Edifier ... Continued Page L:11

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