200 hrs of Skilled Labour/Labor @ Rs. 20 per hr, 400 hrs of SemiSkilled 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 Semiskilled 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 SemiSkilled 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/GangComposition 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 SubPart 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 Mix − Standard Cost of Actual Time
For each Labour/Labor type Separately
For all Labour/Labor types together [Total Labour/Labor Mix/GangComposition Variance :: TLMV/TGCV]
When two or more types of labour/labor are used for the manufacture of a product, the total Labour/Labor Mix/GangComposition Variance is the sum of the variances measured for each labour/labor type separately.
Direct Formula

LMV/GCV » Formula interpretation



The above formulae for Labour/Labor Mix/GangComposition Variance, can be used in all cases i.e. both when AT _{Mix} = ST _{Mix} as well as when AT _{Mix} ≠ ST _{Mix}. When AT _{Mix} ≠ ST _{Mix}, the ratio AT _{Mix}/ST _{Mix} 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/GangComposition Variance, the (Net) time should be considered for actual time.
Where AT_{Mix} = ST_{Mix}
AT_{Mix}/ST_{Mix} 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 AT_{Mix} = ST_{Mix}.
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 

= 

Where there is only one labour/labor type being used, there is no meaning in thinking of the Labour/Labor Mix/GangComposition 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
 when the LMV/GCV on account of each labour/labor type is zero, or
 when the proportion of labour/labor times interse between them both as per the standard and the actual is the same. ST_{1} : ST_{2} : ... = AT_{(N)1} : AT_{(N)2} : ...
 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 
= 
({ 

× ST_{Lab}} − AT_{(N)Lab}) × SR_{Lab} 

Labour/Labor Mix or Gang Composition Variance due to labourers/laborers who are
• Skilled 
= 
({ 

× 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/GCV_{Sk} 
= 
+ Rs. 288 
[Fav] 
• Semiskilled 
= 
({ 

× 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/GCV_{Se} 
= 
+ Rs. 162 
[Fav] 
• Unskilled 
= 
({ 

× 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/GCV_{Un} 
= 
− Rs. 252 
[Adv] 


Total Labour Mix/GangComposition Variance 

+ Rs. 198 
[Fav] 

Solution [Using recalculated data]



Where you find that the ST _{Mix} ≠ AT _{(N)Mix}, you may alternatively recalculate the standard to make the ST _{Mix} = 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}/ST _{Mix}).
From the data relating to the problem, it is evident that ST_{Mix} ≠ 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/GCV_{Sk} 
= 
+ Rs. 288 
[Fav] 
Semiskilled 
= 
(460.8 hrs − 450 hrs) × Rs. 15/hr 

= 
(+ 10.8 hrs) × Rs. 15/hr 

= 
− Rs. 162 
⇒ LMV/GCV_{Se} 
= 
− Rs. 162 
[Adv] 
Unskilled 
= 
(172.8 hrs − 198 hrs) × Rs. 10/hr 

= 
(− 25.2 hrs) × Rs. 10/hr 

= 
− Rs. 252 
⇒ LMV/GCV_{Un} 
= 
− Rs. 252 
[Adv] 


Total Labour Mix/GangComposition Variance 

+ Rs. 198 
[Fav] 
Note:
This formula can be used only when AT _{(N)Mix} = ST _{Mix}
You don't need to recalculate the standard
The formula with the adjustment factor AT _{(N)Mix}/ST _{Mix} can be used in all cases i.e. both when AT _{(N)Mix} = ST _{Mix} and AT _{(N)Mix} ≠ ST _{Mix}. 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} = ST _{Mix}.

Formulae using Interrelationships among Variances



These formulae can be used both for each labour/labor type separately as well as for all the labour/labor types together
 LEV/LUV_{N} = LMV/GCV + LYV/LSUV ⇒ (1)
For each Labour/Labor Type Separately
For All Labour/Labor Types Together
 LCV = LRPV + LMV/GCV + LYV/LSUV_{N} + LITV ⇒ (2)
For each Labour/Labor Type Separately
For All Labour/Labor Types Together

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.


