# Illustration - Problem

7,500 units of a product are planned to be produced using 200 hrs of Skilled Labour/Labor @ 20 per hr, 400 hrs of Semi-Skilled Labour/Labor @ 15/hr and 150 hrs of Unskilled Labour/Labor @ 10 per hr at a total cost of 11,500. 7,200 units of the product were manufactured using 240 hrs of skilled labour/labor @ 22 per hr, 500 hrs of Semi-skilled labour/labor @ 14/hr and 220 hrs of Unskilled labour/labor @ 12 per hr. 20 hrs of Skilled Labour/Labor time, 36 hrs of Semi-Skilled Labour/Labor time and 34 hrs of Unskilled Labour/Labor time were lost due to break down which is abnormal.

Calculate Labor/Labour Variances.

# Working Table

Working table populated with the information that can be obtained as it is from the problem data

Standard Actual
for SO Total Idle
ST SR SC AT AR IT
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
240
500
220
22
14
12
20
36
34
Total 750 11,500 960 90
Output 7,500
SO
7,200
AO

Output (_O) is in units, Times (_T) are in hrs, Rates (_R) are in monetary value per unit time and Costs (_C) are in monetary values.

The rest of the information that we make use of in problem solving is filled through calculations.

# Formulae - Labor/Labour Mix/Gang-Composition Variance (LMV/GCV)

What is the variation in the total cost on account of the actual labour/labor time mix ratio being different from the standard labour/labor time mix ratio?

It is the difference between the Standard Cost of Standard Time for Actual Input (Productive Time) and the Standard Cost of Productive Time.

⇒ Labour/Labor Mix Variance (LMV/GCV)

 = SC(AI) − SC(PT) Standard Cost of Actual Input − Standard Cost of Productive Time

SC(AI) = SC ×
 AI SI
Or = ST(AI) × SR

## Standard Cost of Productive Time

 SC(PT) = PT × SR

## Formula in useful forms

 LMV/GCV = SC(AI) − SC(PT) Standard Cost for Actual Input − Standard Cost of Productive Time Or = [ST(AI) − PT] × SR Difference between Standard Time for Actual Input and Productive Time × Standard Rate

## Note

• Labour/Labor Mix Variance is a part of Labour/Labor Efficiency Variance whose calculations are based on the Productive time and as such the Labour/Labor Mix Variance should also be based on productive time.

Thus, the actual input (AI) considered in the formulae is the sum of productive times, PTMix.

• ×  AI SI
(where AI = PTMix) replaces the suffix (AI) in calculations

## For each Labour/Labor type separately

Labour/Labor Mix Variance

 LMV/GCVLab = SC(AI)Lab − SC(PT)Lab Or = [ST(AI)Lab − PTLab] × SRLab

## For all Labour/Labor Types together

Total Labour/Labor Type Mix Variance

 TLMV/TGCV = ΣLMV/GCVLab Sum of the variances measured for each labour/labor type separately

Labour/Labor Mix/Gang-Composition variance for the Mix

 LMV/GCVMix = SC(AI)Mix − SC(PT)Mix Or = [ST(AI)Mix − PTMix] × SRMix (conditional) This formula can be used for the mix only when the productive time mix ratio is the same as the standard time mix ratio.

TLMV/TGCV = LMV/GCVMix, when LMV/GCVMix exists.

# Illustration - Solution (by recalculating standards)

We need to recalculate standards based on AI for finding LMV/GCV.
Working Table with recalculated standards
Standard Actual
for SO for AI Total Idle Productive
ST SR ST(AI) SC(AI) AT AR IT PT SC(PT)
Factor 1.16
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
232
464
174
4,640
6,960
1,740
240
500
220
22
14
12
20
36
34
220
464
186
4,400
6,960
1,860
Total 750 870 13,340 960 90 870 13,220
Output 7,500
SO
8,700
SO(AI)
7,200
AO
1. (AI) =
 AI SI
 PTMix STMix
=
 870 hrs 750 hrs
= 1.16
2. ST(AI) = ST ×
 AI SI
= ST × 1.16

3. SC(AI) = ST(AI) × SR

4. SO(AI) = SO ×
 AI SI
= SO × 1.16

5. PT = AT − IT

6. SC(PT) = PT × SR

LMV/GCV = SC(AI) − SC(PT)

Labour/Labor Mix Variance due to

 Skilled Labour/Labor, LMV/GCVsk = SC(AI)sk − SC(PT)sk = 4,640 − 4,400 = + 240 [Fav] Semi Skilled Labour/Labor, LMV/GCVss = SC(AI)ss − SC(PT)ss = 6,960 − 6,960 = 0 Unskilled Labour/Labor, LMV/GCVus = SC(AI)us − SC(PT)us = 1,740 − 1,860 = − 120 [Adv] TLMV/TGCV = + 120 [Fav] LMV/GCVMix = SC(AI)Mix − SC(PT)Mix = 13,340 − 13,220 = + 120 [Fav]

## Alternative

Where LMV/GCV is the only variance to be found, we may avoid calculating the cost/value data in the working table and use the formula involving times and rates.

LMV/GCV = [ST(AI) − PT] × SR

Labour/Labor Mix Variance due to

 Skilled Labour/Labor, LMV/GCVsk = [ST(AI)sk − PTsk] × SRsk = (232 hrs − 220 hrs) × 20/hr = 12 hrs × 20/hr = + 240 [Fav] Semi Skilled Labour/Labor, LMV/GCVss = [ST(AI)ss − PTss] × SRss = (464 hrs − 464 hrs) × 15/hr = 0 hrs × 15/hr = 0 Unskilled Labour/Labor, LMV/GCVus = [ST(AI)us − PTus] × SRus = (174 hrs − 186 hrs) × 10/hr = − 12 hrs × 10/hr = − 120 [Adv] TLMV/TGCV = + 120 [Fav]

Standard Time Mix Ratio

 STMR = STsk : STss : STus = 200 hrs : 400 hrs : 150 hrs = 4 : 8 : 3

Productive Time Mix Ratio

 PTMR = PTsk : PTss : PTus = 220 hrs : 464 hrs : 186 hrs = 110 : 232 : 93

Since this formula involves the term PT × SR and STMR ≠ PTMR, it cannot be used for calculating the variance for the mix.

# Solution (without recalculating standards)

Where SI ≠ AI, we can use the adjustment factor
 AI SI
in the formula itself for finding the variance.
• ## Calculating Costs in a working table

Calculate SC and SC(PT) based on the given data in a working table and then use formulae based on costs.
Working Table
Standard Actual
for SO Total Idle Productive
ST SR SC AT AR IT PT SC(PT)
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
4,000
6,000
1,500
240
500
220
22
14
12
20
36
34
220
464
186
4,400
6,960
1,860
Total 750 11,500 960 90 870 13,220
Output 7,500
SO
7,200
AO

1. SC = ST × SR

2. SC(PT) = PT × SR

LMV/GCV = SC × AI SI
− SC(PT)
• ## Using Formula with Times and Rates

Using the time and rate data from the working table built using the problem data we may do all the working in the formula itself if we expand the formula using the relation cost = time × rate.
Working Table
Standard Actual
for SO Total Idle Productive
ST SR SC AT AR IT PT
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
240
500
220
22
14
12
20
36
34
220
464
186
Total 750 11,500 960 90 870
Output 7,500
SO
7,200
AO

PT = AT − IT

LMV/GCV = (ST × AI SI
− PT) × SR

Since this formula involves the term PT × SR and STMR ≠ PTMR, it cannot be used for calculating the variance for the mix.

# LMV/GCV - Miscellaneous Aspects

• ## Productive Time

Since labour/labor mix variance is a part of labour/labor efficiency variance measured using productive time, the actual time considered in this variance is also Productive time.

Thus, AI = ΣPT

Where there is no idle time loss, the actual (total) time is productive time.

• ## LEV vs LMV/GCV

Variance Formula Measures Variation in
LEV
LMV/GCV
SC(AO) − SC(PT)
SC(AI) − SC(PT)
Productive Labour/Labor Time used
Labour/Labor Time Mix Ratios
• ## Nature of Variance

Based on the relations derived from the formulae for calculating LMV/GCV, we can identify the nature of Variance

• SC(AI) ___ SC(PT)
• ST(AI) ___ PT

## LMV/GCVLab

• SC(AI)Lab ___ SC(PT)Lab
• ST(AI)Lab ___ PTLab

## LMV/GCVMix

• SC(AI)Mix ___ SC(PT)Mix

The variance would be

• zero when =
• Positive when >
• Negative when <

We do not draw such a conclusion based on ST(AI)Mix ___ PTMix as they both are the same.

### TLMV/GCV

Variance of Mix and Total Variance are the same.

VarianceMix provides a method to find the total variance through calculations instead of by just adding up individual variances.

• Where there is only one labour/labor type being used, there is no meaning in thinking of the Labour/Labor Mix Variance. TLMV/TGCV = 0 as well as LMV/GCVLab = 0 in such a case.

• ## Interpretation of the Variance

For each labour/labor type, for the input time used

Variance Productive Time used is indicating
None as per standard efficiency
Positive lesser than standard efficiency
Negative greater than standard inefficiency

Using a labour/labor type for a time lesser than the standard is considered efficiency only in terms of cost.

To conclude that using a lesser time is efficiency in general may not be appropriate as it results in other labour/labor types being used for greater times. Changing the mix ratio may affect the quality of the output also.

Similar conclusions can be drawn for the mix based on the mix variance. The value of mix variance should not be viewed in isolation as it is an aggregate of individual variances and as such reflects their net effect.

Mix variance data would be helpful to get an overall idea. In terms of cost, the mix variance data would give an immediate understanding of the gain/loss on account of variation in ratio of time mix. In taking corrective actions both the mix as well as individual variances should be considered.

Eg: When the Total Variance is zero, we cannot conclude that the cost incurred on all labour/labor types is as per standard, as it might have been zero on account of

1. each labour/labor variance being zero, or
2. 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.

If the total variance is zero on account of this reason, it would be wrong to conclude that the STMR and PTMR are the same.

• ## Who is answerable for the Variance?

Since this variance is on account of the variation in the ratio in which the times of constituent labour/labor types are mixed, the actual ratio being different from the standard ratio, the people or department responsible for authorising the usage and composition of times of component labour/labor types for production would be made answerable for this variance.
• ## Conclusions based on Mix Ratios

If the Standard Mix Ratio (STMR) and the Actual Mix Ratio (ATMR) are the same, then there is no Mix variance either for individual labour/labor types or for the total mix.

STMR and ATMR being different is an indicator of existence of mix variance relating to individual labour/labor types.

Standard Time Mix Ratio ~ STMR

sk : ss : us = 200 hrs : 400 hrs : 150 hrs
= 4 : 8 : 3
=  4 15
:  8 15
:  3 15
[= PTsk PTMix
:  PTss PTMix
:  PTus PTMix
]
= 0.267 : 0.533 : 0.2 (approximately)

Productive Time Mix Ratio ~ PTMR

sk : ss : us = 220 hrs : 464 hrs : 186 hrs
= 110 : 232 : 93
=  110 435
:  232 435
:  93 435
[= STsk STMix
:  STss STMix
:  STus STMix
]
= 0.253 : 0.533 : 0.214 (approximately)

We will be able to tell which labour/labor types are causing the variance by comparing the terms of the ratio.

• PTMR value = STMR value

No variance since the Labour/Labor times have been taken in the same proportion as the standard

• PTMR value < STMR value

Labour/Labor times have been taken in a lesser proportion compared to the standard resulting in a negative variance

• PTMR value > STMR value

Labour/Labor times have been taken in a greater proportion compared to the standard resulting in a negative variance

PTMR STMR Variance
Skilled
Semi Skilled
Unskilled
0.253
0.533
0.214
<
=
>
0.267
0.533
0.2
Positive
None
Negative

### Alternative 1

Standard Time Mix Ratio ~ STMR

sk : ss : us = 200 hrs : 400 hrs : 150 hrs
= 4 : 8 : 3
Multiplying all terms with  AI SI
, 1.16.

Make it a whole number and multiply. 29 (1.16 × 25)

= 116 : 232 : 87

We get values that can be straight away used for comparison

Productive Time Mix Ratio ~ PTMR

 sk : ss : us = 220 hrs : 464 hrs : 186 hrs = 110 : 232 : 93
PTMR STMR Variance
Skilled
Semi Skilled
Unskilled
110
232
93
<
=
>
116
232
87
Positive
None
Negative

### Alternative 2

Comparing the proportion of PT to ST with (AI) value.

(AI) = 1.16

 PTsk STsk
=  220 hrs 200 hrs
= 1.1 (approx)
< (AI)
Positive Variance
 PTsk STsk
=  464 hrs 400 hrs
= 1.16
= (AI)
No Variance
 PTus STus
=  186 hrs 150 hrs
= 1.24
> (AI)
Negative Variance

# Formulae using Inter-relationships among Variances

• LMV/GCV = LEV − LYV/LSEV
• LMV/GCV = LCV − LRPV − LITV − LYV/LSEV

## Verification

In problem solving, these inter relationships would also help us to verify whether our calculations are correct or not.

Building a table as below would help

Skilled Semi Skilled Unskilled Total
LYV/LSEV
+ LMV/GCV
− 800
+ 240
− 1,200
0
− 300
− 120
− 2,300
+ 120
LEV
+ LITV
− 560
− 400
− 1,200
− 540
− 420
− 340
− 2,180
− 1,280
LUV/LGEV
+ LRPV
− 960
− 480
− 1,740
+ 500
− 420
− 760
− 3,460
− 420
LCV − 1,440 − 1,240 − 1,200 − 3,880

By including a column for formula, this format would also work as the simplest format for calculating and presenting variances after building the working table