# Labour/Labor - Mix/Gang-Composition Variance

# Illustration - Problem

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)

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 |

## Standard Cost of Actual Input

SC(AI) | = | SC ×
| ||

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, PT

_{Mix}. - ×

(where AI = PTAI SI _{Mix}) replaces the suffix (AI) in calculations

## For each Labour/Labor type separately

Labour/Labor Mix Variance

LMV/GCV_{Lab} | = | SC(AI)_{Lab} − SC(PT)_{Lab} |

Or | = | [ST(AI)_{Lab} − PT_{Lab}] × SR_{Lab} |

## For all Labour/Labor Types together

Total Labour/Labor Type Mix Variance

TLMV/TGCV | = | ΣLMV/GCV_{Lab}Sum of the variances measured for each labour/labor type separately |

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

LMV/GCV_{Mix} | = | SC(AI)_{Mix} − SC(PT)_{Mix} |

Or | = | [ST(AI)_{Mix} − PT_{Mix}] × SR_{Mix} (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/GCV _{Mix}**, when LMV/GCV

_{Mix}exists.

# Illustration - Solution (by recalculating 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) | = |
| ||||

| = |
| |||||

= | 1.16 |

2. | ST(AI) | = | ST ×
| ||

= | ST × 1.16 |

3. SC(AI) = ST(AI) × SR

4. | SO(AI) | = | SO ×
| ||

= | 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/GCV_{sk} | = | SC(AI)_{sk} − SC(PT)_{sk} | ||

= | 4,640 − 4,400 | = | + 240 [Fav] | |

Semi Skilled Labour/Labor, | ||||

LMV/GCV_{ss} | = | SC(AI)_{ss} − SC(PT)_{ss} | ||

= | 6,960 − 6,960 | = | 0 | |

Unskilled Labour/Labor, | ||||

LMV/GCV_{us} | = | SC(AI)_{us} − SC(PT)_{us} | ||

= | 1,740 − 1,860 | = | − 120 [Adv] | |

TLMV/TGCV | = | + 120 [Fav] | ||

LMV/GCV_{Mix} | = | SC(AI)_{Mix} − SC(PT)_{Mix} | ||

= | 13,340 − 13,220 | = | + 120 [Fav] |

## Alternative

**LMV/GCV = [ST(AI) − PT] × SR**

Labour/Labor Mix Variance due to

Skilled Labour/Labor, | ||||

LMV/GCV_{sk} | = | [ST(AI)_{sk} − PT_{sk}] × SR_{sk} | ||

= | (232 hrs − 220 hrs) × 20/hr | |||

= | 12 hrs × 20/hr | = | + 240 [Fav] | |

Semi Skilled Labour/Labor, | ||||

LMV/GCV_{ss} | = | [ST(AI)_{ss} − PT_{ss}] × SR_{ss} | ||

= | (464 hrs − 464 hrs) × 15/hr | |||

= | 0 hrs × 15/hr | = | 0 | |

Unskilled Labour/Labor, | ||||

LMV/GCV_{us} | = | [ST(AI)_{us} − PT_{us}] × SR_{us} | ||

= | (174 hrs − 186 hrs) × 10/hr | |||

= | − 12 hrs × 10/hr | = | − 120 [Adv] | |

TLMV/TGCV | = | + 120 [Fav] |

Standard Time Mix Ratio

STMR | = | ST_{sk} : ST_{ss} : ST_{us} |

= | 200 hrs : 400 hrs : 150 hrs | |

= | 4 : 8 : 3 |

Productive Time Mix Ratio

PTMR | = | PT_{sk} : PT_{ss} : PT_{us} |

= | 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)

AI |

SI |

## 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

Unskilled200

400

15020

15

104,000

6,000

1,500240

500

22022

14

1220

36

34220

464

1864,400

6,960

1,860Total 750 11,500 960 90 870 13,220 Output 7,500

SO7,200

AO1. 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

Unskilled200

400

15020

15

10240

500

22022

14

1220

36

34220

464

186Total 750 11,500 960 90 870 Output 7,500

SO7,200

AOPT = 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/GCVSC(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/GCV

_{Lab}- SC(AI)
_{Lab}___ SC(PT)_{Lab} - ST(AI)
_{Lab}___ PT_{Lab}

## LMV/GCV

_{Mix}- 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}___ PT_{Mix}as they both are the same.### TLMV/GCV

Variance of Mix and Total Variance are the same.Variance

_{Mix}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/GCV

_{Lab}= 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- each labour/labor variance being zero, or
- 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

:PT _{sk}PT _{Mix}

:PT _{ss}PT _{Mix}

]PT _{us}PT _{Mix}= 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

:ST _{sk}ST _{Mix}

:ST _{ss}ST _{Mix}

]ST _{us}ST _{Mix}= 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

Unskilled0.253

0.533

0.214<

=

>0.267

0.533

0.2Positive

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

, 1.16.AI SI 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

Unskilled110

232

93<

=

>116

232

87Positive

None

Negative### Alternative 2

Comparing the proportion of PT to ST with (AI) value.(AI) = 1.16

PT _{sk}ST _{sk}= 220 hrs 200 hrs = 1.1 (approx) < (AI) Positive Variance PT _{sk}ST _{sk}= 464 hrs 400 hrs = 1.16 = (AI) No Variance PT _{us}ST _{us}= 186 hrs 150 hrs = 1.24 > (AI) Negative Variance - PTMR value = STMR value

# 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