Calculate Labor/Labour Variances.

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

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.

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)

Standard Cost of Actual Input

Standard Cost of Productive Time

Formula in useful forms

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.

• ×

  AI

  SI

  (where AI = PT_Mix) replaces the suffix (AI) in calculations

For each Labour/Labor type separately

Labour/Labor Mix Variance

For all Labour/Labor Types together

Total Labour/Labor Type Mix Variance

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

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

3. SC(AI) = ST(AI) × SR

5. PT = AT − IT

6. SC(PT) = PT × SR

LMV/GCV = SC(AI) − SC(PT)

Labour/Labor Mix Variance due to

Alternative

• 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.

• 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/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

  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

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

Verification

Building a table as below would help

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