# 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 - Labour/Labor Idle Time Variance ~ LITV

What is the variation in the total cost on account of the time lost on account of abnormal reasons (idle time)?

It's value is equal to the Standard Cost of Abnormal Idle Time.

⇒ Labour/Labor Idle Time Variance (LITV)

 = − SC(IT) − (Standard Cost of Idle Time)

## Standard Cost of Idle Time

 SC(IT) = IT × SR

## Formula in useful forms

 LITV = − SC(IT) Standard Cost of Idle Time Or = − (IT × SR) Idle Time × Standard Rate

## For each Labour/Labor type separately

Labour/Labor Idle Time variance for a labour/labor type

 LITVLab = − SC(IT)Lab = − ITLab × SRLab

## For all Labour/Labor Types together

Total Labour/Labor Idle Time Variance

 ⇒ TLITV = ΣLITVLab Sum of the variances measured for each labour/labor type separately

Labour/Labor Idle Time variance for the Mix

 LITVMix = − [ITMix × SRMix] This formula can be used for the mix, only when the idle times mix ratio is the same as the standard time mix ratio.

LITVMix = TLITV, when LITVMix can be calculated.

# Recalculating Standards does not effect LITV Calculations

The formulae for calculating Labour/Labor Idle Time Variance involves IT and SR. They do not contain any terms involving standard time (ST). Since recalculation of standard affects standard time (ST) and thereby standard cost (SC) only, we do not need the recalculated standards for finding out labour/labor idle time variance.

The data used for calculating Labour/Labor Idle Time Variance, IT and SR does not change on standards being recalculated either based on the output or input.

Standard Actual
for SO for AO for AI Total Idle
ST SR ST(AO) SC(AO) ST(AI) SC(AI) AT AR IT SC(IT)
Factor 0.96 1.16
Skilled
Semi-Skilled
Unskilled
200
400
150
20
15
10
192
384
144
3,840
5,760
1,440
232
464
174
4,640
6,960
1,740
240
500
220
22
14
12
20
36
34
400
540
340
Total 750 720 11,040 870 13,340 960 90 1,280
Output 7,500
SO
7,200
SO(AO)
8,700
SO(AI)
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.

(AO) =
 AO SO
=
 7,200 7,500
= 0.96
(AI) =
 AI SI
=
 PTMix STMix
=
 870 750
= 1.16
1. ST(AO) = ST ×
 AO SO
= ST × 0.96

2. SC(AO) = ST(AO) × SR

3. SO(AO) = AO

4. ST(AI) = ST ×
 AI SI
= ST × 1.16

5. SC(AI) = ST(AI) × SR

6. SO(AI) = SO ×
 AI SI
= SO × 1.16

7. SC(IT) = IT × SR

Standard Time Mix Ratio

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

Idle Time Mix Ratio

 ITMR = ITsk : ITss : ITus = 20 hrs : 36 hrs : 34 hrs = 10 : 18 : 17

# Solution [in all cases]

Standards need not be recalculated. But we need SC(IT) for calculating this variance.

LITV = − SC(IT)

Labour/Labor Idle Time Variance due to

 Skilled Labour/Labor, LITVsk = − SC(IT)sk = − 400 [Adv] Semi Skilled Labour/Labor, LITVss = − SC(IT)ss = − 540 [Adv] Unskilled Labour/Labor, LITVus = − SC(IT)us = − 340 [Adv] TLITV = − 1,280 [Adv] LITVMix = − SC(IT)Mix = − 1,280 [Adv]

# Illustration - Solution (alternative)

If calculating the idle time variance is the only requirement, we may avoid calculating the cost/value data in the working table and use the formula involving times and rate. We need only the data relating to IT and SR for this calculation.
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

LITV = − IT × SR

Labour/Labor Idle Time Variance due to

 Skilled Labour/Labor, LITVsk = − ITsk × SRsk = − 20 hrs × 20/hr = − 400 [Adv] Semi Skilled Labour/Labor, LITVss = − ITsk × SRss = 36 hrs × 15/hr = − 540 [Adv] Unskilled Labour/Labor, LITVus = − ITsk × SRus = 34 hrs × 10/hr = − 340 [Adv] TLRPV = − 1,280 [Adv]

Since the forumula involves the term IT × SR and STMR ≠ ITMR, it cannot be used for the mix.

# LITV - Miscellaneous Aspects

• ## It is Always Negative

Labour/Labor Idle Time Variance is always negative as it represents a loss in all cases. It represents the value of time lost on account of abnormal reasons. The measure of this variance is just a value and is not the difference between two values.

There is no possibility for this variance to generate a positive value. It can only be zero when there is no abnormal loss time in which case the total time and the productive time are the same.

### Gross Efficiency Variance = Efficiency Variance + Idle Time Variance

 LGUV/LGEV = [ST(AO) − AT] × SR = [ST(AO) − {PT + IT}] × SR = (ST(AO) − PT − IT) × SR = [(ST(AO) − PT) − IT] × SR = [ST(AO) − PT] × SR − IT × SR = {(ST(AO) − PT) × SR} + [− (IT × SR)] = LUV/LEV + LITV

That part of the standard cost of actual labour relevant to the abnormal loss is put aside and is named idle time variance. This is always negative.

• ## LUV/LGEV vs LEV

In measuring the efficiency of labour/labor employed, we need to think in terms of the output that has been achieved in the time they have worked if they are working under standard conditions.

If the time they worked for includes time that has been lost on account of abnormal reasons like breakdown of machinery, power shut down, natural calamities, etc., it would not be possible to measure their efficiency accurately.

Labourers/Laborers cannot be held responsible for idle time loss as it is something beyond their control. Efficiency in work should be measured taking the actual productive time only.

• ## Who is answerable for the Variance?

Since this variance is on account of abnormal reasons, the responsibility for it can be attributed to some department or person in-charge only after knowing the reasons for the abnormal loss of time.

Say, if the reason for the laborers/labourers sitting idle is breakdown of machinery, then the person who is to keep the machinery in shape by conducting regular maintenance check may have to answer.

Alternatively, when there is a power failure on account of a natural calamity, no one can be blamed, but the organisation has to take note of the variance so that it can get itself prepared to face such a possibility in the future.

# Formulae using Inter-relationships among Variances

• LITV = LUV/LGEV − LEV
• LITV = LCV − LRPV − LEV

## 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/Mix
LYV/LSEV
+ LMV/GCV

LEV
+ LITV

− 400

− 540

− 340

− 1,280
LGEV/LUV
+ LRPV
− 960
− 480
− 1,740
+ 500
− 760
− 440
− 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