Industrial Engineering Test 2

Concept:

By the exponential smoothing method:

\({F_t} = {F_{t - 1}} + \alpha \left[ {{D_{t - 1}} - {F_{t - 1}}} \right]\)

If we have \(\alpha = 1\)

\({F_t} = {D_{t - 1}}\)

Explanation:

Three-week moving average,

\({x_1} = \frac{{72 + 65 + 58}}{3}\)

∴ x₁ = 65

Now,

Four-week moving average,

\({x_2} = \frac{{72 + 65 + 58 + 60}}{4}\)

∴ x₂ = 63.75

⇒ x₁ – x₂ = 65 – 63.75

Concept:

F_n+1 = F_n + α (D_n – F_n)

Calculation:

Given:

D₁ = 115, F₁ = 110, α = 0.3

Now,

F₂ = F₁ + α (D₁ – F₁)

F₂ = 110 + 0.3 (115 - 110)

Concept:

\({\rm{Mean\;forecast\;error\;}}\left( {MFE} \right) = \frac{{\sum \left( {{D_i} - {F_i}} \right)}}{n}\)

\({\rm{Mean\;absolute\;deviation\;}}\left( {MAD} \right) = \frac{{\sum \left| {{D_i} - {F_i}} \right|}}{n}\)

Calculation:

\(MFE = \frac{{\mathop \sum \nolimits_{i = 1}^4 \left( {{D_i} - {F_i}} \right)}}{4}\)

\(\therefore MFE = \frac{{21}}{4}\)

\(MAD = \frac{{\mathop \sum \nolimits_{i = 1}^4 \left| {{D_i} - {F_i}} \right|}}{4}\)

\(\therefore MAD = \frac{{45}}{4}\)

Now,

\({\rm{Required\;ratio\;}} = \frac{{MFE}}{{MAD}} = \frac{{21}}{{45}}\)

Concept:

The absolute deviation is |D – F|

The forecast for each period can be calculated from the above regression line equation.

Calculation:

Sum of absolute deviations is = 1 + 1 + 0 + 3 = 6

Concept:

For regression model

y = a + bx

∑ y = na + b ∑ x

∑ xy = a ∑ x + b ∑ x²

Where, a = constant

b = slope of equation

∴ From given data,

5432 = 8a + b (36)   …1)

Now,

26108.8 = 36a + 204b   …2)

On solving, equation 1) and 2)

We get,

Average job completion time \( = \frac{{59}}{5}\) days.

Total lateness = 6 days

Required ratio \( = \frac{{\left( {\frac{{59}}{5}} \right)}}{6} = 1.97\)

Concept:

The jobs will be sequenced using the Johnson rule and then the idle time will be calculated.

Steps:

• Find out the minimum of Ai and Bi.
• If the minimum is for a job on machine A then perform that job at the start.
• If the minimum is for a job on machine B then perform that job at the last.
• A job should be assigned only once.

Calculation:

Using the Johnson rule, sequence is:

We have the table:

Idle time = make span time – working time =

Idle time (Facing) = 43 – 42 = 1 min

Idle time (Threading) = 43 – 37 = 6 min