# Production Planning and Control

 Question 1
Parts P1-P7 are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required for carrying out both the operations for all 7 parts is __________ hours.
$\begin{array}{|c|c|c|} \hline \text{Part} & \text{Milling (hours)} &\text{Polishing (hours)} \\ \hline P1 & 8 &6 \\ \hline P2 & 3& 2\\ \hline P3& 3& 4\\ \hline P4& 4& 6\\ \hline P5& 5&7 \\ \hline P6& 6 & 4\\ \hline P7& 2& 1 \\ \hline \end{array}$
 A 31 B 33 C 30 D 32
GATE ME 2022 SET-2   Industrial Engineering
Question 1 Explanation:
Sequencing model :
$\begin{array}{|c|c|c|}\hline \text{Part}&\text{Milling (hours)}& \text{Polishing (hours)} \\ \hline P_1&8&6\\ \hline P_2&3&2\\ \hline P_3&3&4\\ \hline P_4&4&6\\ \hline P_5&5&7\\ \hline P_6&6&4\\ \hline P_7&2&1\\ \hline \end{array}$
Optimum job sequence (According to Johnson's algorithm)
$P_3,P_4,P_5,P_1,P_6,P_2,P_7$
Optimum Make-span (Minimum total completion time)
$\begin{array}{|c|c|c|c|c|c|c|}\hline \text{Part}& \text{Milling}& & &\text{Polishing}&& \\ \hline & \text{In time}& \text{Processing time} &\text{Out time}&\text{In time}& \text{Processing time} &\text{Out time}\\ \hline P_3& 0 & 3 & 3 & 3 &4 &7\\ \hline P_4& 3 & 4 & 7 & 7 &6 &13\\ \hline P_5& 7 & 5 & 12 & 13 &7 &20\\ \hline P_1& 12 & 8 & 20 & 20 &6 &26\\ \hline P_6& 20 & 6 & 26 & 26 &4 &30\\ \hline P_2& 26 & 3 & 29 & 30 &2 &32\\ \hline P_7& 29 & 2 & 31 & 32 &1 &33\\ \hline \end{array}$
Minimum total completion time of all parts = 33 hours
 Question 2
An electric car manufacturer underestimated the January sales of car by 20 units, while the actual sales was 120 units. If the manufacturer uses exponential smoothing method with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is _______units (in integer).
 A 96 B 104 C 120 D 128
GATE ME 2022 SET-2   Industrial Engineering
Question 2 Explanation:
Actual sales in Jan ($D_{Jan}$) = 120 units
Under estimate in Jan = $D_{Jan}- F_{Jan}=20$
$D_{Jan}$ = 100 units
Smoothing constant ($\alpha = 0.2$)
Forecast for Feb ($D_{Jan}$) = ?
$F_{Feb} = F_{Jan} + \alpha (D_{Jan} - F_{Jan})= 100 + 0.2 (120 - 100) = 104 \;units$
 Question 3
The demand and forecast of an item for five months are given in the table.

$\begin{array}{|c|c|c|}\hline \textbf{Month} & \textbf{Demand} & \textbf{Forecast} \\ \hline \text{April} & \text{225} & \text{200} \\ \hline \text{May} & \text{220} & \text{240}\\ \hline \text{June} & \text{285} & \text{300} \\ \hline \text{July} & \text{290} & \text{270} \\ \hline \text{August} & \text{250} & \text{230} \\ \hline \end{array}$

The Mean Absolute Percent Error (MAPE) in the forecast is _______% (round off to two decimal places)
 A 4.45 B 12.25 C 18.42 D 8.08
GATE ME 2021 SET-2   Industrial Engineering
Question 3 Explanation:
$\begin{array}{|c|c|c|c|c|} \hline \text { March } & \mathrm{Di} & \mathrm{Fi} & \mathrm{ei} & \left|\frac{\mathrm{ei}}{\mathrm{Di}} \times 100\right| \\ \hline \text { April } & 225 & 200 & 25 & 11.11 \% \\ \hline \text { May } & 220 & 240 & -20 & 9.09 \% \\ \hline \text { June } & 285 & 300 & -15 & 5.26 \% \\ \hline \text { July } & 290 & 270 & 20 & 6.896 \% \\ \hline \text { August } & 250 & 230 & 20 & 8.0 \% \\ \hline & & & & \sum \frac{e i}{D i} \times 100 \mid=40.356 \\ \hline \end{array}$
$\text{MAPE}=\frac{\sum\left|\frac{e i}{D i} \times 100\right|}{n}=8.0712 \%$
 Question 4
Daily production capacity of a bearing manufacturing company is 30000 bearings. The daily demand of the bearing is 15000. The holding cost per year of keeping a bearing in the inventory is Rs. 20. The setup cost for the production of a batch is Rs. 1800. Assuming 300 working days in a year, the economic batch quantity in number of bearings is ______ (in integer).
 A 36254 B 20145 C 40250 D 42145
GATE ME 2021 SET-2   Industrial Engineering
Question 4 Explanation:
\begin{aligned} Q^{\star} &=\sqrt{\frac{2 D \times C_{0}}{C_{h}} \times \frac{P}{P-d}} \\ &=\sqrt{\frac{2 \times 15000 \times 300 \times 1800}{20} \times\left(\frac{30000}{30000-15000}\right)} \\ &=40249.2 \simeq 40250 \text { units } \end{aligned}
 Question 5
The forecast for the monthly demand of a product is given in the table below.

The forecast is made by using the exponential smoothing method. The exponential smoothing coefficient used in forecasting the demand is
 A 0.1 B 0.4 C 0.5 D 1
GATE ME 2020 SET-2   Industrial Engineering
Question 5 Explanation:
\begin{aligned} F_{t}&=F_{t-1}+\alpha\left(D_{t-1}-F_{t-1}\right)\\ \text{For 2nd month }F_{t}&=31.8, \text{ for }1^{\text {st }} \text{month}\\ F_{t-1} &=32 \text { and } D_{t-1}=30 \\ 31.8 &=32+\alpha(30-32) \\ 2 \alpha &=32-31.8 \\ \alpha &=0.1 \end{aligned}
 Question 6
The table presents the demand of a product. By simple three-months moving average method, the demand-forecast of the product for the month of September is
 A 490 B 510 C 530 D 536.67
GATE ME 2019 SET-1   Industrial Engineering
Question 6 Explanation:
3 month moving average method :
\begin{aligned} \mathrm{F}_{\mathrm{sep}} &=\frac{\mathrm{D}_{\mathrm{Aug}}+\mathrm{D}_{\mathrm{July}}+\mathrm{D}_{\text {June }}}{3} \\ &=\frac{560+475+495}{3}=510 \end{aligned}
 Question 7
The time series forecasting method that gives equal weightage to each of the m most recent observations is
 A Moving average method B Exponential smoothing with linear trend C Triple Exponential smoothing D Kalman Filter
GATE ME 2018 SET-1   Industrial Engineering
Question 7 Explanation:
It gives equal weightage to all data points.
 Question 8
The demand for a two-wheeler was 900 units and 1030 units in April 2015 and May 2015, respectively. The forecast for the month of April 2015 was 850 units. Considering a smoothing constant of 0.6, the forecast for the month of June 2015 is
 A 850 units B 927 units C 965 units D 970 units
GATE ME 2016 SET-3   Industrial Engineering
Question 8 Explanation:
\begin{aligned} F_{May} &=F_{April} +0.6(D_{April}-F_{April})\\ &=580+0.6(900-850) \\ &= 850+30\\ &= 880\; unit\\ F_{June} &=F_{May} +0.6(D_{May}-F_{May})\\ &=880+0.6(1030-880) \\ &= 880+90\\ &= 970\; unit\\ \end{aligned}
 Question 9
Sales data of a product is given in the following table:

Regarding forecast for the month of June, which one of the following statements is TRUE?
 A Moving average will forecast a higher value compared to regression. B Higher the value of order N, the greater will be the forecast value by moving average. C Exponential smoothing will forecast a higher value compared to regression. D Regression will forecast a higher value compared to moving average.
GATE ME 2015 SET-2   Industrial Engineering
Question 9 Explanation:
$\text{(forecast)}_{\text {June }}$ according to regression $\gt 25$
but according to moving average,
$T_{\text {June }} \lt 25$
 Question 10
For a canteen, the actual demand for disposable cups was 500 units in January and 600 units in February. The forecast for the month of January was 400 units. The forecast for the month of March considering smoothing coefficient as 0.75 is ________
 A 569 B 986 C 451 D 258
GATE ME 2015 SET-1   Industrial Engineering
Question 10 Explanation:
\begin{aligned} F_{\mathrm{Feb}} &=F_{\mathrm{Jan}}+\alpha\left[D_{\mathrm{Jan}}-F_{\mathrm{Jan}}\right] \\ &=400+0.75[500-400] \\ &=475 \\ F_{\mathrm{March}} &=F_{\mathrm{Feb}}+\alpha\left[D_{\mathrm{Feb}}-F_{\mathrm{Feb}}\right] \\ &=475+0.75[600-475] \\ &=568.75 \approx 569 \end{aligned}
There are 10 questions to complete.

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