# Production Planning and Control

 Question 1
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 1 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 2
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 2 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 3
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 3 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 4
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 4 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 5
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 5 Explanation:
It gives equal weightage to all data points.
 Question 6
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 6 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 7
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 7 Explanation:
$\text{(forecast)}_{\text {June }}$ according to regression $\gt 25$
but according to moving average,
$T_{\text {June }} \lt 25$
 Question 8
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 8 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}
 Question 9
The actual sales of a product in different months of a particular year are given below:

The forecast of the sales, using the 4-month moving average method, for the month of February is _______
 A 156 B 240 C 654 D 852
GATE ME 2014 SET-3   Industrial Engineering
Question 9 Explanation:
$F=\frac{280+250+190+240}{4}=240$
 Question 10
In exponential smoothening method, which one of the following is true?
 A $0\leq \alpha \leq 1$ and high value of $\alpha$ is used for stable demand B $0\leq \alpha \leq 1$ and high value of $\alpha$ is used for unstable demand C $\alpha \geq 1$ and high value of $\alpha$ is used for stable demand D $\alpha \leq 0$ and high value of $\alpha$ is used for unstable demand
GATE ME 2014 SET-1   Industrial Engineering
Question 10 Explanation:
High value of $\alpha$ shows more weightage is given to immediate forecast. Less value of $\alpha$ shows less weightage is given to immediate forecast or almost equal weightage is given. So high value of $\alpha$ is chosen when nature of demand is not reliable or unstable.
There are 10 questions to complete.