GATE Past Year Questions: Production Planning | Industrial Engineering - Mechanical Engineering PDF Download

Q1: A set of jobs U, V, W, X, Y, Z arrive at time t = 0 to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e. the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.

The sequence in which the jobs must be processed by the production line if the total make span of production is to be minimized is  [GATE ME 2024]
(a) W-X-Z-V-Y-U
(b) W-X-V-Z-Y-U
(c) W-U-Z-V-Y-X
(d) U-Y-V-Z-X-W
Ans: (a)
By J ohnson's rule of sequencing mark minimum time consuming operation for each process.
According to question, work on work station (1) is followed by work on workstation (2).
Perform that job in mark station which is minimum time consumption.
It is W-X during this Z on work station-2 will be performed.
So, W - X - Z
After W − X − Z, V, will be performed on workstation (1).
So, W − X − Z − V, in between Y-work on workstation will perform.
As minimum time in workstation is U, so will be performed at last.
So, W - X - Z - V - Y - U

Q1: A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are  [GATE ME 2023]
(a) 3 and 3, respectively
(b) √3 and √3 , respectively
(c) 0.015 and 0.015, respectively
(d) 3 and 9, respectively
Ans: (a)
P = 0.015
n = 200
mean = λ = np = 200 × 0.015 = 3
variance = σ² = λ = 3

Q1: 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.  [GATE ME 2022 SET-2]
(a) 31
(b) 33
(c) 30
(d) 32
Ans: (b)
Sequencing model :
Optimum job sequence (According to Johnson's algorithm)
P₃, P₄, P₅, P₁, P₆, P₂, P₇
Optimum Make-span (Minimum total completion time)
Minimum total completion time of all parts = 33 hours

Q2: 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 α = 0.2, then the sales forecast for the month of February of the same year is _______units (in integer).  [GATE ME 2022 SET-2]
Ans: 104 to 104
Actual sales in Jan (D_Jan) = 120 units
Under estimate in Jan = D_Jan − F_Jan = 20
D_Jan = 100 units
Smoothing constant (α = 0.2)
Forecast for Feb (D_Jan) = ?
F_Feb = F_Jan + α(D_Jan − F_Jan) = 100 + 0.2(120 − 100) = 104 units

Q1: The demand and forecast of an item for five months are given in the table.

The Mean Absolute Percent Error (MAPE) in the forecast is _______% (round off to two decimal places)  [GATE ME 2021 SET-2]
Ans: 6 to 10
MAPE =  

Q2: 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).  [GATE ME 2021 SET-2]
Ans: 40200 to 40300

= 40249.2 ≃ 40250 units

Q1: 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 [GATE ME 2020 SET-2]
(a) 0.1
(b) 0.4
(c) 0.5
(d) 1
Ans: (a)
F_t = F_t−1 + α(D_t−1 − F_t−1)
For 2nd month F_t = 31.8, for 1^st month
F_t−1 = 32 and D_t−1 = 30
31.8 = 32 + α(30 - 32)
2α = 32 - 31.8
α = 0.1

Q2: In Materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches should be used?  [GATE ME 2020 SET-2]
(a) Economic Order Quantity
(b) Lot-for-Lot
(c) Base Stock Level
(d) Fixed Period Quantity, for 2 periods
Ans: (b)
In Lot-for-lot, holding cost is high and ordering cost is less.

Question for GATE Past Year Questions: Production Planning

Try yourself:The Product structure of an assembly P is shown in the figure.Estimated demand for end product P is as follows:​Ignore lead times for assembly and subassembly. Production capacity (per week) for component R is the bottleneck operation.Starting with zero inventory, the smallest capacity that will ensure a feasible production plan up to week 6 is

[2008]

• A.

  1000
• B.

  1200
• C.

  2200
• D.

  2400

Explanation

The M .R.P. f or R is given by
If 6P – 12800 ≥ 0 then the capacity is f easible \ Minimization ,
6P = 12800⇒
  P ≌ 2200

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Question for GATE Past Year Questions: Production Planning

Try yourself:The table gives details of an assembly line.​What is the line efficiency of the assembly line?

[2006]

• A.

  70%
• B.

  75%
• C.

  80 %
• D.

  85%

Explanation

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