List of top Industrial Engineering Questions asked in GATE PI

Consider an assembly line producing an item through a process involving three activities in the following order: cutting, welding, and polishing. There are three workers available: one is assigned only for cutting, one is assigned only for welding, and one is assigned only for polishing.
The activity time per item is given in the table.

Activity name	Cutting	Welding	Polishing
Activity time/item (in minutes)	30	40	25

Assuming that the process is running in steady state, the total number of items coming out of the assembly line in six hours is ______ (in integer).
Note: Assume that workers, items, and machines/tools are available as and when needed.

A time study was carried out for a job broken into two elements. For each element, three iterations of task were observed, and observed time was recorded. The observed times (in seconds) and the rating factor for each element are given in the table.

Work element	Observed time (seconds)	Rating factor
A	20; 25; 21	105%
B	19; 17; 18	90%

If a further 20% needs to be added for allowances, then the standard output of the worker is ______ units per hour (in integer).

In an M/M/1 queuing system, the customers arrive at a rate of 3 per minute, and the average number of customers in the system is \( n \) at steady state. Assume that the server utilization is less than 1.
Which ONE of the following is the average time a customer spends in the system (in minutes) at steady state?

The function, \( r(t) \), signifies the likelihood that a component has survived up to time \( t \) and fails in the next instant of time.
\[ r(t) = f(t) / (1 - F(t)) \]
where \( f(t) \) denotes the probability density function for time to failure with corresponding cumulative distribution function given by,
\[ F(t) = 1 - e^{-at^b}, \quad a > 0, b > 0 \]
Which ONE of the following represents \( r(t) \)?

A customer has made a lumpsum investment of INR 2,00,000 with a bank. The discount rate is 15% per year. The investment enables the customer to receive a payout of INR 1,00,000 yearly for next three consecutive years.

The net present value (NPV) of his/her investment is INR ______ (rounded off to the nearest integer).

Consider the aggregate planning problem for a toy car manufacturing organization whose demand at a plant is as follows:

Month	September	October	November	December
Demand (in units)	8000	6500	10500	9500

The organization has ONLY the following options available for aggregate planning to meet the demand: (1) in-house production, (2) subcontracting, and (3) inventory holding. Assume that the quantity subcontracted in a given month is available in the same month.

A part of their optimal solution is as follows:
Inventory at the end of October = 1500 units
Units produced in-house in November = 8000 units
Units subcontracted in November = 1000 units

The inventory at the end of November is ______ units (in integer).

Painting is one of the activities in a construction project. For the painting activity that takes 6 days, both the total float and the free float are zero.
Which ONE of the following is TRUE for the painting activity?

Which ONE of the following is NOT an assumption of the economic order quantity (EOQ) model?

In a time study, the average time taken for packaging a product in a warehouse by a worker with 120% performance rating is observed as 9 minutes. Assuming an allowance of 10% of the standard time, the standard time (in minutes) for packaging is ______ . (Answer in integer)

The solidification time of a cube and a cylinder of the same material, produced through the same sand casting process, is found to be equal. Each side of the cube is \(a\), and the radius and the length of the cylinder are \(r\) and \(4r\), respectively. If the solidification time is governed by Chvorinov's equation, then the ratio \(\frac ra\) is

Consider the following linear programming problem with two decision variables \(x_1\) and \(x_2\). There are three constraints involving resources \(R_1, R_2\) and \(R_3\) as indicated.
Maximize \(Z = 6x_1+5x_2\)
Subject to
\(2x_1+5x_2\leq 40\)       \(R_1\)
\(2x_1 + x_2 \leq 22\)         \(R_2\)
\(x_1 + x_2 \leq 13 \)           \(R_3\)
\(X_1 \geq0, \ X_2 \geq 0\)
The optimal solution of the problem is: \(x_1 =9\)  and \(x_2=4\)
For which one of the following options, the shadow price of the resource(s) will have non-zero value(s)?

Match the configurations of the listed 3 degrees-of-freedom industrial robots with the type of joints.

Configuration		Type of joints
P	Cartesian	1	One prismatic and two rotary
Q	Cylindrical	2	Three rotary
R	Spherical	3	Two prismatic and one rotary
S	Articulated	4	Three prismatic

In the iron-carbon equilibrium phase diagram, the temperature and composition of the eutectoid point are 727 °C and 0.77 weight % carbon, respectively. If a steel specimen with 1.2 weight % carbon is cooled from 1000 °C to the room temperature, then the fraction of pro-eutectoid cementite phase in the steel is _____ . (Rounded off to 2 decimal places)

Which of the following areas is/are supply chain decision(s)?

Which one of the following methods requires the least amount of data for forecasting?

Which one of the following is not true about Total Productive Maintenance (TPM)?

If work sampling is carried out using a large number of observations, then the required sample size is estimated using

The following layout of four departments P, Q, R and S is provided as input to CRAFT (Computerized Relative Allocation of Facilities Technique). Which one of the following department pairs cannot be considered for exchange in CRAFT?

Which of the following concepts is not closely inter-related with INTERCHANGEABILITY in the context of product design?

In a single server Markovian queuing system, if the customers arrive following the Poisson distribution, then the inter-arrival time follows

Which of the following is NOT an assumption of a linear programming problem?