List of top Operations Research and Operations Management Questions

A project has six activities and the precedence relationship among them is shown in the table.

Activity	Precedent activities
A	None
B	None
C	None
D	A, B
E	B,C
F	A, B

The minimum number of dummy activities needed to draw an activity-on-arrow (AOA) representation of the project network is ___ .

A company purchased two machines, Machine A and Machine B, at the same time. The purchase price, estimated useful life and the estimated salvage value of the two machines are given in the table.

	Machine A	Machine B
Purchase price	INR 20,000	INR 15,000
Estimated useful life	10 years	20 years
Estimated salvage value	INR 5,000	INR 5,000

Using the straight-line depreciation method for both the machines, the difference (in INR) between the value of Machine A and the value of Machine B at the end of five years is _____ . (Answer in integer)

A company orders an item using the classical economic order quantity formula. If the ordering cost per order is increased by 20% and the demand per unit time is also increased by 20%, then the time between orders increases (in %) by ____ . (Answer in integer)

Five jobs A, B, C, D and E are available at time t = 0 for processing at a machine, and their processing times are listed.

Job	A	B	C	D	E
Processing time (in days)	9	6	4	5	8

If the jobs are processed using the shortest processing time (SPT) rule, the average flow time (in days) is _____ . (Rounded off to 1 decimal place)

An assembly line consists of three work stations ($S_1, S_2$ and $S_3$) in series to assemble a toy. The times required to perform tasks at these stations are 6, 4 and T minutes, respectively. If the efficiency of the assembly line in the steady state is 75%, then the maximum value of T (in minutes) is _____ . (Answer in integer)

A project comprises of seven activities. The expected durations of activities and their variances are as follows: \[ \begin{array}{|c|c|c|} \hline \text{Activity} & \text{Expected duration (min)} & \text{Variance (min)} \\ \hline A & 4 & 1 \\ B & 5 & 1 \\ C & 4 & 1 \\ D & 1 & 0 \\ E & 7 & 4 \\ F & 6 & 1 \\ G & 8 & 4 \\ \hline \end{array} \] The critical path consists of activities B, E and G. The standard deviation (in minute) of the project duration is $\underline{\hspace{2cm}}$. [round off to two decimal places]

A vaccine has to be distributed from two warehouses (W1 and W2) to three hospitals (H1, H2, H3). Supplies at W1 and W2 are 200 and 150. Demands at H1, H2, H3 are 100, 150 and 125. Transportation cost (₹ per vaccine) is shown below. Using the Northwest-Corner method, the total transportation cost (₹) is $\underline{\hspace{2cm}}$ (round off to nearest integer). \[ \begin{array}{c|ccc} & H1 & H2 & H3 \\ \hline W1 & 5 & 7 & 3 \\ W2 & 4 & 6 & 7 \end{array} \]

Given LP:
Max $z = 20x_1 + 6x_2 + Px_3$, subject to:
$8x_1 + 2x_2 + 3x_3 \le 250$,
$4x_1 + 3x_2 \le 150$,
$2x_1 + x_3 \le 50$,
$x_1,x_2,x_3 \ge 0.$
Optimal solution: $x_1^*=0,\;x_2^*=50,\;x_3^*=50.$
Optimal dual variables: $y_1^*=0,\;y_2^*=2,\;y_3^*=8.$
Find the value of parameter $P$ such that the solution remains optimal (round off to one decimal place).

A company is planning to produce 24 electric cars per day. The setup cost of the plant is estimated as ₹ 19476 million and the variable cost is ₹ 0.6 million per car. The car will be sold at a price of ₹ 1.5 million. The number of days required for achieving the breakeven is $\underline{\hspace{2cm}}$. [round off to nearest integer]

A company forecasts the weekly demand of oxygen cylinders using exponential smoothing with smoothing constant $\alpha = 0.2$. The actual demands in Week 1 to Week 4 were 375, 412, 592 and 439 units. The forecast for Week 3 was 500 units. The forecast (in unit) for Week 5 is $\underline{\hspace{1cm}}$. [in integer]

A company procures 384 parts annually. The annual holding cost per part is ₹30. If the ordering cost is ₹1000, then the economic order quantity is $\underline{\hspace{2cm}}$. [in integer]

A company buys a machine worth ₹65000, which has a salvage value of ₹5000. The annual depreciation cost is ₹10000 based on the straight-line depreciation method. The useful life (in years) of the machine is $\underline{\hspace{2cm}}$ (in integer).