Operation Research (CE-604 (D)) - Important Questions

Explain the phases of Operations Research.

Define model and discuss the steps of modeling.

Explain the characteristics of Operations Research and state the limitations of O.R. models.

Use the simplex method to maximize $Z = 3x_1 + 7x_2$ subject to $2x_1 + 5x_2 \le 20$, $x_1 + 2x_2 \le 4$, $x_1, x_2 \ge 0$.

Formulate an LP to schedule police officers to meet daily requirements while minimizing the number with non-consecutive days off.

Use the Big-M method to minimize $Z = 12x_1 + 20x_2$ subject to $6x_1 + 8x_2 \ge 100$, $7x_1 + 12x_2 \ge 120$, $x_1, x_2 \ge 0$.

Define basic feasible solution, optimal solution, and unbounded solution.

Solve the following travelling salesman problem.

Draw the project network diagram and find the critical path.

Draw the project network, identify the critical path and expected completion time, and find the probability of completion in a given time.

What is degeneracy in Transportation Problem? Discuss its consequence and how it is overcome?

Construct the project network diagram, find the critical path and project completion time, determine expected completion time, and compute free slack and total slack.

Compute the economic order quantity in the basic EOQ model given annual demand, ordering cost, holding/carrying cost and unit cost.

Write about the following:

Explain the economic order quantity (EOQ) model with a suitable example.

Define queue and explain queuing systems with neat sketch and characteristics.

For an M/M/1 queue with given mean service time and Poisson arrival rate, find the expected idle time per day.

Explain service disciplines FIFO, LIFO, Priority Service and Random Service with examples.

For an M/M/1 queue with given mean service and inter-arrival times, find the average queue length and expected waiting time in queue.

Write short notes explaining basic game theory terms such as pay off matrix, saddle point, zero-sum/fair game and related concepts

The owner of a chain of four grocery stores has purchased six crates of fresh strawberries. The estimated probability distribution of potential sales of the strawberries before spoilage differs among the four stores. The following table gives the estimated total expected profit at each store, when it is allocated various numbers of crates. For administrative reasons, the owner does not wish to split crates between stores. However he is willing to distribute zero crates to any of his stores.