Operations Research (OR) — Winter 2022

Define Operation research and discuss various applications of OR.

Solve the following LP problem using graphical method. Maximize Z = 60x + 40x , subject to the constraints12 x ≤ 251 x ≤ 352 2x + x ≤ 6012 x , x ≥

Solve the following LP problem using simplex method. Maximize Z = 4x + 3x , subject to the constraints12 2x + x ≤ 100012 x + x ≤ 80012 x ≤ 4001 x ≤ 7002 x , x ≥

Solve the following LPP using Big Mmethod. Minimize Z = 600x + 500x , subject to the constraints12 2x + x ≥ 8012 x + 2x ≥ 6012 x , x ≥

Acompany has two grades of inspectors 1 and 2, the members of which are to be assigned for a quality control inspection. It is required that at least 2000 pieces be inspected per hour day. Grade 1 inspectors can check pieces at the rate of 40 per hour, with an accuracy of 97 per cent. Grade 2 inspectors check at the rate of 30 pieces per hour with an accuracy of 95 per cent. The wage rate of Grade 1 inspector costs Rs 5 per hour while that of a Grade 2 inspector is Rs 4 per hour. An error mad by an inspector costs Rs 3 to the company. There are only nine Grade 1 inspectors and eleven Grade 2 inspectors available to the company. The company wishes to assign work to the available inspectors so as to minimize the total cost of the inspection. Formulate this problem s an LP model so as to minimize the daily inspection cost. Page 1 of

Explain the structure of a Queuing system.

Determine initial feasible solution for the following Transportation problem using (1) NWCM (ii) Vogel’s Approximation Method. D1 D2 D3 D4 Supply S1 2 3 11 7 S2 1 0 6 1 1 S3 5 8 15 9 Demand 7 5 3

Differentiate between PERT Vs CPM.

Differentiate Transportation problem Vs Assignment Problem.

Adepartment of a company has five employees with five jobs to be performed. The time (in hours) that each man takes to perform each job is given in the effectiveness matrix. Employees I II III IV V A 10 5 13 15 16 B 3 9 18 13 Jobs C 10 7 2 2 D 7 11 9 7 E 7 9 10 4 How the jobs should be allotted, one per employee so as to minimize the total man-hours?

Discuss various cost components of inventory system.

An aircraft company uses rivets at a constant rate of 2500 per year. Each unit costs Rs 30. The company personnel estimate that it costs Rs 130 to place an order and that carrying cost of inventory is 10 per cent per year. How frequently should orders be placed? Also determine the optimum size of each order.

Define simulation. Discuss various applications of simulation.

The cost of a machine is Rs 6100 and its scrap value is only Rs 100. From experience the maintenance costs are found to be : Year 1 2 3 4 5 6 7 Maintenance Cost Rs When should the machine be replaced?

What is game theory? Explain two person zero sum game with payoff matrix and saddle point.

Explain queue discipline and service process of queuing system

Discuss PERT/CPM network components and explain constructing network diagram. What is error and dummy activity in network diagram? Page 2 of