Operation Research — Summer 2025

Define the following terms 1. Operation research 2. Gradual failure 3. Inventory 4. Carrying (Holding) cost of an inventory 5. Dummy activity 6. Optimistic time in PERT 7. Balking

State advantages and applications of operation research

Explain the procedure to solve a Linear programming problem using the simplex method.

Write a dual of the following LP problem. Minimize Z = 3x – 2x + 4x x 1 2 subject to, 3x + 5x + 4x ≥ 7,123 6x + x + 3x ≥ 4,123 7x – 2x – x ≤ 10,123 x – 2x + 5x ≥ 3,123 4x + 7x – 2x ≥ 2123 and x , x , x ≥ 0123

For the given LP model, find the solution using the simplex method. Maximize Z=80x +70x12 Subjected to 4x +6x ≤ 120,12 8x +6x ≤ 192,12 x , x ≥012

Find the initial basic feasible solution for the transportation problem given in the table using Vogel’s approximation method. Distribution centers D1 D2 D3 D4 Supply Production S1 22 26 34 28 500 plant S2 32 36 28 20 600 (Sources) S3 42 48 26 20 800 Requirement (Demand)1

Explain in detail the Hungarian method to solve an assignment problem.

Explain the MODI method (u, v method) to solve a transportation problem.

Apharmaceutical company producing a single product sold it through five agencies situated in different cities. As a result of increased demand for the product in another five cities that didn’t have any agency of the company. The company is now facing the problem of deciding how to assign the existing agencies to dispatch the product to needy cities so that the travelling distance is minimized. The distance between the surplus and deficit cities (in km) is given in the following table. Solve the assignment problem. Deficit cities A B C D E C1 160 130 115 190 200 C2 135 120 130 160 175 Surplus C3 140 110 125 170 185 cities C4 50 50 80 80 110 C5 55 35 80 80 105

The cost of a laser printing machine is Rs. 45000 and its scrap value is Rs. 3000. The maintenance and refilling costs (in Rs.) for each year are as given below: Year 1 2 3 4 5 6 Maintenance and refilling 2000 4000 7000 10000 16000 22000 32000 cost When should the printer be replaced?

What is Economic Order quantity (EOQ)? Amanufacturing company purchases raw materials at a cost of 16 rupees per unit. The annual demand is 25,000 units. The cost associated with the storage per unit is 6.40 rupees and the cost of placing an order is 32 rupees. Calculate all the inventory costs and economic order quantity.

Explain various inventory cost components with suitable examples.

What is Replacement? Explain the types of failures with suitable examples.

Compare PERT and CPM.

Explain Kendall’s notation to represent a queuing system in detail.

An established company has decided to add a new product to its line. It will buy the product from a manufacturing concern, package it, and sell it to several distributors that have been selected on a geographical basis. Market research has already indicated the expected volume and the required size of the sales force. The steps shown in the following table are to be planned. Draw a network diagram for the following project and find its critical path.2

Explain Johnson’s procedure(steps) to process n jobs through two machines.