Production Optimization Techniques — Winter 2018

“Every Linear programming problem exists in pair” Evaluate.

With reference to the graphical method, discuss (i) Feasibility of an Unbounded solution space with an Optimum solution for a maximization problem (ii) Similarity and difference between an unbounded and infeasible solution.

Define the following 1. Redundant constraint 2. Slack Variable 3. Artificial variable

What do you understand by shadow price? What is the reason of selecting the minimum value of b / a as the basis for an outgoing variable? i ij

Solve Maximize Z = 2x – 3y + z Subject to 3x + 6y + z ≤ 4x + 2y + z ≤ x – y + z ≤ and x ≥ 0, y ≥ 0, z ≥ 0

Amachine tool company conducts a job-training programme at a ratio of one for every ten trainees. The training programme lasts for one month. From past experience it has been found that out of 10 trainees hired, only seven complete the programme successfully. (The unsuccessful trainees are released). Trained machinists are also needed for machining. The company's requirement for the next three months is as follows: January: 100 machinists, February: 150 machinists and March: 200 machinists. In addition, the company requires 250 trained machinists by April. There are 130 trained machinists available at the beginning of the year. Pay roll cost per month is: Each trainee Rs. 400/- per month. Each trained machinist (machining or teaching): Rs. 700/- per month. Each trained machinist who is idle: Rs.500/- per month. (Labor union forbids ousting trained machinists). Build a LPP for producing the minimum cost hiring and training schedule and meet the company’s requirement. Do not solve.

Solve : Maximize Z = 8x2 Subject to : x - x ≥ 0; 2x + 3x ≤ - 6; and x , x unrestricted

Explain the significance of sensitivity analysis in a LPP.

Solve using two phase method Min Z = x – 2x – 3x123 Subject to – 2x + x + 3x = 2123 2x + 3x + 4x = 1123 and x ≥ 0, x ≥ 0 , x ≥ 0123

Explain the following related to simplex table:

Degeneracy & cycling (ii) Unbounded solution (iii) Alternate multiple solution

Compare and Contrast : Assignment and transportation problem

Discuss the techniques for obtaining an optimum solution to a transportation problem.

Acompany has three factories X, Y, and Zand four warehouses A, B, C, and D. It is required to schedule factory production and shipments from factories to warehouses in such a manner so as to minimize total cost of shipment and production. Unit variable manufacturing costs (UVMC) and factory capacities and warehouse requirements are given below: Find the optimal production and transportation schedule

Explain merge and burst event.

Discuss different types of floats in network analysis

Explain the significance of Crashing and Resource allocation with a suitable example. Explain the Johnsons rule of Sequencing with a suitable example.

Explain the Kendalls notation to a queuing problem

Discuss the types of inventories with suitable example.

Acompany has 5 jobs to be done. The following matrix shows the return in terms of rupees on assigning ith ( i = 1, 2, 3, 4, 5 ) machine to the jth job ( j = A, B, C, D, E ). Assign the five jobs to the five machines so as to maximize the total expected profit.

Explain Dangling and Looping. Why they should be avoided?

Discuss: EOQ, Price-break, Lead-time, Buffer stock.2

The following matrix gives the payoff of different strategies (alternatives) A, B, and C against conditions (events) W, X, Yand Z. Identify the decision taken under the following approaches: (i) Pessimistic, (ii) Optimistic, (iii) Equal probability, (iv) Regret, (v) Hurwicz criterion. The decision maker’s degree of optimism (α) being 0.7.

Differentiate between Decision node and Chance node.

Explain: Decision making under risk & under uncertainty.

Afleet owner finds form his past records that the cost per year of running a vehicle whose purchase price is Rs. 50000/- are as under: Thereafter running cost increases by Rs.2000/- per year but resale value remains constant at Rs. 2000/-. At what stage the replacement is due?