A cloud services provider buys data storage at Rs. 20 per GB and sells it to clients at Rs. 25 per GB. Any unsold storage capacity is wasted. The daily demand for storage has the following probability distribution. If each day's demand is independent of the previous day, using the marginal analysis approach calculate the required measures. (a) Calculate the maximum expected profit. (b) Find the expected profit with perfect information (EPPI). (c) Compute the expected value of perfect information (EVPI). (d) What will be the maximum amount the cloud provider would be willing to pay for perfect and reliable information?
A project consists of nine activities whose time estimates (in weeks) and other characteristics are given below. What is the expected project completion time and its variance?
A software company wants to assign its technical support agents to different regions to maximize customer satisfaction. The company has four agents, each with varying effectiveness in different regions. The table below shows the expected satisfaction score if each agent is assigned to a specific region. Use the Hungarian method to assign each technical support agent to a region in a way that maximizes overall customer satisfaction.
ABC Manufacturing Company produces three products: Tables, Chairs, and Desks. These products require processing through three departments: Cutting, Assembly, and Painting. These three departments have limited working time to 300 hours, 450 hours, and 200 hours per week respectively. Each table requires 4 hours for cutting, 5 hours for assembly, and 1 hour for painting and contributes Rs. 1000 to profit. Each chair requires 3 hours for cutting, 4 hours for assembly, and 1 hour for painting and contributes Rs. 800 to profit. Each desk requires 2 hours for cutting, 3 hours for assembly, and 2 hours for painting and contributes Rs. 1200 to profit. To maintain balance, the total production of all three products must not exceed 150 units per week. Formulate objective (profit) function and constraints for this LPP.[5]
5.
Explain the algorithm of the Modified Distribution (MODI) method for testing the optimality of the transportation problem.[5]
6.
Write short notes on:(a) Vogel's Approximation Method (VAM)(b) Dominance rule of game theory[0+2.5+2.5]
Queuing Models
1.
A bank operates a single-channel queuing system with customers arriving at a rate of 6 per hour and each customer being served at an average rate of 8 per hour. Calculate (a) the average number of customers in the system and (b) the average waiting time.
λ=6perhour
μ=8perhour
[5]
Theory of Games
1.
The following table gives a payoff in millions in the competitive situation between telecom companies ABC and XYZ. Determine the optimal strategies for each company and find the game value.