Queuing theory - 2018

Question 1: Arrival rate and service rate at a service centre follow Poisson distribution with mean 25 per hour and 40 per hour respectively. A person doesn't join such system if there is at least one person waiting for the service in addition to the one getting served.

a) What is the probability that this person will join the system?                                                 3 marks

b) Management wants that the probability of such persons joining the system be 0.9. What should be the mean service rate?                                                                                                                  5 marks

Answer can be seen at

https://drive.google.com/file/d/1G0zr5SHv3izAZqeDulpNQ0KLpyS1B1M7/view?usp=sharing

Inventory control - 2018

Question 2: Consumption rate of an item is 50000 units/ month. Ordering and related cost is Rs. 1000 per order. The unit price of the item is Rs. 10. The rate of inventory carrying cost is 10% of average inventory value per month. The supplier offers a 20% discount in unit price of the item if the order quantity is more than or equal to 11000 units.

a) What should be the order quantity to minimize the overall cost?                                           3 marks

b) Rate of inventory carrying cost got increased due to increase in loan interest and cost of storage space. What will be the impact on economic order quantity?                                                     4 marks

Answers can be seen at

https://drive.google.com/file/d/1SfERvFW_1fp06Rp8mPnao6WUdLYx5IPB/view?usp=sharing

Work Measurement - 2018

Question 3: In a work measurement exercise, an operation is studied to find the Standard Time for that operation. In this study, observed time and rating are given for five observations. Observed time in five observations were 2 minutes, 1.5 minutes, 4 minutes, 3 minutes and 2.5 minutes. The corresponding ratings recorded by the work measurement team were 110, 180, 70, 90 and 90 respectively. This operation requires a lot of physical and mental concentration. Hence, a 30% allowance is given to get the Standard Time.  

a) What is the Standard time for this operation?                                                                         7 marks

b) A person works for 5 hours and does this operation 100 times. What is his productivity?     3 marks

Answers can be seen at

https://drive.google.com/file/d/1EYcHbBgyWFNRKjfJoRpjlwfDbm3FWcDm/view?usp=sharing