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

Question 1 -- 2016, Capacity Planning

Question 1:A service facility has 6 workstations as ws1, ws2, ws3, ws4, ws5 and ws6. The outputs of ws1 and ws2 are required in the ratio of 2:3 in ws3 to get 5 units of output of ws3. Similarly, the outputs of ws3, ws4 and ws5 are required in the ratio of 4:2:3 in ws6 to get 9 units of output at ws6.

Capacities of these workstations are given as 3000, 4200, 7800, 3200, 5000 and 16000 units/ day respectively.

a)      What is the capacity of this complete service facility?                                         6 marks

b)      How much surplus capacity is available at each of the workstations?                 3 marks

c)      If you are allowed to increase the capacity of any one service station so that overall capacity increases, which service station you will choose for this?                     1 marks

Answers can be viewed and downloaded from https://drive.google.com/file/d/0B6PHuk6I5SxbN3ozb00wV3pvdkE/view?usp=sharing. 

Question 2 - 2016, Sequencing Rules

Question 2:A service provider charges for his service on per minute basis and the customers have to buy the service time in advance. 8 customers have bought the service time as 12, 8, 5, 16, 10, 14, 7 and 5 minutes respectively. They arrive at the service provider at different times. Their arrival time are 10, 18, 20, 23, 27, 40, 45 and 48 minutes after opening of the office.

a)      Find the average time customers spend in the system if First Come First Serve (FCFS) sequencing rule is applied.                                                                                   3 marks

b)      What will be the impact on this average time if the sequencing rule is changed to Shortest Service Time First?                                                                                              4 marks

c)      Suppose the service provider creates facilities for self-service 3 minutes of the service time requirement. It means that a customer will require to be in queue only for service time bought minus 3 minutes. For example, the customer who has bought 16 minutes of service time will self-serve for 3 minutes and wait to be served for remaining 13 minutes. What will be the impact of this change on the average time customers remain at the service facility? Assume FCFS sequencing rule for this part of the question.    3 marks

Answers can be viewed and downloaded from https://drive.google.com/file/d/0B6PHuk6I5SxbVmdLNTdyVzQ1czQ/view?usp=sharing. 

Question 3 -- 2016, Inventory Control

Question 3: Assume a single item deterministic situation with constant demand and lead time.

a)      Derive a formula for finding Economic Order Quantity (EOQ).                     2 marks

b)      For an order quantity Q1, the total ordering cost is X and inventory carrying cost is Y. X is less than Y. If we change the order quantity to Q2, total ordering cost X gets reduced. Which is closer to EOQ; Q1 or Q2? Why?                                                     3 marks

 Answer video can be viewed and downloaded from https://drive.google.com/file/d/0B6PHuk6I5SxbODhITFhfMnM3M3M/view?usp=sharing.

Inventory Management

Question:

(i) An item is required in 5000 units/ year. The consumption rate is constant. The rate of inventory carrying cost is 25% of the average inventory value per year. You have two options to meet this requirement.

Option A: The supplier supplies the item at Rs. 200/ unit and charges Rs. 2000 per delivery as packing and transportation cost.

Option B: The supplier supplies the item at Rs 190/ unit and charges Rs 4000 per delivery as packing and transportation cost. The item supplied by this vendor has r% rejection. (To get r divide your roll number by 5. r = 5 if your roll number is divisible by 5 else it is equal to the remainder). Assume that you pay for the rejected items also.

Which option is better and why? (After showing all the calculations, you must write a concluding paragraph of about 3-4 sentences clearly mentioning the better option and giving the values of your decision parameters).                                                          

(ii) Assume that items received pass through the quality check and only good items are stored. What should be the minimum reorder point to keep the probability of shortage below 0.3, if the consumption during lead time is variable and uncertain with mean 600 units and standard deviation 100 units? 

Answer: It has two parts. Answers to them are discussed in 2 different videos given below.

Part (i):

Part (ii):