Megacard Corporation

OPERATIONS MANAGEMENT II Assignment -1

MEGACARD CORPORATION

Submitted by Group 9 Section F Phanindra Kumar J Maitreyee Korgaonkar S M Prasanna Kumar Neha Hajela Nitin Nagori Subhanan Sahoo Vijay Khuman C

Q1. For Indianapolis, the maximum number of expected calls in the peak hour (10AM to 10:59 AM) is

108 calls. Now let us assume we need to serve all the customers (including peak hours) hence for a stable system λ≤s

(Arrival rate ≤ No. of Servers*Mean service rate)

As we know that each call takes 5 minutes average service time, hence µ=12 calls/hr. Thus, s ≥ 9 108/12

(For stable system)

Also there are 2 conditions that the average “hold” ( Waiting) time is only 1 minute.

Now let us take s=10, 11, 12 & so on till this condition is satisfied. The values for different variables for the iterations are as follows No. of servers 10 11 12

Po( Idle time Prob.) 0.00006959687 0.00009955626 0.00011279897

Lq (No. of calls waiting) 6.018584 1.937116 0.798104

Wq (seconds) 200.6194572 64.57053701 26.60346845

Hence the minimum number of servers for Indianapolis BTC is 12, for maintaining the desired service levels at each hour.

No. of servers s = 12

Hence the management has to hire 12 Travel counsellors.

Q2 a) If the average service time is halved to 2.5 minutes

Now we have µ=24calls/hr. Hence for a stable system

λ≤s

Hence, Now

s ≥ 4.5 108 24

Thus we now calculate the various values for s=5 with the condition of 1 minute ( 60 seconds) waiting time

No. of servers Po( Idle time Prob.) Lq (No. of calls waiting) 5 0.00495854962 6.862439 6 0.00914011511 1.264956 We can find that 6 servers are now sufficient for handling the same BTC

Wq (seconds) 228.7479662 42.16520758

No. of servers s = 6

Q2 b) If the on-hold time is increased to 120 seconds (2 minutes)

Now we assume µ=12 calls/hr. & same arrival rate, but only the waiting time can be increased to 2 minutes or 120 seconds. Everything in Q1 will remain same, but now we can take the minimum number of servers as 11, rather than 12. No. of servers 10 11

Hence

Po( Idle time Prob.) 0.00006959687 0.00009955626

Lq (No. of calls waiting) 6.018584 1.937116

Wq (seconds) 200.6194572 64.57053701

No. of servers s = 11

Q3) Economic impact when the 3 centres (Indianapolis, Kansas & Dallas) have a centralized BTC

Carrying out a similar analysis on Kansas City & Dallas we find that the total number of servers required for each of them is: BTC

No. of servers

Indianapolis Kansas City Dallas

12 7 8 27

Total

Thus, total no. of servers required is 27 When we centralize then all the traffic is centralized; hence the maximum arrival rate is now 201 calls in the peak hour. Again for a stable system, the number of servers should be more than s ≥ 16.75 201/12

Hence once again we try to find the appropriate number of servers for which the waiting time is less than 60 seconds No. of servers 17 18 19 20

Po( Idle time Prob.) 0.00000000756 0.00000002834 0.00000003957 0.00000004572

Lq (No. of calls waiting) 62.30933 9.199211 3.689692 1.801165

Wq (seconds) 1115.987999 164.7619833 66.08403584 32.25967723

Hence the number of servers required is 20 for the centralized BTC. Hence in a centralized system 7 less travel counsellors are required. Thus the economic impact of having a centralized BTC is Savings = 7*30,000 =$ 210,000 (As we are saving the salaries of 7 travel counsellors, which is $30,000 per annum) Savin s= 210 000

But there are certain set-up & maintenance costs which will be incurred for this centralized BTC.

Ex enses= 160 000 Hence the overall benefit for year 1992, will be Benefit= 50 000

Thus the annual costs reduce by $50,000