(solution) OPERATIONS MANAGEMENT - DSC 410 FALL 2016 - WAITING LINES -

Can anyone who is really good at linear programming, product mix and etc can help me with these assignments? Please

OPERATIONS MANAGEMENT ? DSC 410

FALL 2016 ? WAITING LINES ? HW #1

DUE MONDAY OCT 10th, 2016

NAME:

1. De Morgan?s Bank is the only bank in a small town in Georgia. On a

typical Friday, an average of 13.6 customers arrives per hour at the

bank to transact business. There is one single teller at the bank, and

the average time required to transact business is 4 minutes. It is

assumed that service times are exponentially distributed. Although

this is the only bank in town, some people in the town have begun

using the bank in a neighboring town about 20 miles away. A single

line is used and the customer at the front of the line goes to the first

available bank teller. It is estimated that waiting time cost per

customer per hour is \$25. A bank teller is paid \$12 per hour

Arrival rate = 13.6 customers per hour

Service time = 4 minutes = 0.0666666 hours

Cost per server = \$12 per hour

Waiting cost = \$25 per hour per customer

This problem was run using computer software. Time units were

hours. The problem was run twice, first under the assumption of one

teller, and secondly under the assumption of 2 tellers. Below is the

computer output:

De Morgan's Bank (1 Teller)

QUEUE 1 : M / M / C ?[TIME UNITS = HOURS]

Q U E U E S TAT I S TI C S

Number of identical servers . . . . . . . . .

Mean arrival rate . . . . . . . . . . . . . .

Mean service rate per server . . . . . . . . 1

13.6000

15.0000 Mean server utilization (%) . . . . . . . . .

Expected number of customers in queue . . . .

Expected number of customers in system . . .

Probability that a customer must wait . . . .

Expected time in the queue . . . . . . . . .

Expected time in the system . . . . . . . . . 90.6667

8.8076

9.7143

0.9067

0.6476

0.7143 1 De Morgan's Bank (1 Teller)

QUEUE 1 : M / M / C [TIME UNITS = HOURS]

COST ANALYSIS PER UNIT TIME

Current System

Optimal System *

Number of servers |

1

|

2

|

Cost per server

| 12.0000

| 12.0000

|

Cost of service

|

12.0000|

24.0000|

Mean number in system | 9.7143

| 1.1412

|

Waiting cost/customer | 25.0000

| 25.0000

|

Cost of waiting

|

242.8600|

28.5300|

------------------TOTAL COST

254.8600

52.5300

* Optimization is over number of servers

De Morgan's Bank (1 Teller)

QUEUE 1 : M / M / C

PROBABILITY DISTRIBUTION OF NUMBER IN SYSTEM

Number Prob 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

+----+----+----+----+----+----+----+----+----+----+

0 0.0933|*****

|

1 0.0846|****+---|

2 0.0767|****--------|

3 0.0696|***+-----------|

4 0.0631|***+--------------|

5 0.0572|***------------------|

6 0.0518|***---------------------|

7 0.0470|**+-----------------------|

8 0.0426|**+-------------------------|

9 0.0386|**----------------------------|

10 0.0350|**------------------------------|

11 0.0318|**--------------------------------|

12 0.0288|*+---------------------------------|

13 0.0261|*+----------------------------------|

14 0.0237|*+-----------------------------------|

15 0.0215|*+-------------------------------------| 2 De Morgan's Bank (2 Tellers)

QUEUE 2 : M / M / C [TIME UNITS = HOURS]

Q U E U E S TAT I S TI C S

Number of identical servers . . . . . . . . .

Mean arrival rate . . . . . . . . . . . . . .

Mean service rate per server . . . . . . . . 2

13.6000

15.0000 Mean server utilization (%) . . . . . . . . .

Expected number of customers in queue . . . .

Expected number of customers in system . . .

Probability that a customer must wait . . . .

Expected time in the queue . . . . . . . . .

Expected time in the system . . . . . . . . . 45.3333

0.2345

1.1412

0.2828

0.0172

0.0839 De Morgan's Bank (2 Tellers)

QUEUE 2 : M / M / C [TIME UNITS = HOURS]

COST ANALYSIS PER UNIT TIME

Current System

Optimal System *

Number of servers

|

2

|

2

|

Cost per server

| 12.0000

| 12.0000

|

Cost of service

|

24.0000|

24.0000|

Mean number in system | 1.1412

| 1.1412

|

Waiting cost/customer

| 25.0000

| 25.0000

|

Cost of waiting

|

28.5300|

28.5300|

------------------TOTAL COST

52.5300

52.5300

* Optimization is over number of servers

De Morgan's Bank (2 Tellers)

QUEUE 2 : M / M / C

PROBABILITY DISTRIBUTION OF NUMBER IN SYSTEM

Number Prob 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

+----+----+----+----+----+----+----+----+----+----+

0 0.3761|*******************

|

1 0.3410|*****************+-----------------|

2 0.1546|********------------------------------------ |

3 0.0701|****------------------------------------------- |

4 0.0318|**-----------------------------------------------|

5 0.0144|*------------------------------------------------|

6 0.0065|+------------------------------------------------|

OVER 0.0055|+------------------------------------------------| 3 +----+----+----+----+----+----+----+----+----+----+ Use the above computer output to respond to the following

questions.

(a) On the average, how many minutes does a customer spend in the

line before getting served if one bank teller is on duty?

(b) On the average, how many minutes does a customer spend in the

line before getting served if two bank tellers are on duty?

(c) On the average, how many minutes does a customer spend in the

bank both waiting to be served and being served if one teller is on

duty?

(d)On the average, how many minutes does a customer spend in the

bank both waiting to be served and being served if two tellers are

on duty?

(e) On the average, how long is the waiting line if one teller is on

duty?

ANSWER (f) On the average, how long is the waiting line if two tellers are on

duty?

ANSWER 4 (g) On the average, how many customers are in the bank if one teller

is on duty?

(h) On the average, hoe many customers are in the bank if two tellers

are on duty?

(i) What percentage of the time is a teller busy if one teller is on

duty?

(j) What percentage of the time is a teller busy if two tellers are on

duty?

(k)If the bank opens for service 8 hours on Fridays, what is the

expected cost for both waiting and service for the day if one teller

is used?

(l) If the bank opens for service 8 hours on Fridays, what is the

expected cost for both waiting and service for the day if two tellers

are used?

(m) What measures of performance are cut into half when two

tellers are on duty as opposed to one teller on duty?

ANSWER 5 (n) How come other measures of performance are not cut into half

when we double the number of tellers?

schedule one teller on duty or two tellers on duty?

Solution details:
STATUS
QUALITY
Approved

This question was answered on: Jan 30, 2021

Solution~0001000395.zip (25.37 KB)

This attachment is locked

We have a ready expert answer for this paper which you can use for in-depth understanding, research editing or paraphrasing. You can buy it or order for a fresh, original and plagiarism-free solution (Deadline assured. Flexible pricing. TurnItIn Report provided)

STATUS

QUALITY

Approved

Jan 30, 2021

EXPERT

Tutor