Chapter 17, Problem 3PA

a)

Summary Introduction

To determine: The offered load.

Explanation of Solution

Given information: The following information are provided in the problem about company LARA,

$\begin{array}{c}\text{Number of reporters = 5}\\ \text{Time taken to complete the process = 3 hours}\\ \text{Standard deviation}=\text{2 hours}\\ \text{Interarrival time}=\text{30 mintues}\\ \text{Standard deviation of Interarrival time}=\text{30 mintues}\end{array}$

Calculation of offered load:

. $\begin{array}{c}\text{Offered load}\left(r\right)=\frac{p}{a}\\ =\frac{3\text{hours}}{0.5\text{hours}}\\ =6\end{array}$

Offered load is the ratio of average processing time (p) to average interarrival time (a) that is 3 hours divided by 0.5 hours gives 6 as offered load.

b)

Summary Introduction

To determine: Implied Utilization.

Explanation of Solution

Given information: The following information are provided in the problem,

$\begin{array}{c}\text{Number of reporters = 5}\\ \text{Time taken to complete the process = 3 hours}\\ \text{Standard deviation}=\text{2 hours}\\ \text{Interarrival time}=\text{30 mintues}\\ \text{Standard deviation of Interarrival time}=\text{30 mintues}\end{array}$

Calculation of implied utilization:

$\begin{array}{c}\text{Implied utilization = }\frac{p}{a\times m}\\ =\frac{3hours}{0.5hours\times 5reporters}\\ =1.2\end{array}$

Implied utilization is the ratio of average processing time to the product of average interarrival time and number of servers. Therefore 3 hours divided by the product of 0.5 hours and 5 reporters gives the implied utilization of 1.2.

c)

Summary Introduction

To determine: The capacity to complete the assignments.

Explanation of Solution

Given information: The following information are provided in the problem,

$\begin{array}{c}\text{Number of reporters = 5}\\ \text{Time taken to complete the process = 3 hours}\\ \text{Standard deviation}=\text{2 hours}\\ \text{Interarrival time}=\text{30 mintues}\\ \text{Standard deviation of Interarrival time}=\text{30 mintues}\end{array}$

Calculation of capacity:

$\begin{array}{c}\text{Capacity = }\frac{m}{p}\\ =\frac{5\text{reporters}}{3\text{hours}}\\ =1.67\end{array}$

Capacity to complete the assignment is the ratio of number of resources to the average processing time which is product of 5 reporters with 3 hours gives the capacity as 1.67.

d)

Summary Introduction

To determine: The probability that an incoming text message is not pursued.

Explanation of Solution

Given information: The following information are provided in the problem,

$\begin{array}{c}\text{Number of reporters = 5}\\ \text{Time taken to complete the process = 3 hours}\\ \text{Standard deviation}=\text{2 hours}\\ \text{Interarrival time}=\text{30 mintues}\\ \text{Standard deviation of Interarrival time}=\text{30 mintues}\end{array}$

Calculation of probability that three pumps are being used by that an incoming text message is not pursued:

Probability that incoming text message cannot be pursued can be found from Erlang loss table, for r is 6 and number of server m is 5, the corresponding value is 0.3604. Therefore, probability that incoming text message cannot be pursued is 0.3604.

e)

Summary Introduction

To determine: Flow rate of completed assignments.

Explanation of Solution

Given information: The following information are provided in the problem,

$\begin{array}{c}\text{Number of reporters = 5}\\ \text{Time taken to complete the process = 3 hours}\\ \text{Standard deviation}=\text{2 hours}\\ \text{Interarrival time}=\text{30 mintues}\\ \text{Standard deviation of Interarrival time}=\text{30 mintues}\end{array}$

Calculation of flow rate of completed assignments:

$\begin{array}{c}\text{Flowrate}=\frac{\text{1}}{\text{a}}\left(\text{1}-{\text{P}}_{\text{m}}\right)\\ =\frac{\text{1}}{\text{0}\text{.5}\text{hour}}\left(\text{1}-\text{0}\text{.3604}\right)\\ =\text{1}\text{.28}\end{array}$

The Flow rate of completed assignments is 1.28.

f)

Summary Introduction

To determine: Utilization of LARA reporter.

Explanation of Solution

Given information: The following information are provided in the problem,

$\begin{array}{c}\text{Number of reporters = 5}\\ \text{Time taken to complete the process = 3 hours}\\ \text{Standard deviation}=\text{2 hours}\\ \text{Interarrival time}=\text{30 mintues}\\ \text{Standard deviation of Interarrival time}=\text{30 mintues}\end{array}$

Calculation of utilization:

$\begin{array}{c}\text{Utilization=}\frac{\text{flowrate}}{\text{capacity}}\\ =\frac{1.28}{1.67}\\ =0.77\end{array}$

Utilization is calculated by dividing flowrate with capacity which is the ratio of 1.28 to 1.67 which yields 0.77.

g)

Summary Introduction

To determine: The number of reporters needed for 85% of the text message to be attended.

Explanation of Solution

Given information: The following information are provided in the problem,

$\begin{array}{c}\text{Number of reporters = 5}\\ \text{Time taken to complete the process = 3 hours}\\ \text{Standard deviation}=\text{2 hours}\\ \text{Interarrival time}=\text{30 mintues}\\ \text{Standard deviation of Interarrival time}=\text{30 mintues}\end{array}$

Calculation of number of reporters:

Probability $\begin{array}{c}{P}_m=1-0.97\\ =0.15\end{array}$

For r = 6 & P_m as 0.15, the number of operators required is between 7 and 8.

Therefore, the number of reporters required for 85% of text messages to be attended is 8.