OM $235$ Homework$-3$

Please place each of your answers inside the rectangular box that is next to each question. Each question is worth one

point unless otherwise indicated. There is a total of $29$ potential points. $($Revised: August $31,2023.)$

Name:

Question $1.$ A diagram of a service process is given below. The process runs on the JIT principle $($in other words customers

cannot leave the waiting room and start through the process at Operation $1$ more often than the process can finish them.

Customers arrive every $6$ minutes. Note that the abbreviation $$custs$$ stands for customers. The capacities are shown for each

Note: Feel free to handwrite answers to this and other homework sets so long as they are legible.

a$.$ Identify the bottleneck

b$.$ What is the process capacity in customers per hour?

c$.$ What is the throughput $($flow rate$)$ of the process?

d$.$ What is the percentage utilization of Clerk D assuming that customers arrive every

$6$ minutes?

e$.$ What is the average overall percent labor utilization for the $4$ clerks assuming that

customers arrive every $6$ minutes?

OP

$1$

OP

$2$

OP

$3$

OP

$4$

Waitin

g

Room

WIP

$1$

WIP

$2$

WIP

$3$

$20$

custs$/$hour

$15$

custs$/$hour

$12$

custs$/$hour

$30$

custs$/$hour

Clerk

A

Clerk

B

Clerk

C

Clerk

D

$2$

f$.$ To increase the capacity of the process, to which operation would you add an

additional clerk?

g$.$ If a clerk is added to increase the capacity of the process $($you can assume the new clerk

is as efficient as the old clerks at any of the $4$ operations$),$ what is the new process

capacity in customers per hour?

Question $2.$ Consider the process for a store below.

a$.$ What is the bottleneck?

$3$

b$.$ What is the process capacity in customers per hour?

c$.$ If the process is operating at capacity, what is the average amount of time between customers

completing the process and leaving the store?

For the remaining problems, assume customers arrive every $5$ minutes.

d$.$ What is the percent utilization of the clerks performing Operation A$?($Hint: the utilization of the

two clerks will be the same because they are in parallel.$)$

e$.$ What is the percent utilization of Charlie?

f$.$ What is the percent utilization of Dave?

g$.$ What is the rush order flowtime in minutes?

h$.$ If Erin leaves for the day and Bob covers for her, what is the new process capacity in custs$/$hr$?$

$4$

Question $3.$ Are the statements below regarding Just$-$in$-$Time $($JIT$)$ processes true or false? Note: answering $$True$$ indicates

that the statements are always true.

a$.$ Utilization of non$-$bottleneck resources can reach $100\%$

b$.$ Average WIP cannot keep growing indefinitely.

c$.$ Jobs start in the process at the same rate as they leave it$.$

d$.$ In real life JIT practice, there is never any WIP inventory.

Question $4.$ Are the statements below regarding starved processes true or false? Note: answering $$True$$ indicates that the

statements are always true.

a$.$ Jobs start in the process at the same rate as they leave it$.$

b$.$ There is never any WIP inventory

c$.$ The bottleneck resource has less than a $100\%$ utilization.

d$.$ The bottleneck resource always has the highest utilization.

e$.$ The flow time of any job is always the rush order flowtime.

Question $5.$ Which of the below is associated with increasing WIP and RMI inventories? Please indicate True or False.

a$.$ Defects generally decrease

b$.$ There is less free cash available to the firm.

c$.$ Flow time increases

d$.$ Process visibility increases.

e$.$ Warehousing costs increase