The process flow diagram below illustrates bread making

Exam 1
1. Please answer problems 1 through 3 in a Word or Excel file, and problem 4
in an Excel file.
2. For full credit, please show your work/calculations, and the reasoning
leading to a numerical answer, do not just state the answer.
Problem 1
The process flow diagram below illustrates bread making on two baking lines that can
work in parallel, feeding into a packaging line. Each baking line bakes a batch of 100
loaves at a time, and the batches are then sent for packaging. FG stands for “Finished
Goods”, CT for Cycle Time.

Bread Making
CT = 1hr/100 Loaves

WIP

Packaging

FG

CT = 1hr/100

Bread Making
CT = 1 hr/100 Loaves

(a) Suppose that the capacity of the packaging line is 100 loaves every hour.
Identify the bottleneck operation and compute the steady state capacity of
the process.
(b) By how much should the start times of the two bread making lines be
staggered so that each batch of 100 loaves has the same lead time?
(c) What is the lead time of a batch of 100 loaves in (b) above?
(d) Estimate the average capacity utilization of each bread-making line and of
packaging when the process is run as per the rule you specified in your
answer to (b).
Problem 2

Consider the following project network. The numbers represent activity times in weeks.

A, 2

B, 1

C, 1
E, 3

H, 5
J, 4
I, 5

Carry out a forward and backward path analysis and calculate ES, EF, LS, LF, and slack
for each activity.
Problem 3

A, 2

B, 1

C, 1
E, 3

H, 5
J, 4
I, 5

Suppose the number against each activity represents the expected activity times rather
than the actual activity times. The estimated activity standard deviations are A = 1, H =
2, I = 3, J = 2, E = 5. Estimate the probability that the project will finish within 21 weeks
using the PERT method.

Problem 4
A book store needs to place an order for calendars. Each calendar sells for $10.
Customer demand is assumed to be normally distributed with mean 200 and standard
deviation 60. The number of calendars that the book store’s supplier can supply is
uniformly distributed between 125 and 200.
The book store first places an order, and then the supplier determines the number of
calendars he can actually supply. The supplier charges $8 per calendar if he can supply
the entire order; otherwise he charges only $7.50 per calendar.
The manager of the book store has decided to order either 150 or 175 calendars.
Use Monte Carlo simulation to help the manager choose between these two order
quantities.