OREGON DSC 335, Spring 2014 Homework Assignment #2

Homework
Assignment #2
DSC 335, Spring 2014
1.
(Estimating capacity
requirement) The Southeast Manufacturing Company is producing two types of
products: A and B. Both of these products are produced at the same workstation,
called the Automatic Lathe. It works 250 days per year with two 8-hour shifts
and desires a 25 percent capacity cushion. Demand forecasts for the next year
and other production-related information are provided in the following table:

Product
A

Product
B

Demand
forecast (units/yr)

4,000

12,000

Batch
size (units/batch)

80

150

Processing
time (hr/unit)

2.5

2.0

Setup
time (hr/batch)

18

24

1)
What’s the number of
automatic lathes required to meet the demand for both products?

2.
(Continue from
Problem 1.) Suppose the company has 12 automatic lathes, and financial
constraints prevent buying new machines for the next year. Consider the
following alternatives:
2)
The company can
increase the batch size of product B to reduce the number of setups. What is
the minimum batch size of product B that leads to a capacity requirement of 12
lathes or less?

3)
The company can
decrease the capacity cushion. At what cushion level the demand can be met with
the current capacity of 12 lathes?

3.
(Bottleneck analysis
and inventory buildup) Wally’s Widget Warehouse accepts customer orders, pick
them up from customers’ locations and then pack them. The manager wants to analyze the process and
has provided the process flow diagram shown below.
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The
first step is to take the orders. The order taker accepts order from 7am to
7pm, and stops taking orders after 7pm.
If the order taker is busy, an arriving customer is put on hold, and
after 7pm all unaccepted customers orders will be lost. The second step is to pick the order from the
customer by staff A. In the third step, the order is packaged for shipping by
staff B. The capacity rates of the three
workers are marked in the above diagram. Wally promises that every order
accepted today gets shipped tomorrow. That is, staff A and staff B must finish
all orders before they are shut down.
4)
What’s the capacity
rate of the whole process?

5)
Wally had a very busy
day, with demand rate being consistently higher than the capacity rates of all
the three workers. Draw two inventory buildup diagrams (one for the buffer
between the order taking and order picking, one for the buffer between the
order picking and order packing). [Hint:
here we do not need the actual demand rate, since it is consistently higher
that the capacity rate of all workers. To draw an inventory buildup diagram for
a buffer, we only need to know the actual input rate of the corresponding
buffer, which should be restricted by the order taker.]
a)
Inventory buildup diagram for buffer 1 (the buffer between order taking and
order picking):

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b)
Inventory buildup diagram for buffer 2 (the buffer
between order picking: and order packing):

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6)
How long would staff
A and staff B have to work to finish all orders received for the day, respectively?
(Hint: you may use buffer buildup diagrams you draw to assist your analysis.)

7)
Throughout that day,
what would be the highest number of orders waiting to be picked?

8)
Throughout that day,
what would be the highest number of orders waiting to be packed?

4.
(Continue from
problem 3.) We now double staff B’s capacity rate. That is, the company can
package for 120 customers per hour.
9)
How long will staff A
and staff B have to work if we have a day with the maximum orders?

10)
What is the maximum
number of orders waiting to be picked?

11)
What is the maximum
number of orders waiting to be packed?

5.
(Bottleneck analysis
and capacity management) Daffi Dave’s Sub Shop makes custom submarine
sandwiches to order. They are analyzing the processes at their shop. The
general flow of the process is shown below. There are four workers working in
the process.
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12)
What is the capacity
rate of the process?

13)
If we add another
Staff E to perform one of the four tasks, who can take the order for 1
minute/order, slice bun and add meat/cheese for 2 minutes/order, add toppings
and condiments for 4 minutes/order, and bag the orders for 1 minutes/order.
Where should we add him/her? What’s the new capacity rate of the process?

14)
Answer this question
independent of question 13). What’s the new capacity rate of the process, if we
ask staff C and staff D to work in parallel, i.e. both of them add the toppings
and condiments and bag the orders? Assume
that staff C can bag the orders for 2 minutes/order, and staff D can add the
toppings and condiments for 4 minutes/order.