Houston Downtown FINANCE 3305 MBA 6325 Decision Models for Supply Chain Managers

MBA 6325 Decision Models for Supply Chain Managers
Linear Programming Case: A Production Problem at TS6 Fabricators Inc.
Steven Coy, Ph.D.
©
2010-2015
"I think that will do it. Thanks Mr. Bear. I will send the order in today. As always, it is a pleasure
doing business with you." Helena Troya returned the phone to its cradle and leaned back in her
chair smiling. In four years as Vice President of Marketing at TS6 Fabricators Inc., Helen had
never had such a good month. She laughed and said to the empty room, "The economy must be
moving again. This is the fourth big order this month!" Helen mused for another moment and
then picked up the phone and punched in a familiar number.
"Production scheduling. This is Francisco Pizaro."
"Francisco! This is Helen. I just closed a deal with Bear industries for another big order."
Dead silence.
"Francisco! Are you there?"
"Helen, you said big order?"
"Yes. Why?" Helen asked.
"When is the deadline?" Francisco replied.
Helen hesitated and then said, "Ninety days—just like the others. Francisco is something
wrong?"
"No. Nothing is wrong, Helen. But, with the three orders that we already have, we are already
nearly at capacity. We may have to outsource some of the order."
Helen thought for a moment and said, "That will be okay Francisco. I have enough margin built
into the price to cover a substantial purchase."
"Good. Then email me the order and I will see what I can do…And Helen…"
"Yes, Francisco?"
"Take it easy for the rest of the month. Okay?"
Helen laughed and said, "No problem Francisco!"

1

TS6 Fabricators Inc.
TS6 Fabricators, which is known in the business as TFab, is a large pipe manufacturer in the Houston,
Texas metropolitan area. T-Fab is a publicly traded
company, which has been in the pipe fabrication
business for 75 years.
T-Fab produces several types of steel pipe for the
energy and utility industries. All of their products are
made from rolled plate steel, which is then welded
into 10 foot sections and assembled and welded into
pipes up to 50 feet long. T-Fab's products are shown
in Table 1.
The production process at T-Fab varies depending on
the product. Each product is produced from steel
plate. Casings are manufactured from ½" plate, and
Rolled and welded (R&W) products are produced
from 1" or 1½" plate. Casings typically require
rolling, welding and visual inspection. R&W pipes
require rolling, welding, visual inspection, x-ray
inspection, sand blasting, and finishing. Longer
sections require additional assembly and welding.
Radius casings are standard casings that are bent into
10 or 20 foot radius arcs for curved assemblies.
Mitered elbows are right angle assemblies of R&W
pipe that require cutting, straight and angle rolling,
welding, visual inspection, x-ray inspection, sand
blasting, and finishing.

Part#
106C
206C
206C10R
206C20R
1012C
2012C
2524RW
5024RW
5036RW
5072RW
5084RW
24ME
36ME
72ME
84ME

Description
10' x 6" Casing
20' x 6" Casing
10' Radius Casing
20' Radius Casing
10' x 12" Casing
20' x 12" Casing
25' x 24" R&W Pipe
50' x 24" R&W Pipe
50' x 36" R&W Pipe
50' x 72" R&W Pipe
50' x 84" R&W Pipe
24" Mitered Elbow
36" Mitered Elbow
72* Mitered Elbow
84" Mitered Elbow

Table 1: TS6-Fabricators' Product Line.

The figures below illustrate how straight pipes are Figure 1: A 10' capacity plate bending rolling machine
assembled. The pipe labeled Cylinder 1 shows a pipe milling a steel plate. (http://www.bisewelding.com)
up to 10 feet long. Plate steel is rolled in a large plate
bending rolling machine as shown in the picture in Figure 1. The two edges of the rolled plate
are welded together to form a seam. The second figure illustrates how a longer pipe is assembled
from smaller sections. The seams are staggered, which inhibits separation along the seam.

Figure 2: Pipe assembly examples. Cylinder 1 is formed from a single steel plate. The pipe at right illustrates
how a longer pipe is formed. (Illustration from http://www.bisewelding.com)

2

Orders to be Completed 90 Days
Helena Troya has secured four orders for the next 90 days. The orders are shown in Table 2
below.

Product
10' x 6" Casing
20' x 6" Casing
10' Radius Casing
20' Radius Casing
10' X 12" Casing
20' x 12" Casing
25' x 24" R&W Pipe
50' x 24" R&W Pipe
50' x 36" R&W Pipe
50' x 72" R&W Pipe
50' x 84" R&W Pipe
24" Mitered Elbow
36" Mitered Elbow
72* Mitered Elbow
84" Mitered Elbow

Part #
106C
206C
206C10R
206C20R
1012C
2012C
2524RW
5024RW
5036RW
5072RW
5084RW
24ME
36ME
72ME
84ME

Total Sales Revenue

Bear
Industries
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Hugo
Energy
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

DR Riley
Drilling
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Bastibug
Water
Treatment
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

?

?

?

?

Table 2: TS6-Fabricators Orders. All orders must be filled during the planning period. Note: ask your professor for your team's
version of this table.

Given the vast quantity of steel
required to fill these orders and the
lead time to resupply, T-Fab must
rely on material on hand to fill these
orders. Table 3 lists the amount of
plate steel required to produce one
unit of each product and the total
amount of steel on hand. T-Fab
orders plate steel in 10' widths. For
assemblies that require different
sizes of plate (i.e., 25 foot pipes and
mitered elbows), the plates must be
cut before rolling.

Part #
106C
206C
206C10R
206C20R
1012C
2012C
2524RW
5024RW
5036RW
5072RW
5084RW
24ME
36ME
72ME
84ME
Total Available

0.5" Plate
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

1" Plate
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

1.5" Plate
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Table 3: Steel requirements for each product and total amount of each type of
plate steel on hand. All values are in square feet. Note: ask your professor for
your team's version of this table.

3

As with raw materials, plant capacity is limited. Each department has a fixed amount of free time
in the next 90 days. The total time available (in hours) and the processing time requirements of
each product (in minutes) are shown in Table 4 below.

Part #
106C
206C
206C10R
206C20R
1012C
2012C
2524RW
5024RW
5036RW
5072RW
5084RW
24ME
36ME
72ME
84ME
Hours
Available

Plate
Cutting
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Rolling
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Bending
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Assembly
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Welding
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Sand
blasting
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Finishing
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

Visual
Inspection
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

X-ray
Inspection
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?

?

?

?

?

?

?

?

?

?

Table 4: Processing time (minutes) required in each department and total number of hours available during the planning period.
Note: ask your professor for your team's version of this table.

Depending on the data, it is quite possible that plant
production capacity and available plate steel will be
insufficient to meet demand. Therefore, Francisco contacted
Midnight Manufacturing, which is a Houston-area pipe
fabricator, to produce product that T-Fab will be unable to
manufacture. Francisco is confident that Midnight has the
capacity to assume as much of the order as necessary. With
the exception of radius casing and mitered elbows, Midnight
is able to produce modest quantities of all of T-Fab's
products, they have similar standards of quality to T-Fab,
and they have been very reliable in the past. Unfortunately,
this reliability comes at a price. Product costs will be
considerably higher than if T-Fab produced the products
themselves. Table 5 contains the cost to manufacture and
purchase each product. Note: material and labor costs are
included in the costs shown in the second column of the
table.

Part #
106C
206C
206C10R
206C20R
1012C
2012C
2524RW
5024RW
5036RW
5072RW
5084RW
24ME
36ME
72ME
84ME

Produce
$512
$925
$650
$1,039
$1,428
$1,817
$2,206
$2,595
$2,984
$3,373
$3,762
$4,151
$4,540
$4,929
$5,318

Purchase
from
Midnight
$640
$1,156

$1,785
$2,271
$2,758
$3,244
$3,730
$4,216
$4,703

Table 5: Product manufacturing and purchase
costs.

4

In the past, Francisco has relied on an in-house team of operations and supply chain
professionals to develop a production schedule when some of the product must be outsourced.
As he has done in the past, he has decided to call on your team to develop a plan. He sent the
following email to your team leader this morning.
From: Francisco Pizaro [mailto:Francisco.Pizaro@TS6.com]
Sent: Tue 9/7/2010 3:21 PM
To: MS Team Leader [mailto: MSTeam.Leader@TS6.com]
Cc: Helen Troya
Subject: 90 Day Plan
Team,
By now I am sure you know that T-Fab's success in the sales office has resulted in a scheduling
problem for us. I am relying on you to determine what products we should make in house and
what products we should outsource. Please refer to the tables in the attached document
[Francisco is referring to Tables 1-5 above] when formulating your linear program.
As before, I would like you to set up a model in Excel and use Solver to find the appropriate
division of products between us and Midnight Pipe Manufacturing. Once you have set up the
model, please answer the questions below.
Questions
1. How much of each product should T-Fab produce in house, and how much should we
outsource to Midnight?
2. What is the expected profit from this decision?
3. What is the additional cost from outsourcing?
4. Which of our resources (material and/or capacity) are constraining our ability to produce
everything in house?
5. Think outside the box. Is there a better way to solve this problem? Am I missing
something? [Note: this question asks you to consider the problem from a fresh
perspective. You should not change any of your preceding analysis. Instead, your
answer should be framed as advice for future order cycles.]
Thanks!
Francisco
Francisco Pizaro
Director of Production Scheduling
TS6 Fabricators Inc.
8512 Nonesuch Drive
Houston, TX 77002

5