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IIE/RA CONTEST PROBLEMS

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CONTEST PROBLEM 10

IIE/RA Contest Problems
Tenth Annual Contest: SM Paints

SM Paints produces a line of house paints at manufacturing facilities in four North
American locations. The finished products are shipped to various distribution centers
that carry the companys inventory. This inventory is then used to replenish depleted
stock at the companys retail stores. We recently embarked on a lean initiative with a
cost-reducing objective of lowering the inventory in the distribution centers while still
meeting the requirements of the retail stores. A study revealed that significant cost
reductions could be achieved if our manufacturing plants could fill orders for the
distribution centers in three working days or less.
Currently none of our manufacturing plants are able to meet this three-day delivery
requirement consistently. In addition, it is not clear what improvements would be necessary in order to remedy this situation. Due to this uncertainty, we are asking you to make
some recommendations based on an analysis of a single manufacturing facility.
You are asked to evaluate the current system and propose modifications that will result
in minimizing operating cost while still achieving the desired performance levels. Although it would be desirable to fill all orders in three working days, it is understood that
any facility can occasionally be overloaded. With this in mind, we would like to achieve a
performance level of filling 98% of all orders in the three working days. This document
describes the current system and provides data and costs where they are available.
The manufacture of paint at this plant is a relatively simple four-step process. It starts
by combining the various components and pigments with a base liquid at the mix and
grind tanks. The components are first ground together and then mixed in a relatively
small tank that looks somewhat like a kitchen mixer. Once this step of the process is
complete, the resulting mixture is pumped to a thinning tank where the remaining liquid
is added. The thin tanks also have mixers that assure that the resulting paint is homogenous. After thinning, the mixture is transferred to a hold tank where the paint remains
until a fill line becomes available. Once the filling process is complete, the resulting finished product is sent to shipping. A high-level view of this flow is shown below.
Mix and Grind

Thin

Hold

Fill

The manufacturing facility under study runs 24 hours a day, seven days a week, with
new orders being released once each day. The number of new orders averages about 23
per day and appears to follow a Poisson distribution. New orders are classified according
to the order batch size as small, medium, or large (in gallons). The small batches make up
10% of the orders. The medium batches make up 35%, and the large batches make up the

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IIE/RA CONTEST PROBLEMS

remaining 55% of the orders. The composition of each of these batches is given in the
table below (e.g., 40% of the medium batches are orders for 6,000 gallons).
Small Batches
Percent
Size (gal.)
60
1,000
40
2,000

Medium Batches
Percent
Size (gal.)
25
4,000
40
6,000
35
8,000

Large Batches
Percent
Size (gal.)
15
10,000
20
12,000
25
14,000
20
16,000
15
18,000
5
20,000

The product for each order can be packaged as quarts, gallons, or five-gallon buckets.
A single order may require one package type (all gallons), two, or all three types. All
orders include a percentage of gallon-size fill. Of the total orders, 75% require quarts and
40% require buckets. If quarts are required for an order, that portion of the order varies
from 10% to 40% by volume. If buckets are required, that portion of the order varies from
5% to 20% by volume. The remainder of the order is packaged as gallons.
There are seven identical mix and grind machines available. The time required to
complete this operation follows a triangular distribution with parameters 1.5, 2.4, and
3.5 (hours). Note that the facility currently only operates the mix and grind system for 16
hours per day. Upon completion of this first operation, the resulting liquid is transferred
to an available thin tank, but this transfer can only occur if a thin tank of the proper size is
available. There are nine thin tanks of differing sizes in the facility. The number and capacity (in gallons) of the nine thin tanks are shown in the following table.
Number of Thin Tanks

Capacity (gallons)

2
2
2
3

6,000
10,000
14,000
20,000

Allocation of product to the thin tanks is controlled by batch size, with the larger
tanks being reserved for larger batch sizes. For example, orders for batches of 6,000
gallons or fewer can only be transferred to the two 6,000-gallon or the two 10,000-gallon
tanks. The table below shows the allowable allocation by batch size to the various thin
tanks. Note that the 12,000- to 14,000-gallon batch sizes can only use two of the three
large 20,000-gallon thin tanks.
Batch Size (gallons)
1,000 to 6,000
8,000 to 10,000
12,000 to 14,000
16,000 to 20,000

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Thin Tanks (capacity in gallons)
6,000 or 10,000
10,000 or 14,000
14,000 and two of the three 20,000
20,000

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IIE/RA CONTEST PROBLEMS

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Once a thin tank is available, the transfer time follows a triangular distribution with
parameters of 20, 35, and 45 minutes. This transfer time is independent of the batch size.
After the transfer is complete, the now-empty mix and grind machine requires a cleaning
cycle before the next batch can be started. This follows a uniform distribution with
parameters of 18, 24 minutes.
The thinning operation consists of adding additional liquid to the product from the
mix and grind operation. The time to complete this operation is dependent upon the
batch size of the order since the liquid is added at a rate of 175 gallons per minute. The
batch is mixed at the same time that the liquid is being added. Once the thinning operation is complete, the batch is transferred to an available hold tank. The transfer rate is 195
gallons per minute. There are 10 hold tanks in this facility, with capacities shown below.
Number of Hold Tanks

Capacity (gallons)

2
4
4

8,000
12,000
20,000

As was the case with the thin tanks, it is not desirable to use the larger tanks for the
smaller batches. The table below shows what batch sizes can use the various hold tanks.
Batch Size (gallons)

Hold Tanks (capacity in gallons)

1,000 to 8,000
8,000 to 12,000
12,000 to 20,000

8,000 or two of the four 12,000
12,000 or one of the four 20,000
20,000

The batches are held in the hold tanks until the required fill lines become available.
There are four quart lines, four gallon lines, and two bucket lines. The fill rates and clean
times for these lines are shown below.
Line
Quart
Gallon
Bucket

Fill Rate (gallons per minute)

Clean Time (minutes)

8
40
38

20
15
18

The filling process is not allowed to start until the entire batch has been transferred to
a hold tank. Once that transfer is complete, the filling operation can start. If a batch
requires all three filler types, the fillers do not all have to be available at the same time.
For example, if only a gallon line is available, that part of the operation can be started.
Once the other lines become available, those remaining portions of the operation can be
started. The hold tank is only made available to the next batch when all of the filling
operations for an order are complete.
The facility has been configured so that any mix and grind tank can be connected to
any thin tank, any thin tank can be connected to any hold tank, and any hold tank can be
connected to any filler.

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A quick examination of the production for the current system indicates that we are
unable to meet the three-day performance target. Thus, the first question we would like
you to address is: What changes would be required in order for the current system to
meet the three-day performance level? Since several configurations are possible that
might meet this level, we would like your recommendation to include the minimum
investment required.
Approximate upgrade costs are given below:
Mix and grind tank
$600,000 per tank
Thin tank
Fixed cost of $1,200,000 per tank
Variable cost of $40,000 per 1,000 gallons of tank capacity
Hold tank
Fixed cost of $900,000 per tank
Variable cost of $30,000 per 1,000 gallons of tank capacity
Quart line
$1,200,000 per line
Gallon line
$1,400,000 per line
Bucket line
$400,000 per line
These costs include both equipment and installation costs. In addition, a third shift
could be added to the existing mix and grind area at a cost of $800 per day.
Furthermore, we are considering accepting a request by a nationwide chain of home
improvement stores to produce paint that would be marketed under their private label.
This paint would be produced in same the facility, and we expect that this would require
the production of an average of three additional orders or batches per day. The estimated
mix of batch sizes is shown below.
Private Label Batches
Percent
Size
25
45
30

10,000
15,000
20,000

We estimate that this would yield an additional income of $50,000 per day.
If we agree to a contract to produce these private-label orders, we would need to be
sure that we could ship 95% of them within five working days.
In summary, your analysis and recommendations should address the following
questions:
Scenario 1: What changes in the current system would be required to meet the
three-day performance level? What is the cost?

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Scenario 2: If we invest in the changes to meet the three-day performance level,
what additional changes would be necessary to meet the additional production
requirements of the private-label contract? Does this scenario make economic
sense?
Scenario 3: If we decide NOT to invest in changes to meet the three-day performance level, what changes in the current system would be required to meet the
existing and private-label production requirements? Does this scenario make economic sense?
Please provide all cost comparisons in dollars per week.

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