Inventory Management and Re-Order Point Analysis at The Client’s
Component Re-Build Center
Prepared by:
Kelley Bessette
Jeff Litchfield
John Johnson
Matt Riskin
April 2002
Introduction
The Client is one of the world’s largest dealers of heavy machinery products. One
subdivision of The Client is the Component Rebuild Center (CRC), which is
located in Edmonton. At the CRC, used parts are refurbished and sold to existing
clients. The Client is interested in accurately assessing the number of refinished
parts needed throughout their network to satisfy demand and allocate as little
capital as possible to dormant inventory. Customers are able to sell their used
parts back to the CRC when they buy a remanufactured part from the CRC, which
makes it a closed loop system. The production manager of the CRC was
concerned that they were holding too much finished goods inventory.
Terminology
Throughout the duration of this project, the following terminology played a major
role in the understanding of the problem and solution.

Branch – Any node in the network.

Demand Center – Any branch in the network with demand over a user
defined critical number of parts per year.

Distribution Center – Services the branches by carrying inventory for
those which do not qualify as demand centers. It is of note that sales occur
here as well, thus inventory carried here serves both its own sales, and
those for the branches for which it carries goods.

Core – Any part in the system.

Core Bank – Cores waiting to be refurbished at the CRC.
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
OR Sales – This is a lost sale due to not carrying adequate inventory. In
this case, a customer goes directly to Caterpillar or another competitor to
purchase a part.
Problem Definition
The Client sells, services and finances the full line of Caterpillar and
complementary equipment throughout British Columbia, Alberta, Yukon, and the
Northwest Territories. Below is a map of the area that The Client services.
When a The Client customer needs an existing part replaced, they have the option
to make use of a used part exchange program. This entails selling back the used
core in return for one of The Client’s refurbished parts. The old core will be
returned to the CRC where it is remanufactured and made available for sale. This
results in a closed loop inventory system, as is shown below.
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Original Inventory Flow
The CRC services five major distribution centers, and over forty-five satellite
branches throughout this area. Inventory decisions must be made for over nine
hundred parts, making inventory management at this center a very complex
process. The three particular areas of concern that the management at the CRC
asked us to address for each individual part were:
1. How many total cores to have in the system
2. Where in the network finished inventory should be stored
3. The re-order points to maintain at the individual branches and
distribution centers
At the time we were presented with this project, The Client did not have a tool to
aid them in making these decisions. The Client’s project team wanted a tool that
would complement the decision maker’s expertise, and assist them in their daily
production decisions. This tool had to be applicable to all nine hundred parts,
and had to be developed in Microsoft Excel. A large portion of the Component
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Rebuild Center’s inventory is composed of smaller components of major
machinery. The life cycle of these components is highly variable and makes the
demand for these parts irregular and unpredictable.
Methodology
After initial meetings with the The Client project team and clarification of what
our project goals were, it was decided a simulation model would be developed.
Simulation is an appropriate method in ambiguous and unknown situations,
especially when there are many complexities and conflicting variables. Due to the
irregular and unpredictable nature of sales, and the lack of historical data, we
determined that forecasting would have been very inaccurate. When simulation is
used, the timing of demand occurrence is irrelevant. We wanted to mimic the
overall demand and observe how a particular set of parameters would perform.
For this reason, we decided to build a simulation tool that enables The Client to
retrieve the information that they originally requested.
The downside associated with using simulation for this purpose is that generally
simulation is more descriptive and should be used cautiously as a prescriptive
tool. The model attempts to develop recommendations by using an interative
process and multiple runs of the simulation to analysis various possible
decisions. The performance of these decisions is measured on criteria that the
The Client management team has deemed most important to the operational
efficiency of the company. Although simulation is not an optimizing tool, the
results provided will offer a clear picture of how the system functions and the
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recommendations can be applied with less cognitive adjustments than previously
required.
Assumptions of the Model
In order to build a tool that would be flexible enough to be applied to all 900
parts, a number of assumptions had to be made. The first assumption is that all
finished goods would be routed through the main distribution center located in
Edmonton, referred to in The Client’s system as number 45, as is shown below.
Modified Inventory Flow
Another assumption of the model is that parts have an infinite life. In reality, a
core will reach a point where refurbishing is no longer possible. At this point, the
core is scrapped out and a new core is introduced into the system to take its
place. After consulting with the management team, it was decided that for the
purposes of this model, this aspect of the system would not be considered. An
additional assumption that the model makes is that the most favorable re-order
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point is obtained when the cost of holding an additional unit becomes greater
than the revenue generated by that unit. Furthermore, we assume that the cost
associated with loss of goodwill is simply equal to the revenue lost from the lost
sale. The final major assumption of the model is that future sales will resemble
past sales.
User Inputs
A portion of this project was spent determining which parameters should be
dynamic. Along with the management team at The Client, the inputs themselves,
and the way they were to be incorporated in the model were determined. The
model sets these inputs to default values, but can be manipulated if the user
chooses to do so.
 Main Distribution Center
Currently the main distribution center is located in Edmonton. This
was added as a user input so that if the location of the main
distribution center were to ever move from 45, the model could be
adapted accordingly.
 Number of Cores in the system at the beginning of the
simulation
There are two ways to use this input. The default setting involves
initializing the model with an arbitrarily high number. This is to
ensure that there are enough cores in the system to satisfy all
demand. Throughout the multiple runs of the simulation, the
fluctuations in the number of cores that are actually required are
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tracked and an average of this is taken. For the final run, when the
ideal re-order points have been established for each branch, the
number of cores is scaled back to this average number of required
cores.
This input can also be used to perform sensitivity analysis. The user
is able to specify the number of cores in the system. In this case, the
number of cores does not fluctuate at all, enabling the user to
observe the effect of keeping a static number of cores in the system.
 Core process time
This is the time it takes to remanufacture a core. This value can be
inputted as a static value, or the user can select one of the following
distributions to be applied to the model:

Normal

Triangular

Uniform

Poisson

Deterministic

Exponential
 Process Capacity
This input allows the client to put an upper bound on the number of
parts that can be processed for a particular part at any one time.
 Costing Information
The end user inputs all costing information. The relevant inventory
costing information for this model is holding cost per year,
investment cost per year and lost contribution per unit. This is
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input as a yearly cost and translated into a daily cost for the
purposes of the simulation.
 Number of Cycles in the Simulation
The number of cycles is essentially the number of days the model
will simulate. The higher this number is set, the more reliable the
results will be. It should be noted that there is an upper bound on
this input of 2000 cycles.
 Demand Multiplier
Because the simulated demand is based on past sales, the demand
figures will be consistent with them. In cases where the client is
anticipating a change in sales levels, the user is able to use the
demand multiplier to magnify demand.
 Sales Criterion
During the data extraction phase of the model, average annual sales
for a core is computed for each branch in the network. If this
number does not equal or exceed this sales criterion, then the part
will not be housed at the branch and will instead be stored at the
local distribution center.
 Used Part Return Time
We have implemented a discrete distribution for the return time
that the user is able to change, as they feel necessary. This can be
used to evaluate the impact of implementing a formal core return
policy.
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 Network Information
The network information lists every branch and includes which
demand center services it. The user is able to update any changes in
the network information directly in the model.
 Process time
This is the time, in days that it takes to refurbish the part being run.
This is a static figure.
Simulation Process
Based on the assumptions stated above, the model is a simplification of reality. It
possesses the aspects which are relevant for the purpose of our analysis. After the
model generates this information, the simulation portion of the model is
activated. The simulation itself accounts for a number of possible occurrences,
including:
1. Simulation of sales at demand and distribution centers
Upon receiving demand figures for fifteen parts, we analyzed the data to
determine if there was a distribution that could be used in the simulation
of demand for all parts. We found that past sales for the parts that were
analyzed were highly sporadic, and showed substantial variation in their
magnitude.
After researching these types of demand profiles it was determined that
the most applicable simulation method would be to use a variation of
Croston's Intermittent Method. This method simulates demand in two
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steps. First, the probability of a sale occurring is calculated. An assigned
distribution is then used to determine the magnitude of a given sale.
Past sales information for the part that is being analyzed is retrieved by the
user from a company database. The model uses those figures to generate
the probability of a sale and its magnitude. For the purposes of simulating
the magnitude of demand, it was determined that the Poisson distribution
would suit the demand profile most accurately.
Within our model, a given sale can be incurred at either a branch which
qualifies as a demand center or a Distribution Center.
2. Lost sales
The second component of the simulation model is to track the number of
lost sales in the network. The model recognizes a lost sale whenever
demand is occurred at a location, and the inventory to meet it is not
available. When this occurs, the value of the lost sale is added to the lost
contribution cost. There is no cost associated with loss of good will taken
into consideration.
3. Return time for used
When demand is incurred in the simulation model, an associated used
core is sent back to the CRC for refurbishing. In reality, there is a delay
associated with this return time. In the model, the core is assigned a return
time using a discrete distribution, which is defined by the user. All
returning cores are assigned a return time; and this delay is incorporated
into the model. At this point, the core arrives at the CRC, where it will be
processed.
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4. Process time for cores at the CRC
Once a core has arrived back at the CRC it is put through the refurbishing
process. Although this process does have a certain degree of variation in
the processing time, this is to be a set time that would be input prior to
running the model.
5. Time to Distribute Cores
Once a core is remanufactured, it is put into finished goods inventory. All
finished goods are routed to the main distribution center in Edmonton
prior to being shipped out to the appropriate demand centers in the
network. For the purposes of the model, distribution from here to each
demand center takes a fixed amount of time.
Financial information for simulation
The financial outputs of the model are a direct function of the cost inputs. The
model tracks the total number of days that finished inventory exists at the
distribution center in Edmonton, en-route to various demand centers and
distribution centers, and any inventory on hand at these centers. The following is
an explanation of how the financial information is incorporated in our model.
Annual investment cost
The annual investment cost is the cost of having a core in the system. Because
this is a closed loop system, The Client incurs this investment cost even when the
core is in the customer’s possession, waiting to be returned. Thus, this cost
accumulates throughout the simulation regardless of the state the core is in.
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Annual holding cost
The annual holding cost is the annualized cost of processing a core. It is the cost
of investing CRC time and resources to refurbish the cores. This cost begins to
accumulate as soon as the core has been refurbished and does so until a customer
purchases that core.
Total contribution cost
The total contribution cost is the profit margin on the core multiplied by the
number of sales lost to a competitor. To determine the return on the core
investment, the contribution cost is multiplied by the total CRC sales.
Finished goods total cost
The total finished goods cost determines the total cost associated with carrying a
refurbished unit. This value is calculated by adding the total investment cost and
the annual cost.
Total investment cost
The total investment cost is essentially just the number of cores in the system
multiplied by the cost of having a core in the system. A portion is deducted to
prevent double counting the cost that is associated with the finished goods.
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The following is the Finished Goods Total Cost:
Notation

FG = finished goods total cost

F = total number of finished inventory days

A = annual investment cost

H = annual holding cost

C = number of cycles
Formulation
FG  F  A  H 365 C 
The following is the Total Investment Cost, which is the cost associated with
holding unfinished goods:
Notation

IC = Investment Cost

A = annual investment cost

N = number of cores in the system

T = total number of finished inventory days

C = number of cycles
Formulation

IC  A
 N  T  A / 365 C
365
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Determination of Re-Order Points
To determine re-order points, the model simulates the system several times.
Initially, the re-order point at each branch is set to one, and the system is
simulated. The re-order point is then increased in increments of one until the reorder point associated with the lowest total cost at a given branch is found. At
this point, the model reports the re-order point for each demand center that was
associated with the lowest cost. Because the simulation model uses an iterative
process to determine the minimum cost level, there may be instances where a
local
optimum
is
reached
before
a
global
optimum.
Therefore,
the
recommendations made by the model must be used in combination with the
users expert knowledge of the system when making a decision.
Determination Of Total Cores In System
The number of cores in the system represents the amount needed in the entire
system to satisfy demand using the determined re-order points. The level the
model determines accounts for the cores that are in process, in transit, in
inventory and those that are currently in the possession of customers.
Model Outputs
In addition to the main outputs of the model, the following more detailed
information on which the recommendations are based is made available. These
pieces of information are daily averages:

Number of cores at the core bank
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
Number of cores in process at the CRC

Number of cores in finished goods inventory

Number of cores in transit

Number of cores on hand at individual demand centers, and distribution
centers

Daily demand

Sales met

Lost sales due to insufficient inventory levels
With this detailed information, the user can see whether the model is accurately
portraying the system, and if not, change the appropriate parameters.
Fill Rate
An additional output of the model is the average fill rate. This value captures
approximately how much of their demand they are able to meet under the
recommended re-order point.
The Client can use this information to make
judgment calls. For example, if the lowest cost solution returns a fill rate that is
below an acceptable level, The Client is able to weigh the costs of increasing the
re-order point for the sake of obtaining a higher fill rate.
The graph displayed below shows that as the total cost function approaches the
minimum cost, the slope of the line approaches zero. The added cost of
increasing the re-order point from three to five is relatively insignificant, however
the increase in fill rate associated with this is quite substantial. In this type of
scenario, the user may wish to set the re-order point to a marginally higher level
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then recommended by the model in an effort to maintain a higher level of
customer satisfaction. This is clearly demonstrated in the graph below.
Conclusions and Recommendations
After working very closely with the The Client project team, a final product has
been developed and installed at the CRC. The model has been tested, and the
initial results confirm that the model accurately represents their system. Before
the model is implemented at The Client, we recommend that the project team at
The Client continue to test the model. The inputs of the model obviously affect
the outputs, thus it is important that the project team is confident with those
values. In addition to this, a thorough examination of the cost information should
be conducted to ensure that it is capturing all costs associated with the
production process.
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