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INVENTORY OPTIMIZATION
OPTIMALIZACE SKLADOVÝCH ZÁSOB
Ing. Kateřina Bajaja
Helvetia Direct Marketing s.r.o.
Abstract
Work focuses on Inventory Stock Optimization. It uses theoretical knowledge of basic
theoretical topics as stock keeping, inventory management, models used for inventory
management and demand forecasting. There are described methods of inventory control – P,
Q, PQ, and further modifications of mentioned methods. Also ABC and XYZ analysis, and in
the last, the effect of demand on the stock reserves and forecasting.
In the practical part we can find the short introduction of the company, the basic principles of
their functioning, especially stock keeping and management. For better orientation with the
situation the actual analyses were proceeded. To obtain the desired objectives, the evaluation
of overall situation is followed by the solution proposition.
Abstrakt
Příspěvek je zaměřen na téma Optimalizace skladových zásob. Využívá teoretické poznatky
z oblasti řízení zásob, používaných modelů P, Q, PQ a predikce poptávky. Použita je i ABC
a XYZ analýza, společně s vlivem poptávky na tvorbu zásob a její předpověď.
V praktické části je představena společnost, základní principy jejího fungování a řízení zásob
na skladě. Pro lepší orientaci a zjištění reálného stavu byly provedeny analýzy. Pro získání
požadovaného cíle následuje zhodnocení celého stavu a navržení řešení pro zlepšení celkové
situace.
Key words
optimization, ABC analysis, demand forecasting, inventory management, P and Q systém,
optimum size of the order
Klíčová slova
optimalizace, ABC analýza, XYZ analýza, predikce poptávky, poptávka, řízení zásob, zásoby,
Q systém, optimální velikost objednávky
INTRODUCTION
One of the main problems for many companies is inventory management and
forecasting. Despite the efforts to implement towing systems into whole supply chain systems
so far they only partly eliminate the negative consequences of Forrester effect.1 Some of the
main reasons causing this situation are deficient demand forecasting and a low level of
cooperation. This paper is focused on the analysis of current state of stock in selected
company and its management. The aim is to illustrate the main problems and to suggest
changes that could lead to an improvement in the current state. The work is based on an
1 FORRESTER J.,W.: Industrial Dynamics. Cambridge: The MIT Press.
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analysis of the company's product portfolio and inventory management problems. Another
important chapter is a description of the real situation in the field of demand forecasting and
inventory management. There are individual analyses described together with models useful
for effective inventory management. It uses theoretical knowledge of inventory management,
P, Q, PQ models and demand forecasting. The third part analyzes the main problems
identified within the previous chapters and suggests possible solutions, together with possible
cost savings. The goal is to find solutions that are workable under the existing conditions and
do not cause problems to end customers.
CURRENT STATUS
The basic goal is to design changes to the system and improve the current situation. In
the first step, it is necessary to analyze and identify current shortage. Appropriate policies and
procedures that will help us to achieve that objective can then be selected. First of all, there is
a basic description of the current situation within the company, which will help us to
determine the factors that negatively affect the current status and show weaknesses in the
whole chain. To obtain relevant data, with inclusion of the seasonal fluctuations, the data for a
period of one year will be processed. That will be followed by an outline of demand
forecasting and the trend of demand. The company Helvetia DM (hereinafter HDM) was
founded in 2008 as a subsidiary of the Czech-Swiss pharmaceutical company Helvetia
Pharma, a leading manufacturer and distributor of pharmaceuticals. Helvetia DM currently
works as a separate company, owned by Czech owners, focusing on the production and
distribution of food supplements. The aim of the company was to create a comprehensive
portfolio of nutritional supplements that would be attractive to direct mail order. The picture
below outlines simplified goods and information flow in the company.
Fig. 1 - Flow of goods and information
Source: own processing
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METHODS OF STUDY AND USED DATA
Material planning and management is necessary to adjust not only to the individual
items, but also suppliers and last but not least, customers. It is no longer possible to use a
unified mode of supply. It is necessary to diversify the approaches for precise supply services
that the customer requires and is willing to pay for. The basic tool is the diversification
according ABC and XYZ analysis. 2
The company currently produces all products under their
own brand, they are packed on behalf of the company and the products can be ordered by any
customer. The main portfolio is formed by 29 major items, which we will investigate further.
All statistics were processed for a period of one year (12 months). Central warehouse covers
three main functions – stock balancing, security and assembly. The location of the central
warehouse is in Bosnia and Herzegovina. This allows to reduce storage costs and staff cost.
On the other hand, there is an increase of the transporting cost, as the production takes place
in Czech Republic.
ABC A XYZ ANALYSIS
ABC analysis is based on rules defined by Vilfredo Pareto. The basic idea is a
statement that a small group of elements is responsible for most of the results. The first step is
to export and process basic data for the main articles. There is also an overview of products
and their distribution according to the percentage of sales. Additionally, items are split into
groups and the method of classification is chosen. It is also necessary to determine whether
we can apply the strict proportions of the various groups, which are reported in the literature.
In our case, the intervals are for the different groups slightly modified.
Tab 1 - Distribution of products according to ABC analysis
Group A 31% products = 80% sale
Group B 28% products = 15% sale
Group C 41% products = 5% sale
Source: own processing
The basic purpose of XYZ analysis is a division of items, but this time the main
criteria is the stability of demand, which also affects the level predictions. The first step is
identical with ABC analysis. The annual consumption is divided into shorter periods of time,
2 JIRSÁK, Petr, Michal MERVART a Marek VINŠ. Logistika pro ekonomy - vstupní logistika. Vyd. 1. Praha:
Wolters Kluwer Česká republika, 2012, str. 136.
0%
50%
100%
31% 28% 41%
Sale
Products
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in our case to months. Degree of demand stability is expressed by the standard deviation,
which is calculated for each item. We continue with calculating the coefficient of variation as
the standard deviation to the average percentage. Afterwards the items are divided into
intervals according to the size of the coefficient of variation. The intervals are intuitively
designed.
Coefficient of variation 0%-20% - stable demand = group X
Coefficient of variation 21%-100% - moderately stable demand = group Y
Coefficient of variation over 100% - unstable demand = skupina Z
Based on the processed data there isn`t any item considered as an item with stable
demand. This phenomenon is the most threatening factor for the demand forecast of the
company. The Y group contains a total of 21 from 29 products. The group Z contains 8
products.
INVENTORY MANAGEMENT AND DEMAND FORECASTING
There are several processes and methods that can be used for inventory management.
Choosing the right method is totally dependent on the system used within inventory
replenishment. Goods can be ordered at irregular periods at a constant rate (Q system), or
different amounts at regular intervals (P system). These extreme limits are not entirely
appropriate in our situation because the demand is not always regular. Under these
assumptions, the company uses a modification of the Q system. At the moment when stock
reaches the signal level, the order is being issued. In order for this system to work properly, it
is necessary to calculate the threshold level of inventories, the size of the additional order and
upper level ordering. Supply management works based on demand forecasting, which is
converted into the production plan afterwards. Currently, the new products are forecasted
based on an intuitive method. Since these are food supplements, you can usually observe
similar behavior for the products within the same group. If we consider the distribution of
products according to ABC analysis, then different forecasting methods can be assigned to
individual groups of ABC analysis. The moving averages method is often used for group A,
since sales is relatively stable throughout the year. The moving averages method can be
defined by the following formula.
Group B and C use a combination of moving averages along with other factors, such
as regular fluctuations in demand within the year, a trend factor and promotions. Demand is
partly stimulated also by pricing, but that is certainly not the main criterion. Three products,
each representing one of the groups, were selected for the following analyses and simulations.
Product 228 – The first product falls into group A and Y. As can be seen down below, this is
an article with a relatively high sales and moderately stable demand. The red curve represents
the expression of sales for that period of time. To increase the accuracy of prediction, data in
these cases were processed for the last year and a half. The green curve shows the prediction
of demand, or better say trendline, calculated based on moving averages.
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Product 257 – The second product is a representative of the group B and Y. Annual sales are
not so high and the stability of demand is certainly lower than the first sample. The green
curve again expresses trendline of demand.
Product 999 – The last product from group C and Z represents the classic aspects of a
product with low sales and unstable demand. There are two extreme fluctuations in sales,
which can be explained by increased demand during the Christmas season. On the other hand,
we can also observe a period of zero demand or better say sale. Due to pronounced trend there
is an occurancy of distorted predictions.
Fig. 3 - Demand forecasting for article 257 / Source: own processing
0
2000
4000
6000
8000
Fig. 2 - Demand forecasting for article 228 / Source: own processing
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
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Since a large part of these products are items with unstable demand, it is necessary to
adapt the ordering to this situation. The currently used system can be described as a modified
Q system with variable size of the order and fixed low stock signal. The company orders in
most cases variable order in variable ordering deadlines. Ordering limit is determined for each
product itself and new order is issued once the inventory drops below the signal stock.
However, as is evident from the following graphs, in some cases the orders are issued much
earlier and they ignore the moment of achieving the signal of low stock. The size of the order
is calculated based on the demand forecast for the next period of time. In this case, the
company does not use any defined algorithms. The following part uses simulation model for
the optimal order size, length of delivery cycle, the number of orders and total costs
associated with the acquisition and of stock holding. 3
Product 228 – The model based on the following information: consumption is 143 896 units
per year, the price of the product CZK 15 per piece, storage costs 15% of the average
inventory (CZK per year) and the cost of the order in the amount of CZK 2600, shows the
following:
optimal delivery cycle tQ = 45 days
number of deliveries per year o = 8
optimal order size Qopt = 18236 pcs
signal level xs = 12 220 pcs
On the chart down below we can observe real progress of inventory and we can also take
into account the different orders in the course of one year. The blue curve represents the signal
level.
3 GROS Ivan: Matematické modely pro manažerské rozhodování. 1st ed. Praha: VŠCHT Praha, 2009.
Fig. 4 - Demand forecasting for article 228 / Source: own processing
0 500
1000 1500 2000 2500 3000 3500 4000
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Fig. 6 - Inventory progress of product 257 / Source: own processing
0
5 000
10 000
15 000
20 000
25 000
30 000
As it’s quite clear, the ordering was not ideal in the past. It has took places rather in
larger intervals while the order was not large enough to meet the demand. In two cases, stock
approached zero, which very negatively influenced production and distribution. As already
pointed out in the previous chapter, some orders were also issued before reaching the signal
stock level.
Product 257 – The model based on the following information: consumption is 50 759 units
per year, the price of the product CZK 14,9 per piece, storage costs 15% of the average
inventory (CZK per year) and the cost of the order in the amount of CZK 2600, shows the
following:
optimal delivery cycle tQ = 72 days
number of deliveries per year o = 5
optimal order size Qopt = 10867 pcs
signal level xs = 4312 pcs
Fig. 5 - Inventory progress of product 228 / Source: own processing
0
10000
20000
30000
40000
50000
60000
70000
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Fig. 7 - Inventory progress of product 999 / Source: own processing
0
2000
4000
6000
8000
10000
12000
As clear from the above mentioned graph, the excess inventory was held unnecessary.
But at the end of the year there was underestimated demand and inventory levels approached
zero. Again, some orders were also issued before reaching the signal stock level.
Product 999 – The model based on the following information: consumption is 13 026
units per year, the price of the product CZK 26,5 per piece, storage costs 15% of the
average inventory (CZK per year) and the cost of the order in the amount of CZK 2600 ,
shows the following:
optimal delivery cycle tQ = 120 days
number of deliveries per year oq = 3
optimal order size Qopt = 4128 pcs
signal level xs = 1106 pcs
Since it is a slow-moving product, there is usually rather bigger order and long-
term storage. Anyway, it is clear that the previous orders were realized much earlier than
needed. In this case, the situation can be explained by a contract between the company
and a supplier. Deliveries were under conditional offer of better price. Also it should be
emphasized that this is a complementary product, which it is not necessary to watch the
expiry date for.
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ANALYSIS EVALUATION – RESULTS
While we are evaluating the results of the analysis and suggesting the values of control
variables which could lead to savings by decreasing inventory levels, we still need to keep in
check whether the new system won’t negatively affect the level of service to customers.
Meanwhile, it’s necessary to cooperate closely with the suppliers to reach possible
compromises profitable for both sides.
The first two analyses show some specifics in the distribution of articles into groups.
In the ABC analysis an unusally high number of articles belonged to the group A. Table no. 1
shows that to cover 80% of the total turnover as many as 31% of articles need to be included.
But at the same time that is the main portfolio of articles, essential for company‘s sales. The
XYZ analysis then revealed that the demand stability of the article portfolio is moderate to
unstable. None of the articles belonged into the „stable“ group X. Of course, the process of
demand prediction is much more complex due to this fact. Based on historical data from real
orders we can compare theoretical and real costs of ordering of goods. The company is using
modified Q system for placing orders. The main problem seems to be a fixed signal level for
stock quantity. The inventory management would work more effectively by using regular
recalculation of the signal level and, especially, of the optimal order quantity for the next
period. The current approach is unsystematic and lacks necessary dynamics. That’s apparent
from the fact that the cost calculation and consequently the new order is issued only after the
stock quantity drops below the signal level. That increases delays in goods deliveries and in
connection with relatively long delivery times can also cause zero stock level and unsatisfied
customer orders. On the other hand the charts also show ordering without reaching the signal
level. The reason for that might be a contract with the supplier with fixed delivery times, a
discounted price offer or, eventually, inaccurate demand prediction.
Based on the summary of all the above findings I suggest the following steps, which
would lead to better, more effective inventory management in the company. At first I suggest
to withdraw from production articles with annual sales below certain limit. Those are usually
seasonal or complementary articles. Such saving measure would affect the end customers but
only in limited extent. Most of the customers are not interested in these articles so their
withdrawal wouldn’t mean a problem for them. It wouldn’t bring significant financial savings
but the article portfolio would be clarified and the company could focus on the main groups of
articles. Another beneficial step would be more frequent production of high-turnover articles
in smaller batches. But such approach is limited by higher production costs of smaller batches,
which would cause higher unit costs, and also by long delivery times. The company tried to
negotiate shorter delivery times with suppliers but it’s not possible from technological point
of view. The proposal includes changes of the current Q system, which uses variable order
quantity with fixed signal level. In my opinion, a Q system with dynamic changes of order
quantity q and dynamic signal level needs to be implemented. The chart below shows a
progression of orders for article 228 in case the signal level would be calculated and updated
regularly. The blue curve represents inventory level, red curve shows changing signal level.
The standard deviation was determined using the data from previous months. The current
inventory level is compared with the signal level at the end of each month and a new order is
placed if needed. The order quantity is definded as
, that means the
order quantity from previous month plus the difference in signal level between actual and
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previous month. The signal level is calculated by a formula . As you can
see, the orders would be more frequent, but the inventory level would be more under control.
The total ordered quantity in proposed model was 144 236 pieces, ie. about 20 000
pieces less than it was in reality. We will also compare the inventory costs and ordering costs.
The unit price of the article is 15 CZK and a cost of each order is 2600 CZK. Inventory costs
were specified as 15% of annual average inventory level. Now we can calculate and compare
the costs between theoretically implemented modified Q system and real orders. Inventory
costs are calculated separately for each month based on the average inventory level. The total
theoretical costs N, i.e. the sum of inventory costs and ordering costs is 69 973 CZK. In
reality, the costs were 77 592 CZK. While such savings are not huge, we need to keep in mind
that we are only working with costs for single article. In case the new system would be
implemented for all inventory articles the resulting savings would certainly be significant for
the company.
For more graphical explanation of the modified system, the simulation has also been
made for article 999, from a low-turnover group C. The blue curve represents inventory level,
red curve shows changing signal level. The standard deviation was again determined using the
data from previous months. New orders are placed at the end of each month based on the
comparison of current inventory level with the signal level. We can see once again that orders
would be more frequent but the inventory level would be more under control.
Fig. 8 - Inventory progress of product 228, based on Q system modification
Source: own processing
0 5 000
10 000 15 000 20 000 25 000 30 000 35 000 40 000
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The total ordered quantity in proposed model was 13 289 pieces, ie. about 4 000 pieces
less than it was in reality. We will also compare the inventory costs and ordering costs. The unit
price of the article is 26,50 CZK and a cost of each order is 2600 CZK. Inventory costs were
specified as 15% of annual average inventory level. Now we can calculate and compare the
costs between theoretically implemented modified Q system and real orders. Inventory costs are
calculated separately for each month based on the average inventory level. The total theoretical
costs N, i.e. the sum of inventory costs and ordering costs is 30 040 CZK. In reality, the costs
were 33 224 CZK. Again, the savings are quite low, but certainly not negligible, considering the
article is from the C group. For both presented articles the savings are close to 10% of annual
costs of storage and ordering. If the implementation of the modified system for all articles
would bring average savings about 10%, it would undisputably be beneficial for the company.
CONCLUSION
The "inventory optimazation" topic is without a doubt very extensive topic. There can
be different views on inventory management. The aim of the work was to provide information
about the current method of inventory management within the company and to propose
changes that would lead to the improvement of its management. The first important condition
for the successful implementation of the proposed changes is the systematic approach. It is
necessary to follow the changes and make changes in the established processes. In the first
step is necessary to at least start thinking about the improvement of the of the information
system. The next step should be followed by withdrawal of slowly-moving goods and focus
on profitable products. The company has a great advantage in the field of communication
with the customer. The last and the most important part of the change is to focus on demand
prediction and the systematic ordering. The company employs a very competent staff, but
they work very often under unnecessary stress due to errors in the stock keeping and the
ordering of the goods "at the last minute." As previously described, the simulation showed the
considerable savings in the field of inventory management. But changing the system would
certainly guarantee also non-financial benefits. The situation between employees is in critical
periods often tense because of the small control over stock inventory. There is often a concern,
that customer orders will not be covered. System approach would certainly have brought
improvement in this area.
Fig. 9 - Inventory progress of product 999, based on Q system modification
Source: own processing
0 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 9 000
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LITERATURE
[1] FORRESTER, J. W. Industrial Dynamics. Cambridge: The MIT University Press, 1999,
ISBN 978-1614275336
[2] GROS, Ivan. Kvantitativní metody v manažerském rozhodování. Praha: Grada publishing,
2003. ISBN 80-247-0421-8.
[3] GROS, Ivan. Matematické modely pro manažerské rozhodování. Praha: VŠCHT, 2009.
ISBN 978-80-7080-709-5
[4] JIRSÁK, Petr, MERVART, Michal, VINŠ, Marek. Logistika pro ekonomy - vstupní
logistika. Praha: Wolters Kluwer, 2012. ISBN 978-80-7357-958-6.
Reviewers:
prof. Ing. Vladimír Strakoš, DrSc., VŠLG Přerov,
Ing. Filip Beneš, PhD., VŠB – TU Ostrava.
