*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, SI 1000 Ljubljana, Slovenia, tomaz.berlec@fs.uni-lj.si 317
Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325 Received for review: 2023-03-17
© 2023 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2023-05-16
DOI:10.5545/sv-jme.2023.577 Original Scientific Paper Accepted for publication: 2023-05-30
Inventory Risk Decision-Making Techniques  
Using Customer Behaviour Analysis
Marc, I. – Berlec, T.
Ivan Marc – Tomaž Berlec
*
University of Ljubljana, Faculty of Mechanical Engineering, Slovenia
More recent research shows the significant impact of accurate demand forecasting on the operation of supply chain system and thus on 
the performance of the company. Inventories in the production process could represent waste, which results in higher storage costs and 
consequently a higher product price, which in turn reduces company's competitiveness on the market. Nevertheless, a company must 
implement a lean production process and consequently carefully control storage and inventory costs. The introduction of a lean production 
process is closely linked to the risk of stock-outs, and knowledge of this risk in relation to customer habits is therefore a useful piece of 
information for the line manager's decision-making. This paper will present a mathematical model that relates customer demand for a product 
to the inventory level in the warehouse or between the work operations of the production process and the risk of potential penalties that 
arises with the introduction of a lean production process. With this model we can simulate, how to improve the production processes with still 
acceptable risk, with the goal of achieving a balance between stocks and the leanness of the production process. The paper demonstrates the 
use of a mathematical model on a concrete example from practice for risk simulation when choosing different production scenarios resulting 
from changed customer behaviour.
Keywords: lean production, customer demand, risk simulation, inventory optimisation
Highlights
• 	 A mathematical model is presented that allows fast and easy simulations of inventory management based on consumer buying 
behaviour.
• 	 The probability density function of demand was chosen in the mathematical model.
• 	 The changes in the production process can be monitored in terms of inventory costs and the risk that there may be insufficient 
products available to meet customer needs.
• 	 By simulating three different scenarios, the optimum inventory level was found to be 30,000 pieces, at which the inventory 
costs are minimal with a moderate risk of 17 %.
0  INTRODUCTION
Nowadays, companies decide to implement lean 
production which aims to reduce costs by eliminating 
all activities that do not add value [1]. In doing so, 
companies usually first decide to reduce inventories, 
that create unnecessary costs, mainly by tying up 
capital and occupying production areas. Of course, 
caution should be exercised when reducing inventory, 
as excessive inventory reduction can lead to business 
consequences and risks. It is important to determine 
where the lowest limit of inventory minimization can 
be and which parameters have a dominant influence. 
The aforementioned problem can be described with 
a mathematical model that can serve as a basis for 
simulating various scenarios that management can 
predict based on what is happening on the market. 
This paper presents the results of a follow-up study 
[2] in which, by using a mathematical model, a 
significant correlation between a product demand 
E[X], the optimal inventory level z
0
 and the average 
cost of product (ACP), as well as the impact of 
excess inventory and storage costs E[C] in the 
production process on the average cost of product 
was demonstrated. An excess inventory level in the 
production process was found to raise the average 
cost of product ACP, weaken a company's position on 
the market and increase the company's inefficiency. 
To this end, control charts have been developed 
that can be used to control the inventory level in 
the work operations of the production process and, 
consequently, to control the average cost of product 
ACP. The paper [2] concludes with the measures to be 
implemented to correct the production flow y
0 
and to 
correct the optimal inventory level z
0
 in the production 
process depending on the changed demand E[X].
Introducing lean principles into the production 
process means making changes to the existing 
production process, which often entails risks such 
as interruptions in the production process, non-
fulfilment of contractual obligations to customers, 
loss of goodwill, loss of market, loss of revenue, non-
competitiveness, payment of penalties, etc. This paper 
will therefore focus on identifying a risk β that may 
arise in the production process as a consequence of 
inventory level optimisation. A shortage of needed 
products may mean that customer requirements are 
not met and the consequences may be penalties, loss 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325
318 Marc, I. – Berlec, T.
of customers, loss of market share or even loss of 
market. 
Using a mathematical model and simulation, 
we will demonstrate the possibility of implementing 
a lean production process using an example of 
inventory optimisation, so that line management 
will also have control over the risks associated with 
inventory optimisation in the production process. 
The mathematical model allows to simulate different 
production scenarios according to the customer's 
requirements and to determine the level of inventories 
so that the average cost of product is minimised.
The mathematical model can also be extended 
along the entire supply chain, since every link in the 
chain, especially the weakest one, is important for the 
performance, competitiveness and profitability of the 
entire supply chain. 
The aim of this paper is to present a mathematical 
model and its use in a simulation to find the best ratio 
between customer demand for a product, the optimal 
inventory level, including the safety inventory, the 
optimal storage costs, risk, lean production process 
due to inventory and the average cost of product ACP. 
An important advantage of the simulation based on the 
developed mathematical model is to eliminate those 
scenarios where the ACP could exceed the market 
price due to too high storage costs.
1  LITERATURE REVIEW
In the study [2], the authors identify the impact of 
the optimal total inventory level in the production 
process on the average cost of product ACP. Using 
a mathematical model, in which customer demand 
and an intermediate inventory level in the company's 
production process and storage costs are linked 
together, a negative impact of excessive intermediate 
inventory level on the final price of the product 
can be identified. In this paper, the authors prove 
the assumption that, in extreme cases, storage and 
inventory costs can cause the average cost of product 
ACP to rise even to a price level higher than the price 
recognised by the market. Seyedan and Mafakheri 
[3] state that demand forecasting and planning 
refer to forecasting the quantities and timeframes 
of customer requirements. They are of the opinion 
that the objective of such forecasts is to achieve 
customer satisfaction by meeting customer needs in 
a timely manner. Accurate demand forecasting could 
improve the efficiency and robustness of production 
processes and related supply chains, as resources will 
be matched to demands, leading to a reduction in 
inventories and waste. 
Uhrin et al. [4] investigated the role of a company's 
external and internal resources and the impact of 
their variability on the degree of lean production 
implementation. They presented an analysis of the 
effects of environmental risk and past operational 
performance of a company on the level of lean 
production implementation. The paper contributes to 
explaining the circumstances that ultimately lead to the 
implementation of lean production. As a consequence, 
the external and internal environment influences a 
company's commitment to increase lean production. 
Petropoulos et al. [5] assess that demand forecasting 
is a prerequisite for decision-making on inventories 
and plays a key role in supply chain management. 
How to improve the accuracy of forecasts has always 
been a focus of research in academia and business, 
and the study argues that forecasts are designed to 
help business decisions and should be assesses on 
the basis of their economic implications. The study 
compares the performance of several commonly used 
forecasting methods in terms of achieving inventory 
control objectives, taking into account a simulation 
approach. The authors in [6] argue that for any 
company, in addition to reducing lead times, cost 
reduction is also a necessity. Therefore, monitoring 
and controlling manufacturing costs over time can 
be an important driver for improvement. In [7], the 
authors use stochastic and hybrid models, which they 
consider to be very close to reality. They explain the 
structure of supply chains, the decisions to be taken 
in a typical supply chain and the models developed 
for supply chain planning and optimisation. The paper 
further explores simulation and optimisation to solve 
stochastic and hybrid models, their applications in the 
supply chain domain and future research directions 
arising from the emphasis on sustainability, robustness 
and resilience of supply chains and opportunities. 
Authors in [8] highlight the accuracy of demand 
forecasting as it has a significant impact on the 
performance of the supply chain system and thus on 
the performance of company’s business operations. 
An accurate forecast will allow a company to make 
the best use of its resources. Synchronisation of 
customer orders with production is crucial for a 
timely fulfilment of orders. This paper presents a 
system that can improve the accuracy of demand 
forecasting for more efficient inventory management, 
also in a Smart Industry 4.0 concept. In their 
study [9], Pusztai et al. presented a method for 
implementing a risk-adjusted production plan. Two 
examples of order allocation with inventory costing 
were presented, one with inventory costing and one 
without inventory costing. The authors consider that 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325
319 Inventory Risk Decision-Making Techniques Using Customer Behaviour Analysis 
such information can play a key role in the initial 
contract negotiations as it also includes potential 
risks. In their study [10], Perera et al. conclude that 
the success of a supply chain is highly dependent 
on the effectiveness of inventory management by 
taking into account customer behavioural patterns, 
which is largely neglected by decision-makers in 
production. In their study [11], Maheshwari et al. 
pointed out the problem of managing big data also 
in terms of customer behaviour. The role of big data 
analysis related to customer behaviour in supply chain 
management (SCM), logistics (LM) and inventory 
management (IM) is of paramount importance for 
inventory optimisation. Soares do Amaral et al. in 
their study [12] highlight the importance of simulation 
for evaluating different "what-if" system scenarios 
to reduce costs and risks especially in industry and 
service 4.0. The use of modern decision-making 
support analytical tools and simulation are therefore 
indispensable to ensure customer satisfaction and 
cost reduction. In the study [6] and [13], the authors 
present a framework for value flow optimisation by 
combining value flow cost and cost-time profiles. 
Value flow mapping represents a very effective tool 
for visualising activities within a production flow, 
focusing on the duration of activities in order to 
eliminate non-value-added activities. A good cost 
analysis system is useful and applicable in helping 
managers to understand the detailed costs of different 
short-term and long-term activities and processes, 
which is why stochastic production planning models 
have been proposed by various authors [14] and [15] .  
The paper [16] also proposes a stochastic production 
planning model to reduce risk, for a manufacturing 
company with seasonal demand and market growth 
uncertainty, to prevent excess inventory and stockout. 
In the paper [17] even a two-stage stochastic Linear 
Programming approach is proposed to investigate 
a production planning problem where the non-
homogeneous characteristics of logs result in random 
process yields which are modelled as scenarios with 
discrete probability distributions.  Paper [18] focuses 
on developing a stochastic approach to costing systems 
that considers the variability in the process cycle time 
of the different workstations in the assembly line 
and provides a range of values for the product costs, 
allowing for a better perception of the risk associated 
to these costs instead of providing a single value of 
the cost. The proposed model allows a better analysis 
of the margins and optimization opportunities as 
well as investment appraisal and quotation activities. 
Real production systems are characterised by a high 
degree of variability and uncertainty, which can have 
a drastic impact on the price of a product. Uncertainty 
factors in production processes are mainly demand, 
cycle time and available resources. 
Afonso et al. [18] also used a stochastic approach 
to product costing in a production process. Based 
on their work, it is possible to further analyse 
the variation in costs associated with risks. They 
consider that the use of descriptive statistics makes 
sense because it gives the ability to understand and 
evaluate the behaviour of cycle times and their impact 
on costs. The approach allows for a better detection 
of the risks associated with product costs. In his 
study [19], the author concludes that non-economic 
theories, such as psychological or psychoanalytical 
theories, also allow a better understanding of other 
factors influencing consumer behaviour that need 
to be taken into account. Consumer behaviour is 
considered to be a holistic approach and consumer 
behaviour is based on perceptions towards a product. 
The theories and models developed in the study can 
serve as a basis for determining consumer buying 
behaviour. In [20], Radhakrishnan et al. investigate 
the effective inventory management in the supply 
chain and argue that inventory management is one 
of the important areas of supply chain management. 
They have developed a novel and efficient approach 
using a genetic algorithm that clearly determines the 
maximum possible excess inventory level and the 
shortage level required to optimise inventory in the 
supply chain. In the paper [21], Prasertwattana et al. 
investigate material ordering and inventory control in 
supply chain systems. The effect of control policies is 
analysed under three different configurations of supply 
chain systems. The authors consider that the problem 
is solvable using an evolutionary optimization method 
known as differential evolution (DE). The results 
show that the incentive scheme compliance policy is 
appropriate and outperforms other policies and can 
improve the efficiency of the whole system and of all 
members in the supply chain management framework.
Based on the literature review, a new methodology 
for decision-making support on inventory levels 
is proposed in conjunction with an analysis of the 
changing customer habits based on a mathematical 
model and simulation. We have not yet found a similar 
solution in the literature.
2  METHODOLOGY
Knowing the purchase behaviour of customer, a 
probability density function of the product demand 
can be determined. This information is provided by 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325
320 Marc, I. – Berlec, T.
the sales department, using data on sales in previous 
periods and forecasts of future sales. 
The probability density function of product 
demand f
X
(x) is approximated as closely as possible 
to the actual purchase behaviour of the customer. The 
chosen probability density function, (Eq. (1)) of the 
demand X for product is a good approximation of the 
behaviour of customer demand in practice [2].
 Xf xa xe
X
ax
  
 2
. (1)
If the function f
X
(x) is multiplied by x and 
integrated on the interval 0 to ∞, mathematical hope 
E[X] is obtained. The theoretical mean value of E[X] 
(Eq. (2)) is then equated with the mean value �x  
obtained from real customer demand data (Eg. (3)) 
and the constant production flow y
0
 (Eq. (4)).
 EX xf xd x
a
X
   

0
2

, (2)
 
2
a
x = ,
 (3)
 yx
0
= . (4)
If the probability density function of customer 
demand f
X
(x) is known, the probability density 
function of warehouse stock fluctuations f
Z
(z) (Eqs. 
(5) to (7) can also be determined.
 ZyX 
0
, 
 Zz Z 
0
 , 
 XzyZ 
00
, 
 Zf zf x
dx
dz
ZX
    , (5)
 fz az yz e
Z
az yz
    
   2
00
00
, (6)
 fz ae az az e
Z
az az
    



 
0
2
0
2, (7)
where ∆Z is inventory fluctuations due to variable 
demand X, y
0
 constant production flow equal to the 
average demand quantity E[X], X variable product 
demand, a parameter of probability density function 
of customer demand, z
0
 initial inventory level, and 
z inventory level in warehouse or between working 
operations.
Fig. 1 shows the inventory cost fluctuations p, 
q, h in a warehouse or between work operations.
Wherein in Fig. 1 C(z) represents storage cost ⌊€⌋, 
C(z) = p storage cost of a product when it is not in 
stock [€/PC], C(z) = q safety inventory costs [€/PC], 
C(z) = h storage cost of a product when it is in stock 
[€/PC], s safety inventory [PC], and z the number 
of pieces in stock in the warehouse [PC], and PC 
represents piece.
Fig. 1.  Cost fluctuations in a warehouse or  
between work operations 
Here, the key question is, of course, how much 
inventory and how much safety inventory can there 
be between work operations, and what are the costs 
and risks of: 1) not paying penalties for not delivering 
products to the customer on time and 2) having excess 
production in the warehouse and potentially being 
uncompetitive because of excessive storage costs? 
The simplest solution is to opt for more inventory 
in the warehouse or between work operations, which 
means that excess production is created, which in turn, 
from the point of view of lean principles, represents 
wastes such as redundant transport, warehousing, 
processing, poorer product quality, increased 
warehousing costs, inefficiency, uneconomic and 
consequently uncompetitive business. 
The solution to the problem and the elimination of 
waste is seen in the introduction of a lean production 
process with a focus on optimising inventory levels 
in the warehouse and between work operations. 
We believe that this is feasible if we have a good 
knowledge of the customer's buying behaviour and 
of the risk when interruptions (shortages) may occur 
in the production process. In this case, we can set an 
objective that the total waste in the production process 
or logistics chain should be minimal, which can be 
achieved by minimising the initial inventory z
0
.
Fig. 2.  The figure shows the probability density function  
of inventory fluctuations 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325
321 Inventory Risk Decision-Making Techniques Using Customer Behaviour Analysis 
We now define a mathematical algorithm in Eqs. 
(8) to (10) that will relate the parameters with each 
other, namely z
0
 (optimal initial inventory level), 
the risk β of being out of stock at a given moment 
in the warehouse or between work operations due to 
interruptions in the production process, the storage 
costs E[C] as a function of p, q and h, the safety 
inventory s, the customer buying behaviour E[X] and 
the penalties Q that we will have to pay if we fail 
to meet demand due to a production failure. Fig. 2 
shows the probability density function of inventory 
fluctuations in the warehouse or between two work 
operations in relation to the costs p, q and h. The 
mathematical algorithm is given by Eqs. (8) to (10).
   
ECzz pz fz dz qz fz dz
zh fzQ
Z
s
Z
s
yz
Z





    
  




0
0
0
00
,, (8)
 
ECzz hz
a
e
pqa Qe qh as az
az
as





 
    





 
00
2
1
1
0

0 0
2
43 2


       pq aQ eq ha s
as
, (9)
 
dE C
dz


0
0,
z
he pq ah eq ha sa s
ap
optim
az as
0
2 2
0
32 21

       





 
h ha Qe qhas
as
    





1
10 min,( )
To determine the minimum value according to the 
proposed mathematical method, a simulation model 
has been developed and is shown in Fig. 3.
The simulation is carried out using the standard 
software tool MS Excel and is therefore easy to use, 
so that the line management can use it whenever there 
is a change in the input parameters, which depend 
mainly on market conditions.
The following variables appear in the simulation 
model, z
0
 is initial inventory level [PC], s safety 
inventory level [PC], β risk [%], E[C] average storage 
cost as a function of z
0
 [€], and Q penalties that have 
to be paid due to unfulfilled requests to the customer 
[€].
3  CASE STUDY
In the selected company, we have carried out a 
material value flow analysis in the production process 
of a Basic hinge (Fig. 4). We have focused on the cold 
forming and surface protection operations. Using the 
proposed model, we want to determine how much 
inventory should be held to keep the process lean and 
to identify the risk β that may arise from optimising 
the inventory level z
0
. The capacity of the Basic 
hinge assembly system is 68,500 PC per day, which 
corresponds to the customer demand ordering an 
average of y
0 
= E[X] = 50,000 PC of hinges.
The input data of the model shown are p, q, h, 
s, Q, z
0
 and x. The parameter a depends on customer 
buying behaviour, so cannot be influenced, and x 
represents actual monthly orders. When we enter the 
Fig. 3.  Mathematical algorithm for simulation in Excel

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325
322 Marc, I. – Berlec, T.
input data into the Excel software using our algorithm, 
we get the output data β, E[C] and z
0
.
When we solve the equation dE[C]/(d z
0
) = 0 
using numerical calculation methods, we obtain the 
optimum z
0optim
, where the cost E[C] is a minimum. 
In the simulation we use the “What if experiments”. 
In our example we are interested in the function E[C]
(a, h, p, s, q, Q, z
0
, β). β depends indirectly on a and z
0
. 
Using this function, in addition to z
0
, we can simulate 
the behaviour of the cost for different values of a, h, s, 
q, p, Q and β.
If we want to obtain the optimal value z
0optim
 
immediately, it can also be obtained by the exact 
mathematical Eq. (10) and the given parameters a, h, 
s, q, p and Q without simulation. In our case, s can 
also be referred to as the strategic stock necessary for 
the smooth running of the production process.
In this paper, we have limited ourselves to 
presenting three scenarios using a practical example. 
There are many possible combinations, and the choice 
of the best balance between inventory, costs and 
risks is in the hands of management. We have found 
some similar studies in the literature that indicate 
that solving the problem from the point of view of 
the balance between inventory, costs and risks is 
important and at the same time interesting for the 
academic community. We believe that the proposed 
model is therefore interesting and useful for practice.
It can be seen from Fig. 4 that the quantity of 
products transported daily between the two operations, 
or the daily quantity demanded by the customer 
(Q
td.
) is Q
td
 = 50,000 PC/Wd, where Wd represents 
work day. The quantity of products between the two 
operations or the quantity of products in transition 
between the two operations (Q
bo 
) is Q
bo  
= 466,666 
PC. Other used variables in Fig.4 are: W represents 
number of workers at the workplace, WP workplace 
number, Tp process time, Tc cycle time, Ts setup time, 
A availability, Tps process time for series, Qs quantity 
in one series processed and S scrap.  
The status between the two operations is an 
interesting data point for us, because it is clearly an 
overproduction which represents a cost or waste for 
the company. We will verify the claim that waste is in 
question here by applying the proposed mathematical 
model (Eqs. (8) to (10)). Let us assume that the daily 
storage cost of the cup semi-finished product is h = 
0.5 €/PC, the cost of storing the safety inventory of 
the cup semi-finished product q = 1 €/PC, the cost of 
the cup semi-finished product when it is not in stock 
p = 2 €/PC, the quantity of the safety inventory of the 
cup s = 1,000 PC, and the penalties to be paid if there 
is an interruption in the production process and we are 
not able to fulfil the customer's order Q = 10,000 €. 
The customer’s average daily order is E[X] = 50,000 
PC of Basic hinges.
The following findings are also important for 
the simulation, including the data that represent 
limitations in the optimisation process.
The inventory level of the cup semi-finished 
product z
0
 between the cold forming and surface 
protection operations in the existing production 
process is excessive and is in fact overproduction and 
waste. This is in contrast to a lean production process.
Since the inventory level is excessive, the risk 
β of production failure is practically non-existent or 
negligible.
The storage costs of excessive quantities of the 
cup semi-finished product are high and therefore 
increase the average cost of the cup semi-finished 
product, raising the price of the finished Basic hinge 
product and thus weakening the product's position on 
the market. Excessive inventories generate a range of 
different wastes (transport, additional storage space, 
redundant processing, increased changeover times, 
questionable quality and increased defect volumes).
Fig. 4.  Material value flow for the Basic hinge

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325
323 Inventory Risk Decision-Making Techniques Using Customer Behaviour Analysis 
4  ANALYSIS AND DISCUSSION
We have selected three scenarios to analyse the lean 
production process by varying the inventory level 
between the cold forming and surface protection 
operations. The simulation was carried out in MS 
Excel environment.
Scenario 1: Since the daily demand is 50,000 PC, 
the line manager in the first scenario has decided on 
an initial inventory z
0
 = 30,000 PC, i.e., 60 % of the 
daily safety inventory, which can be considered as an 
optimistic decision because in this case there should 
be no production failure of more than half a day.
Scenario 2: In the second scenario, the manager 
has increased the initial inventory to 60,000 PC, 
which represents 110 % of the daily safety inventory, 
which can be considered a plausible scenario. Even if 
there is a slight change in demand, there is still one 
day's safety inventory if a production failure occurs.
Scenario 3: In the third scenario, the initial 
inventory was further increased to 100,000 PC, which 
represents 200 % of the daily safety inventory, which 
can be considered a pessimistic decision because in 
this case there is a safety inventory for two days of 
production failure.
Using the mathematical model and the simulation 
software developed in MS Excel, the line manager 
in charge of production found out very easily what 
the storage costs E[C](z
0
) and the risk β are for each 
scenario chosen.
Fig. 5 shows a possible choice between the 
optimal inventory z
0
, the storage costs E[C](z
0
) and 
the risk costs β. The coloured boxes show the values 
for the selected values for the 3 scenarios previously 
proposed that could allow a lean production process 
in the case of reducing the inventory level of the cup 
semi-finished product between the cold forming and 
surface protection work operations.
Fig. 5.  Possible choice between the inventory z
0
, the storage costs 
E[C](z
0
) and risk costs β
Fig. 6 shows the results from Fig. 5 in graphical 
form. Fig. 6 clearly shows where the minimum value 
E[C](z
0
) is, and hence the optimal inventory level z
0
 is 
Fig. 6.  Storage cost fluctuations E[C](z
0
) as a function of the selected inventory level z
0

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325
324 Marc, I. – Berlec, T.
behaviour. For the mathematical model, the probability 
density function of demand f
X
(x) was chosen which, 
in our opinion [1], best approximates the actual real-
life customer buying behaviour. Based on the chosen 
function f
X
(x), the changes in the inventory fluctuation 
z
0
, the storage costs E[C](z
0
) and the risk costs β can 
be calculated in the production process as a function 
of the changed customer demands. 
This paper is a follow-up to a previous study, 
which presented the negative effects of too high 
inventory levels of semi-finished products per time 
unit of observation on the average cost of the ACP 
product and thus on the final price of the product. This 
time, we have extended and additionally focused on 
the risk that may arise when deliberately reducing 
inventory levels between the work operations of a 
production process with the aim of approaching the 
desired lean production process. Logically, reducing 
the inventory level between work operations increases 
the risk of interrupting the quantities available to 
supply the customer and, of course, vice versa. In 
the practical case under consideration, the proposed 
model was used to simulate three possible scenarios 
of a lean production process on an example of 
inventories, storage costs and risk costs. Only two 
work operations have been chosen, cold forming and 
surface protection, as an example, but the model could 
be extended very easily to the whole logistics chain. 
In the present case, there was clearly 
overproduction and thus waste. Between the two 
work operations observed, an inventory of as many 
as 466,666 PC was determined. By simulating three 
different scenarios, the optimum inventory level 
was found to be 30,000 PC, at which the inventory 
costs are minimal with a moderate risk of 17 %. The 
presented simulation method, based on a mathematical 
optimisation model, is a simple tool that provides the 
line management with an efficient decision-making 
support regarding the quantities to be produced in 
a given time interval, depending on the customer 
behaviour. The simulation can also be useful for the 
sales management to analyse, during the negotiations 
with customers, what the desired quantities mean for 
the production costs and to negotiate the selling price 
accordingly.
The scientific contribution of the presented 
model and simulation for decision-making support 
is that by analysing consumer buying behaviour, the 
changes in the production process can be monitored 
in terms of inventory costs and the risk that there may 
be insufficient products available to meet customer 
needs. There are few useful solutions in the literature 
for solving these problems, which are every-day 
determined. A more detailed analysis of the simulation 
results for all 3 scenarios is as follows:
Scenario 1: The storage costs are the lowest, 
E[C](z
0
) = 28,247.71 €. As a consequence, there is a 
slightly higher risk of production failure β = 17 %. In 
Fig. 5, Scenario 1 is indicated by the red box and in 
Fig. 6 it is indicated by the arrows. 
Scenario 2: It represents higher storage costs 
E[C](z
0
) = 34,910.93 € but a lower risk of production 
failure, β = 6 %. In Fig. 5, scenario 2 is indicated by a 
black box.
Scenario 3: It represents even higher storage costs 
E[C](z
0
) = 51,239.37 € but the lowest risk of process 
disruption β = 1.7 %.
Given the target function, the optimal decision is 
at min z
0
. This target is reached in the first scenario, 
where the selected quantity of the initial inventory 
is 30,000 PC and the cost E[C](z
0
) = 28,247.71 €. 
According to the production management, a risk of 17 
% is acceptable.
Hypothetically, bearing the lean production 
principles in mind, we should have opted for a 
production without inventories, but in this case the 
costs are 43,037.95 € and the risk is 40.6 %, which is 
too high a risk. We have noted that in the mathematical 
model, and therefore in the simulation, the dominant 
variable is Z or z
0
 (optimal value), since this variable 
affects both the cost E[C] and the risk β. The larger 
the inventory Z, the higher the cost and the lower the 
risk, and vice versa. Thus, the management's decision 
depends mainly on the developments on the market. 
The greater the competition, the leaner the production 
process must be (because of lower costs) and the 
quantity Z must be close to z
0
, even if the risk is higher. 
If the risk is higher, it means that the market situation 
must be closely monitored, and the simulation must 
be run again with the proposed model to choose a new 
inventory strategy adapted to the conditions.
Since we did not find a similar approach to 
inventory minimization in the literature, it is not 
possible to compare the results with other similar 
studies. Therefore, the management of the company in 
question has analysed the results in detail and found 
that they are useful for decision making regarding the 
level of inventory.
5  CONCLUSIONS
Inventory management is an important aspect of 
managing the production process and the entire 
logistics chain. This paper presented a mathematical 
model that allows fast and easy simulations of 
inventory management based on consumer buying 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)7-8, 317-325
325 Inventory Risk Decision-Making Techniques Using Customer Behaviour Analysis 
problems in manufacturing. The limitation of the 
study is that the proposed method is only suitable for 
batch production.
Our further research will focus on the 
development of a cost, analysis stream map (CASM) 
model that will offer a detailed overview of the entire 
production process in terms of demand, average cost 
of product ACP and risk. By incorporating CASM, the 
proposed method will be suitable for the optimisation 
of lean processes depending on customer behaviour 
also in industry 4.0. and can be integrated in the ERP 
or MES companies.
8  REFERENCES
[1] Tanasić, Z., Janjić, G., Soković, M., Kušar, J. (2022). 
Implementation of the Lean Concept and Simulations in SMEs 
- a Case Study. International Journal of Simulation Modelling, 
vol. 21, no. 1, p. 77-88, DOI:10.2507/IJSIMM21-1-589.
[2] Marc, I., Kušar, J., Berlec, T. (2022). Decision-making 
techniques of the consumer behaviour optimisation of the 
product own price. Applied Sciences, vol. 12, no. 4, art. 2176, 
art. ID 2176, DOI:10.3390/app12042176.
[3] Seyedan, M., Mafakheri, F. (2020). Predictive big data 
analytics for supply chain demand forecasting: methods, 
applications, and research opportunities. Journal of Big Data, 
vol. 7, art. ID 53, DOI:10.1186/s40537-020-00329-2.
[4] Uhrin, Á., Moyano-Fuentes, J., Cámara, S.B. (2019). Firm risk 
and self-reference on past performance as main drivers of 
lean production implementation. Journal of Manufacturing 
Technology Management, vol. 31, no. 3, p. 458-478, 
DOI:10.1108/jmtm-02-2019-0074.
[5] Petropoulos, F., Wang, X., Disney, S.M. (2019). The inventory 
performance of forecasting methods: Evidence from the M3 
competition data. International Journal of Forecasting, vol. 35, 
no. 1, p. 251-265, DOI:10.1016/j.ijforecast.2018.01.004.
[6] Gracanin, D., Buchmeister, B., Lalič, B. (2014). Using cost-time 
profile for value stream optimization. Procedia Engineering, 
vol. 69, p. 1225-1231, DOI:10.1016/j.proeng.2014.03.113.
[7] Nag, B., Pal, R. (2022). Simulation optimization for supply 
chain decision making. Winter Simulation Conference, p. 
2853-2863, DOI:10.1109/wsc57314.2022.10015379.
[8] El Jaouhari, A., Alhilali, Z., Arif, J., Fellaki, S., Amejwal, M., 
Azzouz, K. (2022). Demand forecasting application with 
regression and IoT based inventory management system: 
A case study of a semiconductor manufacturing company. 
Journal of Engineering Research in Africa, vol. 60, p. 189-210, 
DOI:10.4028/p-8ntq24.
[9] Pusztai, L.P., Nagy, L., Budai, I. (2023). A risk management 
framework for industry 4.0 environment. Sustainability, vol. 
15, no. 2, art. ID 1395, DOI:10.3390/su15021395.
[10] Perera, H.N., Fahimnia, B., Tokar, T. (2020). Inventory and 
ordering decisions: a systematic review on research driven 
through behavioral experiments. International Journal of 
Operations & Production Management, vol. 40, no. 7/8, p. 
997-1039, DOI:10.1108/IJOPM-05-2019-0339.
[11] Maheshwari, S., Gautam, P., Jaggi, C. K. (2021). Role of big 
data analytics in supply chain management: current trends 
and future perspectives. International Journal of Production 
Research, vol. 59, no. 6, p. 1875-1900, DOI:10.1080/00207
543.2020.1793011.
[12] Amaral, J.V.S.D., Montevechi, J.A.B., Miranda, R. de C., Junior, 
W.T. de S. (2022). Metamodel-based simulation optimization: 
A systematic literature review. Simulation Modelling 
Practice and Theory, vol. 114, art. 102403, DOI:10.1016/j.
simpat.2021.102403.
[13] Jordan, E., Berlec, T., Rihar, L., Kušar, J. (2020). Simulation 
of cost driven value stream mapping. International Journal of 
Simulation Modelling, vol. 19, no. 3, p. 458-469, DOI:10.2507/
ijsimm19-3-527.
[14] Orellana, R., Carvajal, R., Escárate, P., Agüero, J. C. (2021). 
On the uncertainty identification for linear dynamic systems 
using stochastic embedding approach with Gaussian mixture 
models. Sensors, vol. 21, no. 11, art. ID 3837, DOI:10.3390/
s21113837.
[15] Wang, C.-N., Nhieu, N.-L., Tran, T.T.T. (2021). Stochastic 
Chebyshev goal programming mixed integer linear model for 
sustainable global production planning. Mathematics, vol. 9, 
no. 5, art. ID 483, DOI:10.3390/math9050483.
[16] Zhang, X., Prajapati, M., Peden, E. (2011). A stochastic 
production planning model under uncertain seasonal 
demand and market growth. International Journal of 
Production Research, vol. 49, no. 7, p. 1957-1975, 
DOI:10.1080/00207541003690074.
[17] Zanjani, M.K., Kadi, D.A., Nourelfath, M. (2013). A stochastic 
programming approach for sawmill production planning. 
International Journal of Mathematics in Operational Research, 
vol. 5, no. 1, p. 1-18, DOI:10.1504/ijmor.2013.050604.
[18] Afonso, P., Vyas, V., Antunes, A., Silva, S., Bret, B.P.J. (2021). 
A stochastic approach for product costing in manufacturing 
processes. Mathematics, vol. 9, no. 18, art. 2238, 
DOI:10.3390/math9182238.
[19] Goswami, K. (2020). To buy or not to buy: An analysis of the 
problematic of consumer behaviour. International Journal of 
Management, vol. 11, no. 10, p. 525-532, DOI:10.34218/
IJM.11.10.2020.050.
[20] Radhakrishnan, P., Prasad, V.M., Gopalan, M.R. (2009) Genetic 
algorithm based inventory optimization analysis in supply 
chain management. IEEE International Advance Computing 
Conference, p. 418-422, DOI:10.1109/IADCC.2009.4809047.
[21] Prasertwattana, K., Shimizu, Y., Chiadamrong, N. (2007). 
Evolutional optimization on material ordering and inventory 
control of supply chain through incentive scheme. Journal of 
Advanced Mechanical Design, Systems, and Manufacturing, 
vol. 1, no. 4, p. 562-573, DOI:10.1299/jamdsm.1.562.