1

Simulation approach in stock control of products with

sporadic demand

Jakub Dyntar, Eva Kemrová, Ivan Gros

The stock management of products with sporadic demand is one of the main problems for

many entrepreneurs. It is possible to find cases of the sporadic demand in the area of car, aircraft

and unique assembly lines spare parts manufacturing and distribution. The problems with

assessing the sporadic demand are caused not only by significant variability and a relatively small

demand but, above all, by prolonged periods with no demand at all. Classical forecasting methods

(for example exponential smoothing, moving average methods, regression analysis, etc.) used in

common supply management systems are ineffective when applied to sporadic demand for

mainly the following reasons:

Classical methods do not take into account the importance of zero demand periods.

Classical methods are not focused on the distribution function forecast of demand during

the order lead time period, which is very important for the effective flow of such

materials.

Application of inappropriate methods in sporadic demand product stock management leads to

insufficient stock and the inability to fulfill orders consequently causing significant economic

loss. Situations leading to high stocks of these products have a similarly negative effect on the

management efficiency. The importance of forecasting influence is obvious from Figure 1,

showing the typical structure of spare parts distribution system. The distributor has to maintain

high stock levels in order to be able to meet orders of repair shops etc., because lead times for

spare parts delivery reorders form manufacturers are relative long. Low increase in accuracy of

forecasting leads in the above mentioned system to significant decrease of stock levels.

Fig.1: Supply system

Part of the research plan MSM 6046137306 Jakub Dyntar, MSc.,PhD., Institute of Chemical Technology Prague, jakub.dyntar@vscht.cz Eva Kemrová, MSc., Institute of Chemical Technology Prague, eva.kemrova@vscht.cz Prof. Ivan Gros, MSc.,CSc., Institute of Chemical Technology Prague, ivan.gros@vscht.cz

Spare parts, medicaments or

capital goods manufacturers

Distributors

Stock level ???

Order level ???

Service Lead time 1-3

days Lead time 1-3

months

2

Introduction

Croston’s method and its modifications are the most commonly used methods in sporadic

demand of product stock management systems. This method eliminates the drawbacks of

classical exponential smoothing and secures sufficient stock levels during order lead time period.

The advantage of this method is its reliability and robustness, but also the relative simplicity in

computer processing. Croston’s method solves only the question of the reorder point, i.e. when to

demand restocking in order to remove the possibility of stock-out. The method does not solve the

problem of restocking delivery volume and the mechanics of ordering. The questions are how to

refill stocks and what level of restocking deliveries to implement in order to secure economic

efficiency while still maintaining demanded service levels.

One of the promising ways of solving stated problems is to apply the dynamic simulation

method. The authors’ workplace has had experience in implementing this method even in other

areas of management. The aim of this article is to introduce sporadic demand product stock

management method based on dynamic simulation, which would offer simple and easily

interpretable answers on basic questions connected to effective stock management, which are:

reorder stock level assessment,

replenishment orders volume assessment,

choice of appropriate ordering manner,

optimal stock level assessment.

1 Theoretical background of research

The majority of common stock management systems utilize restocking level as the leading

variable. This variable represents the level of stock capable, with certain probability, of meeting

the demand during the time period required for order fulfillment. The calculation of reorder point

is often based on the average demand and its variable assessment using forecasting methods.

Further on we will sum up forecasting methods used for reorder stock level determination.

1.1 Exponential smoothing

Simple exponential smoothing (Brown, 1959), alternatively exponential smoothing for time

series with trend (Holt, 1957) or seasonal fluctuations (Winters, 1960) belong to the most

commonly used demand forecasting methods in common stock management systems. These

methods provide unsatisfactory results when applied to sporadic demand, the main reason being

the inability to take note of the zero demand periods´ importance. Exponential smoothing model

can be described by the following equation system:

et = yt – y‘t-1, (1)

y‘t = y‘t-1 – et, (2)

mt = (1-) mt-1 + et, (3)

where yt = demand in time t

3

y‘t = average demand forecast in time t

et = forecast error

mt = average deviation of forecast deficiency

Demand forecast, equations (1) and (2) is therefore weighted average of past demand volume,

where is forecast coefficient, originally inverted value of time series length used for demand

forecast.

Equation (4) than determines the calculation of reorder point level Rt:

Rt = y‘t + k mt, (4)

where k = safety factor dependent on demand distribution type

1.2 Croston’s method

Croston (1972) suggested modification of exponential smoothing for sporadic demand

product time series. The core of this method is not only the estimation of average demand

volume, but also estimation of time interval length between two non-zero demands. Following set

of equations describes Croston’s method:

et = yt – z‘t-1, (5)

z‘t = z‘t-1 – et, (6)

mt = (1-) mt-1 + et, (7)

p‘t = p‘t-1 (1–)+ q, (8)

y‘t = z‘t / p‘t , (9)

Rt = y‘t + k mt, (10)

q = 1, (11)

q = q + 1, (12)

where z‘t = the average demand forecast in time t

p‘t = the estimation of time interval length between two non-zero demands

q = number of periods between two non-zero demand periods

The difference between Croston’s approach and exponential smoothing is that the estimation

of average demand volume takes place only in the non-zero demand periods. If the demand

equals zero, average demand volume is the same as in the previous period.

Rao (1973) pointed out the mistake in deriving some of Croston’s method attributes, without

any effect on the model described by equations (5)-(12).

Many authors have proven better results of Croston’s method when compared to exponential

smoothing. Willemain et al. (1994) compared the efficiency of Croston’s method and exponential

4

smoothing and found that Croston’s method achieves better results, even though the benefit was

insignificant in some cases. Similar results can be found in the work of Johnston and Boylan

(1996), who also pointed out that Croston’s method leads to better results if the average interval

between non-zero demand periods is higher than 1.25. Sani and Kingsman (1997) have tested

various methods of demand forecasting on real data from spare parts warehouse in Great Britain

and found that best result are achieved by using the method of moving average followed by

Croston’s method. Their study is extremely valuable because it is one of the few works focused

on the economic efficiency of the supplying process.

1.3 Croston’s method modifications

Even with its positive attributes, Croston’s method suffers a major drawback. Syntetos and

Boylan (2001) have noted that the demand volume estimation is positively deviated and have

suggested a modification of Croston’s method. This modification consists in adjusting the

equation (9):

y‘t = (1-/2) z‘t / p‘t (13)

Improvement of the methods´ efficiency has been proven by Syntetos and Boylan (2005,

2006) or Syntetos, Boylan and Croston (2005).

Levén and Segersted (2004) have tried to create an universal approach applicable to common

and sporadic demand by modifying equation (9) of original Croston’s method and designed

equation for estimating average demand volume:

y‘t = z‘t / p‘t + (1-) y‘t-1 (14)

However, this modification leads to even higher positive deviations, proven in the work of

Teunter and Sani (2009). These authors have pointed out that Syntetos and Boylan’s modification

removes the positive deviation of the original Croston’s method, but in some cases their

approach can lead to negative deviation, which they called „dumping effect“. Teunter and Sani

point out that Croston’s methods give best results when the portion of zero demand periods is

relatively low, while Synteto’s and Boylan’s modification gives good results in cases where a

high portion of zero demand periods occurs . Based on Synteto’s and Boylan’s work, Teunter and

Sani designed their own modification of Croston’s method (9):

y‘t = (1-/2) z‘t / (p‘t - /2) (15)

Testing their modification on randomly generated data and comparing it with Croston’s

method, Teunter and Sani arrived at several interesting conclusions. Firstly they managed to

prove that the average demand volume estimation described by equation (15) is not deviated.

Furthermore, the deviations of original and modified Croston’s method were proved to be caused

by the probability of demand and forecast coefficient choice , while distribution type and

variability of demand volume is insignificant. Low deviation of the method also suppresses the

necessity of time series classification into groups, as suggested by Syntetos, Boylan and Croston

(2005), significantly simplifying the method for computer processing

5

1.4 Simulation method „bootstrapping“

In 2004 Smart, Willemain and Schwarz have introduced a brand new approach in sporadic

demand product stock management. Their simulation method, known also as „bootstrapping“ is

not aimed at the average demand volume forecast like Croston’s method and its modifications,

but it estimates the distribution function of these volumes. The principle of this method is

simple. From timeline obtained in the past, random k-sets of demands are chosen, where k is the

order lead time length. Sums of k generated values are created by theoretically possible

demanded volumes during the order lead time term. If a sufficient number of generated k-sets is

available, it is possible to create demand frequency distribution during order lead time term and

its distribution function. Reorder point level for required level is then easily identified on the x

axis. The example of demand distribution function during order lead time term and reorder point

identification for 2 periods and required service level 98% is presented in Figure 2:

Fig. 2: Demand distribution function during order fulfillment term

Distribuční funkce poptávek (TVO = 2)

0%

20%

40%

60%

80%

100%

0 1 2 3 4 5 6 7 8

Poptávka [ks]

Pra

vd

ěp

od

ob

no

st[

%]

Reorder point

Distribution function (LeadTime = 2)

Demand [Pieces]

Pro

ba

bil

ity

[%

]

Distribuční funkce poptávek (TVO = 2)

0%

20%

40%

60%

80%

100%

0 1 2 3 4 5 6 7 8

Poptávka [ks]

Pra

vd

ěp

od

ob

no

st[

%]

Distribuční funkce poptávek (TVO = 2)

0%

20%

40%

60%

80%

100%

0 1 2 3 4 5 6 7 8

Poptávka [ks]

Pra

vd

ěp

od

ob

no

st[

%]

Reorder point

Distribution function (LeadTime = 2)

Demand [Pieces]

Pro

ba

bil

ity

[%

]

Smart’s method is simple and fitting for computer processing. Unfortunately its contribution

has not been sufficiently proved, pointed out by Gardner and Koehler (2005) in their

commentary.

1.5 Dynamic simulation

Dynamic simulation presents an approach capable of taking into account various random

factors and complex logic connections, which mathematic models are able to describe only to a

limited measure. Simulation can be described as the creation of a logic-mathematical model of

the real object, its aim being the description of object, determination of its function and

estimation of its future behavior. The object simulation model, created by computer, enables the

user to estimate system behavior during internal and external condition changes, optimize process

regarding set criteria (profit, costs, reliability, etc.), to compare various alternatives of the process

arrangement and choose an arrangement with appropriate efficiency. Computer model removes

the risk of negative impact on real systems and provides required values, matching the aims of

the simulation study. The main advantages of simulations can be summarized by the following

points:

6

Simulation allows user to test suggested variants in advance without the necessity of

allocating resources for their implementation.

Simulation allows user to slow down or accelerate time.

Simulation helps to find the reasons for the phenomena taking place and enables its

detailed study.

Simulation model offers the possibility of creating scenarios and provides answers to

questions „what happens if…“.

Simulation helps to verify efficiency of planned investments before their actual

realization.

There are many specialized software applications based on dynamic simulation. We have

good working experiences with products such as Witness or SIMUL8, providing an environment

for simulation of even complex models. The core of these software products is a set of predefined

elements, connected by logical parameters generated in a simple programming language. The

advantage of these applications is the possibility of visualization of simulated systems. However,

less complex problems can be successfully solved using Visual Basic for Applications, a part of

MS Excel.

2 Dynamic simulation of stock management

2.1 Basic model

Dynamic simulation of stock management is based on the recap of past warehouse stock

movement under conditions of the chosen stock management system. The simulation model input

is past demand time series of product and order lead time term. Stock management system is

described by stock replenishment system, i.e. when to generate replenishment order and how to

determine its size. Warehouse stock movements are the fulfilled needs of customers (stock

decrease) and replenishment order arrivals (stock increase).

The entire system of stock movement for automobile spare part demand time series is shown

in Table 1. Let us consider the order lead time term of the length of 2 periods and stock

management system with constant replenishment order of 5 pieces and reorder point of 2 pieces.

Initial stock of given stock product in period 1 is 2 pieces.

Tab. 1: Spare part movement in Q-System of stock management

Period t 1 2 3 4 5 6 7 8 9 10

Starting stock Pt [Pieces] 2 1 1 1 4 4 4 4 1 0

Demand St [Pieces] 1 0 0 2 0 0 0 3 1 0

Generate order Q [Pieces] 5 5

Order arrival Ot [Pieces] 5

Missing amount Ct [Pices]

Final stock level Kt [Pices] 1 1 1 4 4 4 4 1 0 0

Starting state of system in each period is, with the exception of period 1, described by final

stock level of preceding period. Order generated in the period corresponding to order lead time

term is added to that of the stock and then appropriate demand is subtracted. The following step

is to find out if it is necessary to create a new order. From the logic of the chosen system it is

7

obvious that the order will be generated in case the difference between starting stock level and

demand increased by eventual replenishment order arrival is below the reorder point. With the

exception of cases when replenishment order was generated in preceding periods and are being

realized. Final stock level is used in the next step as the starting state of the system and the entire

calculation is repeated. It is obvious that for set parameters (reorder point= 2 pieces,

replenishment order = 5 pieces) 2 replenishment orders would be generated in period t=1 and t=8

in this stock management system. The key point of dynamic simulation is the choice of the stock

management system and determination of optimal level of parameters, representing the system. If

we are to decide if the chosen solution meets required efficiency, we need to determine the set of

solutions (i.e. group of stock management systems) and criteria of evaluation. This problem will

be examined more closely.

2.2 Stock management system choice

Three basic stock management systems are described in literature. Their main characteristics

are (Winston, 1994):

Q-system, reorder point model with constant order quantity

Operating parameter of this system is reorder point, while replenishment order size is

constant. Order is generated if stock level, represented by final stock level is below reorder point.

P- system, periodic review inventory system with upper replenish level and constant

reorder period

In P-system orders are placed at intervals with constant length, while replenishment order

size is calculated by:

Q = xh – Kt, (16)

where xh = upper reorder level

Kt = warehouse stock level in time t

PQ-system

PQ-system combines both mentioned systems. Term of order generation is based on reorder

point level, replenishment order size is calculated by equation (16).

Operating parameters of mentioned stock management systems are shown in Table 2:

Tab. 2: Operating parameters of stock management systems

System Operating parameters

Q Reorder point, constant replenishment

order

PQ Reorder point, dynamic replenishment

order size

P Ordering interval length, dynamic

replenishment order size

8

2.3 Simulation efficiency evaluation

Let us find an answer to the question of how to determine whether the chosen solution

represented by chosen stock management system and combination of decision parameters will

secure required efficiency of the whole system.

The first step will be the survey weather the customer demands were fulfilled completely or

not in each period. If we assume the situation described it Table 1, missing amount Ct in period t

will be defined as:

Ct = St – Ot – Pt if St > Ot + Pt, (17)

and total missing amount C:

T

t

tCC1

(18)

To assess fulfillment of customers´ demands we use the simple indicator service level SL:

SL = (1 - C/S)100%, (19)

where

T

ttSS

1

= total demanded quantity in period 1,2, ...... T

Therefore service level indicator means what percentage of total demanded quantity can be

immediately released from stock.

To calculate economic efficiency of chosen system we can use stock purchasing and

maintenance costs (Winston, 1994) and taking into account a possible penalization for inability to

fulfill required service level. Stock purchasing costs are expressed as a function of viable orders

number:

No = o no, (20)

where o = number of realized orders

no = costs for one order

Maintenance stock level costs can be determined as a function of average stock level xp:

Ns = xp T c ns, (21)

where T = period length

c = product unite price

ns = maintenance stock costs as % of average stock in monetary units in period of

length T

Total purchasing and maintenance cost can be easily formulated as:

Ntot = No + Ns + P, (22)

where P = the effect of inability to fulfill demanded service level

9

Average stock level can be calculated as arithmetic average of final stock levels in periods 1,

2....T:

T

KT

t

t

x p

1 (23)

If the organization uses continuous stock level monitoring, it is possible to use more accurate

methods of average stock level calculation.

2.4 Decision parameters assessment of chosen stock management system and their

optimization

By the choice of the stock management system from the possible set we determine the

manner of replenishment order generation, time of their generation and their size will be assessed

by systems´ decision parameters calculations. With the exception of P-system, where the order

generation assessment is different, the moment determined by term of stock level decrease on

reorder point can be assessed by some of the forecasting methods. Replenishment order size can

be obtained by repeating the simulation in an appropriate parameters value range by choosing

decision parameters combinations securing required service level. The other possibility of

operating parameters assessing is to repeat the simulation in fittingly defined values ranges of all

decision parameters. Stock management system choice and operating parameters calculation can

be schematically described as follows:

Fig. 3: Stock management system choice and combination of decision operating

parameters generation

Choice of stock management system

Is chosen system a P-system?

Reorder point calculation method

Forecasting method

Generate decision parameters combinations

Simulate warehouse stock movement

Calculate SL by formula (19)

Note operating parameters combinations with corresponding SL

Combine reorder point with other

decision parameters

YES NO

10

It is obvious that by repeating the simulation for various stock management systems and

various combinations of decision parameters we obtain multiple possible solutions securing

required service level. If we add viable order number monitoring and average stock level

calculation to the simulation model, we can optimize it by using the formula (22). The aim of

optimization is to find a stock management system with minimal purchasing and maintenance

costs while retaining required service level described by the formula (19).

3 Application of dynamic simulation on sporadic demand products

The table below shows demanded quantities of a specific automobile spare part in previous

periods.

Tab 3: Automobile spare part demand timeline

Period t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

St 4 5 0 0 0 0 0 0 0 1 6 0 2 4 0 0 5 0 0 1 0 1 8 2 5

Period t 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

St 8 7 0 6 0 5 9 0 0 8 0 0 0 0 0 0 4 0 0 2 0 0 5 0 0

Using dynamic simulation in the setting of MS Excel, the authors have tried to find a stock

management system characterized by decision parameters combinations with minimal purchasing

and maintenance costs while retaining required service level. Values of input parameters used in

calculations are shown in Table 4.

Tab. 4: Experiment input parameters

c 185 Euro/piece

ns 25% % from average stock level in Euro yearly

no 37 Euro/1 order

P 1 000 000 000

S 98 Pieces

T 50 Number of time periods

SL 98% %

Lead time 3 Time periods

Starting stock level 9 Pieces

The choice of system was limited to Q-system, PQ-system and P-system, characterized by

decision parameters shown in Table 2. These parameters were calculated using total simulation or

the reorder point calculation method. Implemented experiment variants including the operating

parameters calculation are shown in Table 5.

Tab. 5: Implemented experiment variants

Variant Description Signal level Replenishment order size

1 Q&B Bootstrapping Smart-Willemain (B) Dynamic simulation

2 PQ&B Bootstrapping Smart-Willemain Dynamic simulation

3 Q&ES Exponential soothing (ES) Dynamic simulation

4 PQ&ES Exponential soothing Dynamic simulation

5 Q&CR Crostons method (CR) Dynamic simulation

6 PQ&CR Crostons method Dynamic simulation

7 Q&SB Syntetos-Boylan method (SB) Dynamic simulation

8 PQ&SB Syntetos-Boylan method Dynamic simulation

11

9 Q&LS Levén-Segersteds method (LS) Dynamic simulation

10 PQ&LS Levén-Segersteds method Dynamic simulation

11 Q&TS Teunter-Sanihs method (TS) Dynamic simulation

12 PQ&TS Teunter-Sanish method Dynamic simulation

13 Q Dynamic simulation Dynamic simulation

14 PQ Dynamic simulation Dynamic simulation

15 P Dynamic simulation Dynamic simulation

Reorder point calculation realized with the aid of forecasting methods was carried out using

forecasting coefficient = 0.1; k = 3; .The total stock management system simulation (i.e.

determination of both parameters using simulation) was carried out by using the total

enumeration method in the value range of 1-98 for decision parameters of the Q and PQ-system

and ordering interval range 1-50 for the P-system. Results of the experiment are shown in Table

6.

Tab. 6: Experiment outputs

Variant Description Signal level

[pieces/priod] Q

[pieces] xp

[pieces] Ns[Euro] No[Euro] Ntot[Euro] C

[pieces] US

14 PQsystem 15 30 14,88 2867 222 3089 0 100%

4 PQstm+SES 20 28 15,60 3006 296 3302 0 100%

6 PQstm+Croston 18 28 15,60 3006 296 3302 0 100%

8 PQstm+S&B 18 28 15,60 3006 296 3302 0 100%

10 PQstm+L&S 20 28 15,60 3006 296 3302 0 100%

12 PQstm+T&S 18 28 15,60 3006 296 3302 0 100%

13 Qsystem 15 25 16,50 3179 185 3364 0 100%

2 PQstm+Bting 22 29 16,52 3183 296 3479 0 100%

15 Psystem 2 28 16,56 3191 407 3598 0 100%

5 Qstm+Croston 18 19 17,66 3403 222 3625 0 100%

7 Qstm+S&B 18 19 17,66 3403 222 3625 0 100%

11 Qstm+T&S 18 19 17,66 3403 222 3625 0 100%

3 Qstm+SES 20 22 20,04 3861 185 4046 0 100%

9 Qstm+L&S 20 22 20,04 3861 185 4046 0 100%

1 Qstm+Bting 22 27 22,80 4393 185 4578 0 100%

Simulated variants were arranged by ascending values of total costs. The best variant would

be PQ-system with reorder point 15 pieces and replenishment order size 30 pieces. The outputs

have verified the assumption that decisive parameter values obtained by total simulations provide

better, or at least the same efficiency of a given system compared to values obtained by the

combination of a forecasting method for calculating the reorder point and dynamic simulation for

assessing restocking order level. It is obvious that when using "Total Enumeration" method in

total simulation of stock movement, a combination containing reorder point level obtained by the

forecasting method will be involved when sufficient parameters value range is used. This fact

evokes not only the question of how to determine decision parameter value range in order to find

optimal value of criterial function, but also in order to search the range of possible solutions.

Total simulation of stock movement will become rational only when system efficiency is

increased compared to using forecasting methods to calculate restocking point and time required

for calculation. This problem is largely insignificant in relation to products with sporadic demand

because of the relatively low demand numbers in the individual period. Total demand is therefore

not great, leading to a relatively narrow range of operating parameter values, and therefore

12

minimal time is required for calculation. The following objective of the authors is to modify the

dynamic simulation method to make it universally applicable even for a large portfolio of

existing items, not showing the attributes of sporadic demand.

Conclusion

The aim of this article was to introduce dynamic simulation as an effective method of

sporadic demand product stock management system. The authors created 15 algorithms working

on the basis of stock movement simulation in the setting of the given stock management system

and additional decision parameter optimizations using cost function. Issuing from experiments

carried out on real auto part demand time series, the hypothesis has proven that operating

parameter values obtained using total simulations provide better, or at least the same efficiency of

the given system compared to values obtained by using the combination of a number of

predicting method for the calculation the restocking point. The ability of dynamic simulation to

find an optimal stock management system characterized by operating parameters combinations

predetermines this method universally not only for sporadic demand products stock management

but also for stock management. The problem of simulation approach in the current form lies in

the manner of searching for possible solutions, the excessive time requirement is for that reason

unsuitable for managing large portfolio of stock with varying demand. It is obvious that further

research activities of the authors will be aimed at targeting this drawback.

Even when considering its drawbacks, dynamic simulation is a promising method, capable of

efficiently managing the process relevant to restocking and maintaining the inventory and,

therefore, contributes to lowering the cost associated with stocks. In the case of many

organizations the costs are enormous and, therefore, even a small decrease of stock levels

represents considerable savings. It is therefore necessary to pay special attention to the

development of appropriate stock management methods.

13

Appendix

Q -system simulation model created in language VBA:

Sub Qsystem()

'Initialization of variables

Q, Signal, StartStock, LeadTime, T

For t = 1 to T

'Set P(t)

If t = 1 then

P(t) = StartStock

Else

P(t) =K(t-1)

End If

'Delivery arrival

If oo = t Then

P(t) = P(t) + Q

oo = 0

End If

'Dispatch of demanded quantity

If P(t) >= S(t) Then 'Sufficient stock

P(t) = P(t) - S(t)

ElseIf P(t) < S(t) Then 'Stock-out

C = C + S(t) - P(t)

P(t) = 0

End If

'Order generation

If P(t) <= Signal And oo = 0 Then

oo = t + LeadTime + 1

End If

'Set K(t)

K(t) = P(t)

Next

EndSub

14

References

[1] Brown, R. G.: Statistical forecasting for inventory control, Mc Graw-Hill, New York,

1959

[2] Croston, J. D.: Forecasting and stock control for intermittent demands, Operational

research quarterly 23, 289-303, 1972

[3] Gardner, Koehler: Comments on a patented bootstrapping method for forecasting

intermittent demand, International Journal of Forecasting 21, 617– 618, 2005

[4] Holt, C. C.: Forecasting seasonal and trends by exponentially weighted averages,

Carnegie Institute of technology, Pittsburg, Pennsylvania, 1957

[5] Johnston, Boylan: Forecasting for items with intermittent demand, Journal of the

operational research society 47, 113-121, 1996

[6] Levén, Segersted: Inventory control with a modified Croston procedure and Erlang

distribution, International journal of production economics 90, 361-367, 2004

[7] Rao, A. V.: A comment on: Forecasting and stock control for intermittent demands,

Operational research quarterly 24, 639-640, 1973

[8] Sani, Kingsman: Selecting the best periodic inventory control and demand forecasting

methods for low demand items, Journal of the operational research society 48, 700-713,

1997

[9] Syntetos, Boylan: On the bias of intermittent demand estimates, International journal of

production economics 71, 457-466, 2001

[10] Syntetos, Boylan: The accuracy of intermittent demand estimates, International journal of

forecasting 21, 303-314, 2005

[11] Syntetos, Boylan, Croston: On the categorisation of demand patterns, Journal of the

operational research society 56, 495-503, 2005

[12] Teunter, R.H., Sani B.: On the bias of Croston’s forecasting method, European Journal of

Operational Research , Volume 194, Issue 1, 1 April 2009, Pages 177-183, ISSN 0377-

2217

[13] Willemain, Smart, Shockor, DeSautels: Forecasting intermittent demand in

manufacturing: a comparative evaluation of Croston’s method, International journal of

forecasting 10, 529-538, 1994

[14] Willemain, Smart, Schwarz: A new approach to forecasting intermittent demand for

service parts inventories, International journal of forecasting 20, 375-387, 2004

[15] Winston, W. L.: Operations research: applications and algorithms, ITP, 1994

[16] Winters, P. R.: Forecasting sales by exponentially weighted moving averages, Mgmt Sci.

6, 324, 1960

15

Simulation approach in stock control of products with sporadic demand

Jakub Dyntar, Eva Kemrová, Ivan Gros

ABSTRACT

Croston’s method and its modifications are the most commonly used methods in sporadic

demand of product stock management systems. This method eliminates the drawbacks of

classical exponential smoothing and secures sufficient stock levels during order lead time period.

The disadvantage of Croston’s method is the fact that it solves only the question of the reorder

point but does not solve the problem of restocking delivery volume and the mechanism of

ordering. The questions are how to refill stocks and what level of restocking deliveries to

implement in order to secure economic efficiency while still maintaining demanded service

levels. One of the promising ways of solving stated problems is to apply the dynamic simulation

method. The aim of this article is to introduce sporadic demand product stock management

method based on dynamic simulation, which would offer simple and easily interpretable answers

on basic questions connected to effective stock management.

Keywords: Forecasting, Simulation, Inventory Management, Sporadic Demand

Jel classification: C53