selecting the right inventory target strategy for

Scientific article – JMR Vrouenraets 1

Selecting the right inventory target strategy for minimizing

inventory levels for products with high variation in the forecast

error using Monte Carlo simulation

Jeroen Marc Roger Vrouenraetsa

03-04-2013

a Faculty of Technology, Policy and Management, Delft university of Technology, Jaffalaan 5, Delft, The

Netherlands

Article info

Keywords:

Inventory management,

Monte Carlo simulation,

supply chain management,

safety time, safety stock

Abstract

In supply chain management, analytical inventory models are used to

prescribe a target safety stock to achieve optimal inventory levels.

These models prescribe either a fixed safety stock or dynamic safety

time. In the existing literature little attention is given to the impacts of

either settings on the inventory performance based on the analytical

inventory models. In this paper is determined: What is the optimal

target safety setting strategy for products with a high variation in the

forecast errors using distribution resource planning, considering

inventory size and service levels? First, a literature review is discussed

on the little known effects on the use of either setting. Based on a case

study, a simulation model is developed to determine the optimal

target setting. The results of the simulation study quantify the

negative effects when using safety time for products which have a high

variation in forecast errors. Furthermore a valid inventory simulation

model for experimenting purposes is proposed.

1 Introduction

The fast moving consumer goods (FMCG) sector

is one in which having an optimal supply chain

(SC) is a great competitive benefit. The goal in

each SC as described by Goldratt & Cox (2004 ),

is to (1) maximize the rate at which the system

generates money through sales, while (2)

minimizing the money that the system has

invested in purchasing things that it intends to

sell and (3) minimize the money that is spend in

order to turn inventory into throughput.

In line with this goal, inventory management is

pursuing to achieve target service levels (1) by

balancing inventory (2), supply chain

capabilities and demand (3). Selected measures

of performance are the service level and the

average inventory size.

To achieve target service levels, literature

describes the use of analytical models. These

models describe reality with mathematical

equations. They attempt to capture the

stochastic nature of inventory drivers in order to

calculate a minimum inventory buffer which

covers for uncertainties in the SC (Silver &

Peterson, 1985).

There are two type of strategies to set the target

minimum inventory buffer: fixed safety stock or

dynamic safety time. A fixed safety stock reflects

a minimum number of products to keep in stock.

The safety time targets inventory replenishment

a certain period before the actual need is

expected(van Goor, Kruijtzer, & Esmeijer,

Goederenstroombesturing, voorraadbeheer en

materials handling, 1990).


Although both strategies can be calculated using

the same analytical equations, it is unclear what

benefits and risks are related to which strategy.

In the literature little has been written on the

different effects of the different strategies on the

SC performance.

The objective of this paper therefore is to fill the

gaps in literature by adding knowledge on the

effects on performance measures in the SC

because of the use of different stock setting

strategies. The following question is central in

this paper: What is the optimal target safety

setting strategy for products with a high variation

in the forecast errors using distribution resource

planning, considering inventory size and service

levels?

This paper will give examples on the use of the

different stock setting strategies through a case

study conducted within an international FMCG

SC.

By means of combining a literature review on

the use of the setting strategies, the use of an

inventory Monte Carlo simulation model for

testing several scenarios and the experiences

during the case study, the effects are analyzed.

The contribution of this paper is the

quantification of the negative effects when using

safety time for products which have a high

variation in forecast errors. Furthermore a valid

inventory simulation model for experimenting

purposes is proposed.

The structure of this paper is as follows. Section

2 provides a literature review to define the

inventory management concepts necessary to

understand the importance of inventory safety

settings. Also, considerations on the use of the

two safety setting strategies will be given.

Furthermore the concept and limitations of

analytical inventory models are discussed.

Section 3 discusses the use of a Monte Carlo

simulation model for inventory management

after which section 4 describes the development

of such a simulation model based on a case study

and explores the use of different safety setting

strategies. Section 5 states the conclusions and

answers the research question. Section 6

provides a discussion on the performed

research.

2. Literature review

2.1 Inventory replenishments cycle

Schneider (1981) summarizes several

definitions for the service level of a supply chain.

A convenient measure to express service is the

so-called case fill rate (CFR), which is the

fraction of demand which can be directly

satisfied from the shelf.

A way to improve the CFR is to keep an optimal

amount of safety stock. This is a part of the

inventory that is held in excess of expected

demand due to variable demand rate and/or

lead time (Stevenson, 2005). Once a target safety

stock level is determined for the SC using

accurate data, the setting would not have to

change until high impact changes in the SC take

place (e.g. extra trade lane which significantly

shorten the lead time).

Once a target is set, one should focus on

maintaining the stock levels near the target

safety stock level by means of replenishing

optimal quantities of stock, called cycle stock.

Multiple methods are available for calculating

the right amount of cycle stock, which depends

on economical and technical constraints(van

Goor, Kruijtzer, & Esmeijer, 1990). E.g. the lot for

lot strategy replenishes the minimum quantity

which is necessary to align with the target safety

stock and technical constraints, but this strategy

does not consider economical constraints like

ordering cost(Silver, Pyke, & Peterson, 1998).

A system to control the time-phased

requirements of replenishment for distribution

centers is called distribution requirements

planning (DRP) (van Goor, van Amstel, & van

Amstel, 1989). By monitoring the inventory

levels, (forecasted) demand and replenishment

lead times, it suggest moments to replenish so to

keep inventory around the target safety stock.

Wrong safety settings fail to cover for demand

due to unexpected variation during the lead

time, resulting in lower than targeted CFR.

Hence, for the ongoing replenishment cycle, the

accurate planning of the initial safety setting is

crucial. Widely used are analytical inventory

models to calculate an optimal safety setting

with.


2.2 Analytical inventory models

Analytical models describe a system using a set

of multiple equations. Analytical equations or

numerical algorithms are used to find one, point-

estimate solution for a problem (Haugh, 2004).

The analytical inventory model is used to

calculate the target safety settings with,

developed by Silver & Peterson (1985). Others,

such as de Kok et al (2012), have improved this

model by eliminating certain constraints of the

model.

Equation 1 shows the key elements in the model

to calculate the safety stock with.

Equation 1

SS = safety stock (product) K = risk factor (unit less) = Standard deviation of the estimated error during the replenishment lead time (product)

(1) The target safety stock. This should be used

as a target when the inventory is replenished so

that a certain target CFR is achieved.

(2) The standard deviation of the estimated

errors resembles the variation in demand and

supply chain elements during the replenishment

lead time. Little variations in these elements

make a supply chain relative predictable (in a

utopia, deterministic), thus a reason to keep less

safety stock.

The errors are driven by multiple elements in

the SC such as forecasting or production issues.

Silver et al (1998) propose an accurate method

to combine these elements.

(3) The k-factor, or the risk factor, determines

how many times the standard deviation should

be kept in stock in order to achieve a target CFR .

The value for k is driven by three parameters

(Equation 2) and a special function of the unit

normal distribution which eliminates the

cumulative density for k smaller than 0 (Rosen,

2013).

Equation 2

= Target service …………….level Q = Average order …………….quantity per …………….cycle = special

…………….function of …………….the standard …………….normal …………….distribution

A short reasoning; if a higher CFR target is

selected or the standard deviation of the

estimated errors increases, the function

returns a higher value for k and thus the safety

factor is relative high.

On the other hand, if the order quantity

increases, the safety factor decreases. This might

seem counterintuitive but with a higher order

quantity, the cycle time increases and thus the

number of replenishments in a period decreases

(ceteris paribus). Given the fact that the risk of a

stock out is higher near the end of a cycle (when

the stock is low), this risk now is reduced due to

the fewer replenishments and thus a smaller

safety factor can be used.

With a unit less risk factor and a standard

deviation expressed in number of products, the

safety stock setting resembles the number of

products that should be kept as safety inventory

to cover for the expected variation in demand

and lead time in order to achieve a target case fill

rate. This is called the safety stock and is

constant unless reviewed.

By dividing the safety stock by the average daily

demand, a safety time (expressed in days) is

calculated. Instead of using a fixed safety stock to

trigger replenishment, safety time sets the target

stock equal to the expected (forecasted) demand

over the safety time. This results in replenishing

inventory an amount of days before it is actual

needed, creating a safety time buffer(van Goor,

van Amstel, & van Amstel, 1989).

2.3 Differences between safety strategies

Literature on the use of safety time is limited, let

alone the differences in performance between

both safety strategies. While the conventional

analytical model simply suggest safety stock to


be used as optimal safety setting, the first

question is why even bother to use safety time?

General reasoning on safety time returns that it

fluctuates with the expected demand. Thus, in

periods of low demand, inventory benefits from

safety time because it reduces total inventory,

whereas, in times of high demand, it provides

extra security.

Rosen (2013) favors this reasoning, suggesting

that safety time is useful near the end of a

product life cycle is preferable. While evidently

the demand will decrease, the safety time will

make the total inventory decrease with the same

pace, resulting with little non-performing

inventory at the end of the life cycle.

Whybark and Williams (1976) pose that

uncertainty in timing of demands should be

dealt with using safety time, whereas

uncertainty in quantity should be dealt with

using safety stock.

Chang (1985) argues that safety stock and safety

time are interchangeable. However, his modeling

of production and demand in essence is

deterministic which makes is less valuable to

apply in practice. Yano (1987) focused on

finding the optimal planning lead time but also

only considered deterministic demand.

Buzacott and Shanthikumar (1994) with the use

of stochastic modeling that safety time is

preferred over safety stock given the condition

that forecast are accurate. Moreover, with

changing customer orders during the lead time

or bad forecasts, inventory performance would

result from fixed safety stock.

Although is general safety stock seems a robust

choice to optimize supply chain performance

with, no studies have been found to quantify the

impact.

3. Monte Carlo simulation

Simulation models mimics the operating

behavior of a system (Verbraeck & Valentin,

2006). To understand the most important

behavior and to create a simulation model often

is more time consuming than the use of an

analytical model.

However, the effects of choosing between safety

stock and safety time are not clear. As stated by

Aguilar et al (1999), for such cases simulation is

an effective tool to communicate results and

performance dynamics.

Monte Carlo (MC) simulation is based on two

mathematical theorems which make it a very

useful simulation type to analyze inventory

behavior with. (1)the law of large numbers and

(2) the central limit theorem. Not only can MC

simulation, considering the first theorem, show

an estimate of the expected result, it also returns

an estimate of the uncertainty in this estimate

(Dunn & Shultis, 2011). These characteristics

make MC useful to account for risk in

quantitative analysis (Palisade, 2013).

Recent studies have been using Monte Carlo

simulation for inventory management problems

(Cáceres-Cruz, Grasman, Bektas, & Faulin,

2012)(Jaio & Du, 2010). However little effort has

been put specifically in using MC simulation to

explore the uncertainty involved with the

analytical model and the use of different safety

setting strategies.

Key differences between the use of an analytical

model and the MC simulation are shown in Table

1.

Analytical model

MC simulation

Input para-meters

Static parameters to describe stochastic behavior with

Used to draw samples from

System characteristics

Analytical equations

Defines operating behavior and functional relationships

Results Point estimates Range estimates

Table 1: Difference between analytical models and MC simulation models


4. Case study

In order to develop a Monte Carlo simulation

model to simulate inventory management

processes with, key system characteristics have

to be selected. In order to do so a system

analysis is performed at an FMCG supply chain.

For the design approach of the simulation model

three viewpoints have been combined. First, the

simulation method of Banks (1999) for the

general modeling methods. Secondly, the META

model (Herder & Stikkelman, 2004) is used. The

model starts with defining the model

requirements and the possible solution space to

answer to these requirements with. Last, the

spiral model (Boehm, 1988) is used for the

approach. The spiral model consists of several

iterative stages in which the model is designed,

tested and adapted resulting in a robust model

design.

To obtain requirements for the model, the TIP-

framework as proposed by Koppenjan and

Groenenwegen (2005) is used to analyze

inventory management from a technology,

institutional and process point of view.

The selected performance measures for the

strategies are (1) the case fill rate (%), (2) and

the average inventory (Statistical units and

days).

The conceptual model consists of four parts: (1)

the sampling demand and a adhering forecast of

demand, (2) the daily inventory position, (3) the

DRP planning of order replenishments and (4)

the production and actual replenishments of

products. These four parts together are able to

simulate the behavior of inventory over time. Of

key interest is the use of safety settings as a

trigger for the DRP planning to replenish.

For the specification of the model, all data could

be retrieved from data sources located within

the company.

However, for the sampling of stochastic values

for the demand, forecast and lead times, accurate

probability distributions need to be selected.

Statistical test on sample data showed that a

gamma distribution fits the distribution of

demand (Vrouenraets, 2013). Silver et al (1998)

show that for both the variation in forecast

errors and lead time errors a normal

distribution can be used. The simulation model

has the property to set the average variation for

the distribution. This allows for experimenting

with accurate and useless forecast and likewise,

high lead time variations.

Multiple experts with different expertise within

the SC, were interviewed for the validation of the

simulation model (Sarikaya, 2013)(van der Oost,

2013)(Alves, 2013). Each expert is asked to

check the dynamics by looking at the specific

parts of the model and the output graphs. All

acknowledged the validity of the model. Alves

recognized the fact that no inventory is

simulated at the plant but agreed to leave it out

of the simulation while it concerns a single stage

simulation model. Moreover, using a binary

search, the average optimal safety stock setting

(after a 1000 iterations) for a 99% case fill rate

according to the simulation model was

compared with the suggested safety stock

setting of the analytical model. The range did not

show any significant deviation from the

analytical model which echoes the validity of the

simulation model.

Two experimental designs are conducted. For

both experiments, 4 product classes (table 3)

were defined using the criteria of daily volume

(threshold; 100 SU/day) and COVFE (threshold;

100%). Products from the company were

selected. All supply chain parameters are

selected in such a way that it would reflect

reality.

For one experiment, the analytical optimal safety

setting was used expressed as safety stock. For

the other experiment, safety time was used.

After using the method for calculating the

number of iterations as described by Verbraeck

and Valentin(2006), both experiments were

executed a 1000 times.

The results were analyzed both on the level of 1

iteration and on the MC simulation as a whole.

Now, the results for the product class with high

daily volume and high COVFE are discussed.

The analysis of 1 iteration using safety time

(Graph 1) show four dynamics:


(1) The first peak in the target safety stock

(4) is exactly matched mainly because of

the good forecasting. The inventory goes

up to match the demand and after the

peak in demand, it lowers again.

(2) The creation of yellow NPI (1) increases

rapidly when only safety time is used.

E.g. due to the last extreme over

forecast, a lot of yellow NPI is created.

The duration of the yellow NPI wave is

larger because it is replenished already

a few days earlier compared with the

previous scenario. The peak of yellow

NPI is higher because the target safety

setting goes up as it ‘looks’ further in the

future.

(3) One of the assumed benefits of safety

time is that it should lower inventory in

case no demand is expected. On the one

hand, this is true. With low forecast of

demand, the target safety setting gets

near 0 which saves inventory costs (3a).

However, at this point the difference

between forecast and actual demand is

rather low. Point (3b) gives an example

where no demand is forecasted which

takes the inventory to 0, but

unfortunately gets surprised by a peak

in demand (1, in graph 3). Now, no stock

can satisfy the unexpected demand

during the lead time: and this is exactly

the type of demand safety stock should be

used for. Demand hurts the most, when

it is least expected. And that is why

there should be safety stock, which now

is not the case.

(4) An example of where the safety time

does prove its benefits is the moment

when the forecast of demand is accurate

(2 in graph 3). The first weeks (4) the

inventory goes up and down with the

accurate safety setting which provides

safety.

The analysis of 1 iteration using safety stock

(Graph 2), using the same initial conditions

(Graph 3) as with the previous iteration, show

other dynamics. Most important findings from

this graph on the dynamics are:

(1) Compared with both of the previous

graph of the inventory results, it

immediately becomes clear the

inventory with the use of safety stock is

more stable: Peaks are less extreme and

only need a shorter time to restore

around the inventory target.

(2) With the use of fixed safety stock, also

there is creation of some yellow NPI.

The largest peak happens near (2),

driven by the over forecast of demand.

Given the fact that in all three scenarios,

an over forecast of demand leads to

yellow NPI, means that yellow NPI can`t

be prevented with high COVFE.

Although the inventory position also reaches

zero in the scenario with the fixed safety stock,

the final score on average total inventory and

case fill rate, show better numbers compared

with safety time.

Both iteration already explain some of the

dynamic behavior, however results of the MC

simulation tell even more on the risk profile of

both safety settings.

Graph 4 and Graph 5 show the ranges of the

performance measures after a 1000 iterations. It

clearly shows how both the average inventort

and CFR score are better when safety stock is

used. Moreover, the ranges wherein these value

lie are more accurate with the use of safety

stock, in other words, the extremes are less

likely to be expected.

5. Discussion of results

Table 1 compares the ranking of the average CFR

score for each product class for the safety

settings scenarios. It clearly shows that in case of

s.k.u. with a high COVFE (Class I and III), a fixed

safety stock setting results in the best CFR score.

This also counts for class II s.k.u. Only, for the

class IV s.k.u. the current situation slightly

outperforms the fixed stock strategy.

Not only does the use of fixed safety stock out-

perform other strategies on the average CFR

score, it also makes the scoring range more

narrow (not shown in table below). This means


that less (extreme) outliers are expected when

fixed safety stock is used.

Table 2 compares the ranking of the average

inventory levels for each class for the safety

setting scenarios. Also for the inventory, all s.k.u.

classes benefit most from a fixed stock setting.

Not only does the use of fixed safety stock out-

perform other strategies on the average

inventory level, it also makes the inventory

range more narrow (not shown in table below).

This means that less (extreme) outliers are

expected when fixed safety stock is used.

6. Conclusion and further research

The use of safety time has positive effects when

the forecast is accurate. Inventory benefits from

accurate low forecasts, which result a decrease

of the total inventory whereas high CFR score

are obtained in case of accurate forecasted peaks

in demand.

However, the negative effects of safety time

perhaps are bigger than currently known at P&G.

On the one hand, when over forecast are made,

the dynamics of safety time enlarges the creation

of excessive inventory. On the other hand, when

the forecast of demand is too low, there is not

enough safety stock to cover for the forecast

error. This leads to the reasoning why inventory

is now at its most vulnerable: Demand hurts the

most, when it is least expected. And that is

exactly when (and why) there should be safety

stock. This is not the case with the use of safety

time.

Safety stock is a robust approach for covering for

errors during the replenishment lead time.

Extreme low values for CFR scores or high

values for total inventory, are not common like

with the use of safety time. Moreover, the

average scores for both CFR and inventory are

better than when safety time is used according

to the simulation study.

Before this paper, little quantitative research

had been performed aiming at quantifying the

differences between the use of two commonly

used safety settings: safety stock and safety time.

Moreover, little effort had been put specifically

in using MC simulation to explore the

uncertainty involved with the analytical model

and the use of different safety setting strategies.

By developing and validating a simulation model

for inventory management, the possibility was

created to test the effects of both settings and

quantify the differences on performance

measures such as inventory and case fill rate.

The conclusion is clear. For DRP system the use

of safety stock for products with a high variance

of the forecast error, safety stock is preferred

over safety time.

The development of a valid simulation model for

inventory management can be used for many

purposes. The focus of this research was to point

out the difference between two types of safety

setting for products with a high variation in

forecast errors. However, by changing initial

parameters in the model, different values for

demand, the forecast errors or lead time errors

can be simulated. Moreover, single iteration

results can be used for educating purpose to

make clear the effects of both using wrong safety

settings values and the use of wrong safety

strategies.

7. Reflection

The design of the simulation model has been

performed with care. Moreover, the final

simulation model has been validated both by the

use of experts validation and a quantitative

validation using the results of the analytical

model. However, still some distinct choices have

been made that can influence the results.

First, the choice for the use of a lot for lot

replenishment strategy was driven by the case

study and the objective to minimize inventory.

However, many supply chains are driven by cost

of the inventory as well, therefore likely to use

other replenishment strategies. Adaption of the

model then is needed to experiment for

analyzing those effects.

Second, the use selection of sued probability

distribution can affect the dynamics in the

results. Especially the gamma distribution has

the feature of simulating a long tail, which might

not be accurate for certain products. This would

make the current simulation model results more


extreme than would be the case for the product

types.

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Graph 1 Results of iteration with use of safety time

Graph 2 Results of iteration with use of safety stock

Graph 3 Input for demand and forecast of demand for both iterations shown above

(1)

(1)

(3b)

(2)

(3a) (4)

(1) (2)

(1) (2)


Graph 4: Results average inventory score of Monte Carlo simulation using safety time and safety stock

Graph 5: Results of CFR score of Monte Carlo simulation using safety time and safety stock

Average CFR ranking Class I Class II Class III Class IV

Scenario 1 (safety time) 2 (80,6%) 2 (87,1%) 2 (92,5%) 2 (98,3%) Scenario 2 (fixed stock) 1 (95,8%) 1 (97,8%) 1 (99,0%) 1 (99,9%) Table 1: Ranking of scenarios on the average CFR score per s.k.u. class

Average inventory ranking Class I Class II Class III Class IV

Scenario 1 (safety time) 2 (6928 SU) 2 (1304 SU) 2 (1768 SU) 2 (44 SU) Scenario 2 (fixed stock) 1 (3640 SU) 1 (985 SU) 1 (705 SU) 1 (41 SU) Table 2: Ranking of scenarios on the average inventory level per s.k.u. class

High COVFE (group A) Low COVFE (group B)

High average demand (Group 1) Class I Class II Low average demand (Group 2) Class III Class IV Table 3: Recap of s.k.u. classification

selecting the right inventory target strategy for

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