CC BY
34Russian Journal of Logistics and Transport Management, Vol.3, No.2, 2016
1 1 © Valery S. Lukinskiy , Yulia Panova and Rustam Soletskiy
1National Research University Higher School of Economics 2,3Emperor Alexander I St. Petersburg State Transport University
SIMULATION MODELLING OF SUPPLY CHAIN WITH ALLOWANCE OF RELIABILITY
Abstract
This study considers terms of supply chain and its reliability, inventory management strategies, as well as examines the 'bullwhip effect'. The analysis is based on the publications, which address the issue of the reliability of supply chains in connection with the inventory management principles. The conclusions have been drawn from the computer experiments with models developed in simulation environments.
Keywords: supply chain, reliability, computer simulation, inventory management, 'bullwhip effect'.
1. Introduction
A well-established supply chain is a key to success for any company. However, due to the difficulties related to the planning of the supply chain, adverse effects can be generated. One of them is the so-called 'bullwhip effect'. The causes of this phenomenon are rooted in the traditional approach to managing the supply chain. In contrast to integrated management of supply chain elements, manufacturers and suppliers are considered individually and interact insufficiently with each other. It leads to the fact that they function as independent units, having their plan of purchasing, sales, customer relationships, logistics flows, inventory management strategy, separate criteria for performance evaluation, as well as guided by their goals and objectives (Zakharov and Tretyakov, 2013; Meschankina, 2005).
The 'bullwhip effect' is manifested as a result of small changes in demand for the end-user that lead to much more significant deviations of demand at all stages of the supply chain. These variations increase in the manufacturer inventory. That is why the American scientist J. Forrester, who for the first time mentioned about this effect, compared it with a whip, whose small force oscillation at one end makes a move with the highest speed and the amplitude of the opposite one (Forrester, 1961).
In the context of globalisation and the introduction of different logistics concepts by enterprises, vulnerability of the supply chain to any deviation from the contract of delivery increases. An insufficient attention to the problem of improving the reliability and sustainability of supply chains can have not only a
negative impact on operating results, but also lead to short-term financial losses, as well as to the deterioration of the general perception of the supply chain on market, which ultimately leads to a decrease in the company's capitalisation.
In this regard, this study unfolds from the traditional approach of describing the individual participants of the supply chain and their inventory management strategies. Further on, an integrated approach is employed to describe the supply chain, consisting of the customer, multiple retailers, and manufacture. Their inventory control strategies are evaluated under the interaction with changing external parameters. The consequences of an unbalanced organisation of cooperation in the supply chain are depicted in the form of bullwhip effect, which is described in connection with the terminology of the reliability of supply chain and inventory management strategies. For these purposes, the dependencies between different operational and financial parameters are reflected in the mathematical formulas and presented graphically through the modified DuPont model and output of the designed computer simulation experiments.
2. Traditional and integrated approaches to the design of supply chains
In the description of the supply chain based on the traditional approach, each participant of the supply chain is considered as a separate system (Lukinskiy et al., 2012, Lukinskiy et al., 2016). At the beginning of this study, the work of the individual participants of the supply chain was regarded from this point of view (i.e., each participant has its own inventory management strategies). The development of inventory management strategies foresees continuous supply of consumer by the material resources, raw materials or finished products through the implementation of an inventory control systems to maintain the stock size in the required limits. Experts identify three following groups of inventory management strategies (Lukinskiy et al., 2016): a) Periodic strategies; b) Strategies with the order point; c) Combined strategies (Fig.1).
a)
Strategy with established intervals for The strategy with a fixed periodicity of replenishment of inventory up to a
the order (t,q) maximum desired level (t,S)
q— Order quantity t — Time between orders
S— Target inventory It — Lead time
I — Inventory level
b)
The strategy with the fixed size Inventory of the order (s,q)
'Minimum-maximum' strategy of (s,S) Inventory
Order level Sm
l5 Order point s
Fl , .
t1 It t2 It t3 It
Inventory J shortage
Time
l4 Order point s
Time
t1 It t2 It t
Inventory shortage
c)
Inventory
Order level Sm
Order point s
t3 It
j,-►
^j! t Inventory It t4 J shortage
Time
Inventory
Order level Sm
Order point s
♦O—, <><>
t1 It t2 It It t3
>o < >oT~ ** Time
t4 It > Inventory ......
4 shortage
Inventory
Order level Sm
10 Order point s
Time
, o> < , <> > o—-» ,
t2 It t3 It It t4 It f Inventory shortage
; / Inventory J shortage
(t, s_S: t+ROP) - Strategy
(t, s_S: t&ROP)-Strategy
(t, s_S: t or ROP) - Strategy
Fig.1. Inventory management strategies.
All strategies of inventory management systematised on the ground of several criteria (Figure 2).
2
Order quanity
Variable Fixed
+ - r Oí™ »
TJ Wm
» to
t »
t »
» »
O
Terms of order point and order interval
Fig.2. Systematization of inventory management strategies.
To describe the operation of the supply chain from the point of view of an integrated approach, it is important to consider the inventory management strategies for different participants in their interaction. For this purpose, it is necessary to describe the work of the supply chain, in which individual units are represented by clients, retailers and manufacturer. By doing so, the designed supply chain will be in compliance with existing the definitions of this term. According to Sergeev et al. (2013), the supply chain is three or more economical units (organisations or individuals) directly involved in the external and internal flows of products, services and/or information from the source or origin to the to the end user.
According to Malikov (2014), the supply chain is a chain or network (depending on the complexity) of independent organisations related to the overall objective of profit maximisation. It is achieved through the most effective co-operation, joint coordination and management processes related to ensuring all the necessary resources, manufacturing and sales of finished products in agreement with the principles of the general theory of systems and business logistics.
One of the basic criteria for assessing the quality and performance of the supply chain is its reliability. Apparently, the poor quality and failure to perform the functions of at least by one of the participants leads to a reduction in the quality of the functioning of the whole supply chain that reduces its economic efficiency (Vokhmyanina, 2013).
Reliability is mentioned in many publications related to logistics and supply chain management, but only some of them define its core concepts. One of the first works in which particular attention was paid to reliability in the
functional areas of logistics, is a monograph of Inyutina (1983), where the author draws attention to the lack of a precise definition of a reliability of procurement, despite its frequent use in the economics literature of that period. In recent years there has been increased interest in the study of the reliability of the supply chain, as evidenced by the growing number of publications, in particular the works of Bochkarev, A.A., Grigoriev, M.N., Dorofeeva, E.A., Ivanov, D.A., Lukinskiy, V.S., Lukinskiy, V.V., Pletneva, N.G. Malevich, Y.V., Sergeev, V.I., Uvarov, S.A., Shurpatova, I.G., Zaitsev E.I. (Sergeev and Dorofeeva, 2010). According to the authors, reliability is one of the most significant indications of the supply chain work, which takes into account the constant changes in the external and internal environment. Therefore, the reliability of the supply chain is closely related to the phenomenon of the 'bullwhip effect'. In particular, minor changes in the external environment (in the demand of the final consumer or order fulfilment time) can lead to much more high deviations in demand at all stages of the supply chain, which creates a deficit or surplus of goods. Many resources are spent on the solution of the related problems, both temporal and financial (Glatzel et al., 2009; Brom, 2008; Dybskaya, 2012). The influence of 'bullwhip effect' is reflected in the various indicators of the functioning of the supply chain, first of all, on the inventory levels and associated costs, which in turn affect the profitability of the entire supply chain. Those dependencies have been identified by the modified DuPont Model (Figure 3).
Gross purchases
Purchases returns, Discounts, Allowances
Gross sales
Sales returns, Discounts, Allowances
Net cost of purchases ^
Gross margin (a.k.a. Gross profit)
Transportation, Insurance, Storage, Taxes
Beginning inventory
Cost of goods available for sale
Net sales
Ending ^ inventory
Cost of goods sold
Average
inventory
value
Ratio of gross margin
Gross margin return on inventory
T/E index
Turnover
+
/
Fig.3. Modified DuPont Model.
For the description of the operation of the supply chain and subsequently assessment of 'bullwhip effect', different approaches can be used, e.g. the object and process approaches. From the point of view of the objective approach of supply chain description, it is represented by the coherent structure of business units, combined with the relations between suppliers - the focal company -consumers in the process of creating and selling goods in the market conditions. In terms of the process approach, the supply chain is a sequence of flows and
processes that take place between the various contractors (links) of the chain that are combined to meet consumer demands for goods and services (Bochkarev, 2009). For the description of the issues related to the operational optimisation and reliability of supply chains, the use of decision support systems is inevitable. The reason behind is that sophisticated information flows, operated by logistics managers, are not always available for precise analysis by the application of traditional methods. Therefore, computer simulation, which is one of the most powerful tools for the design of complicated systems and analysis of the processes of their functioning, is reasonable (Toluev, 2005). The application of simulation modelling allows to experiment with the existing or proposed systems in the cases where experiments with real objects virtually impossible or impractical (Kobelev, 2003). However, in Russia, the modelling of supply chain due to many objective reasons have yet to be a mass product, developed by the experts in simulation (Toluev, 2008). At the same time, simulation of logistics networks for different purposes in industrialised countries is a regular part of projects aimed at creating new or redesign of existing logistics systems.
3. Modelling of inventory management strategies and the 'bullwhip effect' in the supply chain
To make a choice in favor of a particular inventory management strategy it is advisable to simulate the operation of each of them and make them a comparative evaluation using the following indicators: the total deficit, the average stock level, the costs associated with the implementation of this strategy (Lukinskiy et al., 2012, Lukinskiy et al., 2016; Ivanov, D., 2016).
For a description of inventory management strategies, software
3 Demand
AnyLogic was used. To visualise the EOQ-model the following parameters were set (Demand and Order Quantity), as well as variable, the Inventory Level, and event, Ordering, describing the principle of change in the inventory level (e.g., once a day).
^ Qrdermg According to the EOQ-model, change in inventories is a linear function of demand. As a result of the simulation, a clear picture of current inventory levels change process in the warehouse was obtained (Figure 4), According to the specified parameters, demand equalled 80 units, the size of the order (q) = 400 units, the duration of the simulation was set to 30 days. As shown in the graphic, at the beginning of the fourth day, the inventory level equalled to 80, on the fifth day, to avoid a deficit, an instantaneous replenishment of order quantity, 400 units, was provided (Figure 4).
f QrderQuantíty ^ InventoryLevel
B I í, el xt |qr CJ» I Of » Qg |rpot:Main
(n Demand 80
(3 Oi dei'Quantity 400
ijl InventoryLevel SO
Ordering
' n *
\
\ i
\ l\ \
j L L
0 10 20 — /JkiHaMMKa 3anacoB
Fig. 4. Dynamics of inventory levels in the (t,q)- inventory management strategy.
To set the variable values of demand and lead time, additional parameters have been used, i.e. the values of the standard deviations. Then, the classical inventory management strategy (t,q) was transformed into a strategy with an order point. Therefore, instead of the code InventoryLevel + = OrderQuantity; in the cyclic event, the new law code describing the random variable distribution was written. Additionally, the code, which determines the replenishment principle by order point, was set.
Thus, the adjusted model reflected the inventory management strategy (s, q), where the time between the change of inventory levels is 5 days, the order point equal to 240 units, and lead time (without deviation) is 3 days (Figure 5). The model also was added by the several parameters and variables, which helped to analyse the inventory management system: Holding Cost (0.1 USD per day for per unit); Ordering Cost (10 USD for 1 order); Stockout Costs (0.5 USD per unit). The effect from the applied inventory management the strategy was estimated by use of additional parameters - Service Level, Total Sales, and Retail Shortage. The accounting of cost was carried out by a new cyclic event, Costs Update. If costs associated with the storage reserves, was calculated according to the average level of inventory(Inventory Level/2) through the cyclic event, Costs Update, the costs associated with a deficit was calculated through the second event, StockOut, the results of which were updated at the end of the calculation period, i.e. on day the 29 th day. To reflect the level of service and the level of the deficit additional time plots were used (Figure 5).
Fig. 5. The output of model describing the (s, q) - inventory management strategy.
In accordance with the output of the model, the total costs amounted to 584 USD, while the service level by the end of the model time equalled to 59.4% with the level of the deficit of 838 units. In order to improve the output of model, the safety stock was calculated and introduced as the parameter of the model, which was calculated by the formula:
SS = x xac , (1)
where SS is a safety stock, x is a number of standard deviations (i.e., the normal distribution parameter, which corresponds to the probability of the absence stockouts), ° is the value of the standard deviation of demand during lead time.
Based on the table with cumulative normal distribution (when x> 0) for a given x, the value of service level can be determined. According to this table, the service level of 95% corresponds to x = 1.65, while for the value of 99%, x = 2.33.
The accounting for the safety stock results in adjustments to the formula for calculating order point (ROP):
ROP = d x L + SS , (2)
where d is the average demand, which determines the decrease of the inventory level, L is a lead time.
Thus, for the calculation of ROP, three options can be used.
1) When demand is variable and lead time is constant:
JL.
ROP = d x L + x xac x-
(3)
2) When daily demand is constant, while lead time is variable:
ROP = d x L + x xac
xa
3)
Both demand and lead time are the variables:
K^l
ROP = d x L + xy
LxaC+d2xa2
(5)
For further analysis, the first option was applied (ROP = 80 + 3 * 1.65 *18*V3 = = 240 + 52 = 292 units, where 52 units is the amount of safety stock). The amount of EOQ was found by the by Wilson formula:
Q =
i
2x2400x10
3
= 127x 3 = 381 units.
By setting in the model, which describes (s, q) - inventory management strategy, the value of the EOQ (381 units) and ROP (292 units.), its output improved. The overall costs reduced to 431 USD compared to the first experiment (584 USD). The level of service has also increased from 59.4% to 95% at the end of the month; the goods deficit decreased from 838 units up to 103 units. To avoid cases of the deficit, in the EOQ model, the deviation of the demand (80+18=98) can be taken into account:
Q =
¡
2 x2940x 10
3
= 140x3 = 420 units.
By setting this value in the model, the deficit will be zero, and the costs reduce to 420 USD. To compare within one model, four different inventory management strategies (two of them are periodic, and two are with the order point), additional parameters have been set, as well as several experiment windows was developed (Figure 6 a, b).
a)
e
b)
s_q
2,000 -i-
-------___________________________
о -!-
■ Стоимость хранения: 1,023 (98.1%)
■ Стоимость выполнения заказа: 20 (1.9%)
■ Затраты, связанные с дефицитом: 0 (0.0%)
Fig.6. Experiment windows of four inventory management strategies.
The output of the model showed that minimal expenses (897 USD) correspond to (s, S) - inventory management strategy, with the service level of 98%. The highest costs are related to (t, q) - strategy with a fixed order intervals, where the service level equals to 100%. To test strategies sensitivity to environment changes, it was assumed that the average demand for products increased from 80 units to 130 on the 10th day from the beginning of the model operation. Based on the simulation experiments, it was found that a quick response to changes in demand was attained by the (s, q) and (s, S) - strategies (Table 1).
Table 1
Comparative analysis of the output of inventory management strategies.
Inventory Costs Service level
management Without changes in After changes in Without changes in After changes in
strategy demand demand demand demand
s,q 1089 978 100 98
s,S 897 977 98 98
t,q 4269 3774 100 100
t,S 1181 1063 100 98
To analyse the models describing the combined strategies, the data used in the previous experiments have been applied (e.g. the demand is variable, 80 units/day with the standard deviation of 40 units/day, and lead time is constant, 3 days). From the experiments with models, it was found that the more effective among three combined strategies is t, s_S (t + ROP) - strategy. The comparative analysis of all strategies also showed that the most efficient is the (s, S)-strategy (costs are 897 USD with the service level of 98%).
In order to assess the 'bullwhip effect', an additional action chat was introduced. It helped to characterizes the supplier/manufacturer inventory management strategy depending on the retailers inventory policies and demand of clients (in the example, the number of retailers was set to five, each of which has its unique inventory management strategy, i.e. two are periodic, two are with order point, and one is combined). By the variation of the demand of the final clients from 80 to 130 units during the experiments with the model, the 'bullwhip effect' was identified (Figure 7).
Fig. 7. Dynamics of inventory levels of the main supplier in normal conditions and the
case of demand increase.
The analysis of the dynamics of inventories levels of the supplier and retailers showed that the growth in demand from the end-user leads to a greater deviation of changes in inventories amplitude of the manufacturer than in the case of retailers. In particular, the deviation is 13 times greater than the deviation of the mean amplitude of the inventory levels changes among all retailers.
4. Conclusions
In summary, it should be noted that despite the development of logistics and supply chain management, theoretical and practical problems of reliability of supply chains are still unresolved. These issues include the problem of the development of the classification of methods and models for assessing and ensuring the reliability of transactions in the supply chain, as well as the issue of development planning models of individual business processes in supply chains. This study applied computer modelling that allowed to describe and analyses inventory management strategies and simulate 'bullwhip effect'. Different inventory management strategies have been classified, depending on the conditions of placing an order, and principles of inventory control. The associated costs and service levels have been assessed in different inventory strategies. Dependencies between individual parameters of the model were taken into account and reflected in the models describing inventory management strategies. It was found that changes in the conditions of external parameters can lead to the financial losses and decrease of the effectiveness of the strategy as a whole, negatively influencing the capital of the company. Those connections have been identified by the created modified DuPont model, which was comprised of several analytical formulas related to inventory management strategies.
On the whole, the application of mathematical models and computer simulation allows amplifying the evidence of cause-effect relations. With the created computer models, the analysis of the inventory strategies performance under various external parameters has been provided. Moreover, with the help of computer models, the 'bullwhip effect' was simulated. Thus, computer simulation can be considered a convenient environment for studying practical
problems: the performance indicators, comparison of variants of design and algorithms of systems, as well as control of the stability conditions of the system under the variation of input variables.
References
Bochkarev, A.A. (2009). Theory and Methodology of Process Modeling Approach and
Integrated Planning of the Supply Chain. Synopsis of thesis, St. Petersburg, 39. Brom, A.E. (2008). Logistics of synchronized flows in the supply chain. Applied Logistics, 9, 5-7.
Dybskaya, V.V. (2012). Problems of inter-organizational coordination in the supply chain and
'bullwhip effect'. Logistics, 2, 24. Forrester, J.W. (1961). Industrial dynamics. Cambridge Mass: MITPress, 1(961), 1-464. Glatzel, C., Helmcke, S., & Wine, J. (2009). Building a flexible supply chain for uncertain times. Available at URL:
http://www.mckinsey.com/insights/operations/building a flexible supply chain for uncertain times Retrieved: 21.07.2016. Inyutina, K.V. (1983). Improving the Reliability and Quality of Requirenments Planning.
Publishing House of Leningrad. Leningrad, 240. Ivanov, D. (2016). Operations and Supply Chain Simulation with AnyLogic 7.2, Berlin School
of Economics and Law, 97. Kobelev, N.B. (2003). Basics of Simulation of Complicated Economic Systems, Delo Publishing, Moscow.
Lukinskiy, V.S., Lukinskiy, V.V., & Pletneva, N.G. (2016). Logistics and Supply Chain
Management. Yurayt Publishing, Moscow, 359. Lukinsky, V. S., Lukinskiy, V.V., Malevich, J.V., Plastunyak, I.A., & Pletneva, N.G. (2012). Models and Methods of the Theory of Logistics, Publishing of St. Petersburg State University of Engineering and Economics, St. Petersburg, 403. Malikov, O.B. (2014). Supply Chain Management. Lectures. Publishing of Emperor
Alexander I St. Petersburg State Transport University, St. Petersburg, 86. Meschankina, T. (2005). The 'bullwhip effect' or imaginary fluctuations in demand.
Available at URL: http://www.loglink.ru/massmedia/analytics/record/?id=78 Retrieved: 21.07.2016. Sergeev ,V.I., & Dorofeeva, E.A. (2010). Terminological aspects of the concept of
"sustainability" in the supply chain logistics integration focus. Logistics and Supply Chain Management, 3, 38. Sergeev, V.V., Dybskaya, V.V., Zaitsev, E.I., & Sterlingova, A.N. (2013). Logistics. Eksmo, Moscow, 944.
Toluev, Y.I. (2005). Application of simulation for the study of logistics processes. Simulation. Theory and Practice: Proceedings of the second Russian scientific and practical conference, St. Petersburg, 71. Toluev, Y.I. (2008). Simulation of logistics networks. Logistics and Supply Chain Management, 2, 25.
Vokhmyanina, A.V. (2013). Methodological aspects of reliability of logistics supply chain.
Transport of the Russian Federation, 5, 48. Zakharov, M.N., & Tretyakov, V.A. (2013). Criteria of efficiency of production processes of the industrial enterprise. Journal of Engineering. 10, 78-80.
