International Journal of Industrial Engineering, 21(1), 99-111, 2014
PARTICLE SWARM OPTIMIZATION BASED INVENTORY POLICY FOR
WHOLESALE BUSINESS IN DEVS BASED MEDICINE SUPPLY CHAIN
Inventory policy of medicine wholesaler is very important issue because a medicine supply chain is directly related to human's
lives. FOQ (Fixed Order Quantity), POQ (Periodic Order Quantity, (s,S) and (R,S) of inventory policies is widely used to
manage the medicine stock in the present trend. However, effective management of medicine inventory is a difficult problem
due to characteristics of the medicine. We proposed PSO-(s) (Particle Swarm Optimization) based inventory policy for
wholesale dealers in medicine supply chain. We build a DEVS (Discrete event system specification)-based modeling to
implement a virtual medicine supply chain. We also simulate the designed model to measure a performance of management
policies. The proposed PSO-(s) determines optimal volume of products at the specific order time by using current stocks.
Simulation results demonstrate that PSO-(s) is an efficient method for wholesaler's inventory management and medicine
supply chain.
Keywords: Medicine supply chain; wholesaler manage; Inventory policy; DEVS; PSO-(s);
1. INTRODUCTION
Inventory policy of supply chain was focused on a reduction of product costs. However, trends in market demanding are
changing rapidly under the influence of customer's various requirements (Cakravastia et al., 2002). High quantities of the
stock increase a distribution level and inventory cost, and vice versa. Thus, efficient operation of supply chain can be
achieved by maintaining the optimal point of the distribution level and inventory cost (Thomas and Griffin, 1996). In this
regard, several studies are based on the client service level. They proposed the integrated model and optimized structure for
supply chain (Korpela et al., 2001).
A medicine supply chain is directly linked to the human life. Hospitals, pharmacy and every distributor must maintain
an adequate stock of medicines (Fahy et al., 2006). However, the medicine is difficult to manage the product inventory due
to its characteristics such as prices, qualities and expiring dates. A typical policy is requesting a product to the adjacent
hospitals or pharmacy according to the required stock (Lee et al., 2008).
Inventory policy is one of the critical issues in the medicine supply chain. However, studies of that leave much to be
desired. Medicine wholesalers are trying to order quantity and cost savings with managing the supply chain. However, there
is a sharp fluctuation in medicine orders because the wholesaler deals with several hospitals and drugstores. Furthermore,
there are many kinds of medicines that have a direct influence on the patient's life. The exact supply is required for this reason
(Byron, 2002).
Inventory policy in the medicine supply chain is very important, but research so far lacks. In general, medicine
wholesaler by managing inventory in the supply chain, to satisfy the delivery of cost savings and at the same time. However,
medicine wholesalers are greater fluctuation of the order. Because at the same time receives for orders from hospitals and
pharmacy requests. For this reason, wholesaler is difficult to inventory management according to the order. Thus also requires
precise demand and supply of characteristic of medicine. Therefore, inventory control of medicine wholesale need to select
the inventory policy using modeling and simulations (Lee et al., 2015). And it is necessary to establish the most appropriate
inventory policy on medicine supply chain (Kelle et al., 2012). There are several methods for inventory management such as
FOQ (Fixed Order Quantity), Economic Order Quantity, POQ (Periodic Order Quantity), (s, S), (R, S) and so on. All methods
for inventory policy are not suitable for the medicine supply chain. In order to establish the most appropriate policy, it is
necessary to assess the inventory management method conforming to characteristics of medicines.
An inventory policy is a trade-off between demands and orders. Because of this, an inventory policy of the medicine
supply chain requires a lot of experience in order to determine an optimal demands and orders. Moreover, a medicine
inventory is difficult to apply existing policies.
Consequently, a medicine supply chain requires an optimal inventory policy to reduce a difference between demands
and orders. PSO is an optimal method that can apply to handle a non-linear data and support a global optimization. A medicine
inventory increases a wholesaler's net profit by using PSO that can solve a trade-off in the inventory policy (Taleizadeh et
al., 2010) (Park and Kyung, 2014).
In this paper, we proposed PSO-(s) (Particle Swarm Optimization) based inventory policy in medicine supply chain by
using DEVS (Discrete event system specification) (Zeigler et al., 1997) simulation environment. PSO-(s) derives optimal
orders at specific order time "s" by using PSO. We design a virtual medicine supply chain and wholesaler model to compare
ISSN 1943-670X
INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING
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proposed inventory policy to others inventory policies in DEVS based discrete simulation environment. The DEVS based
simulation is based on the actual medicine supply chain, and includes a price, demand and lead time of each medicine.
Through this study, we derive the most effective method for inventory policy in medicine supply chain.
2. RELATED WORKS
2.1 MEDICINE SUPPLY CHAIN
A medicine distribution is almost similar to other logistics. Medicines are exported to wholesalers through the production and
packaging process in a pharmaceutical company (Lee et al., 2008). A shipping method is determined by characteristics of
each medicine. Figure 1 shows a process of medicine supply chain.
Medicines are divided in to prescription type and generic type. A customer can purchase medicines from hospitals and
drugstores. However, a prescription medicine requires an issued prescription like its name. The wholesaler delivers the
medicine to the hospital or pharmacy in accordance with the distribution policy. The subsequent process is separated
according to medicine types. Especially, the distributor must report the supply, purchase and usage history of the prescription
medicine to the government. The hospital administrates the prescription medicine such as injections or mixtures to the patient.
The drugstore sells prescription or generic medicines according to prescriptions. Through this process, medicines are
delivered to the end customer.
Figure 1. Medicine supply chain
2.2 DEVS (Discrete event system specification)
DEVS formalism, specifies discrete event systems in a hierarchical and modular form. The DEVS formalism provides the
framework for information modeling, which has several advantages such as completeness, verifiability, extensibility and
maintainability for analyzing and design complex systems (Zeigler et al., 1997).
DEVS formalism, one can specify a discrete event system more easily by decomposing a large system into smaller
component models. DEVS formalism consists of two kinds of models: the atomic model and the coupled model. An atomic
model is basic model that has specifications for the model. The atomic models M is shown in figure 2 and as follows:
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Figure 2. DEVS Atomic model
M = <X, S, Y, δint, δext, λ, ta>
X is the set of input values,
S is a set of state,
Y is the set of output values
δint : S→S is internal transition function
δext : Q × X → S is an external transition function, where Q = {(s,e)|s ∈S, 0 ≤ e ≤ ta(s) } is the total state set, e is the
time elapsed since last transition
λ : S→Y is the output function
ta :S→Real, a time advance function
A coupled model provides the method of assembly of several atomic and/or coupled models to build complex systems
hierarchy. A coupled model is defined as follows:
DN = < X, Y, M, EIC, EOC, IC, SELECT >
X is a set of input events,
Y is a set of output events,
M is a set of all component models,
EIC ⊆DN.X × jM.X is the external input coupling,
EOC ⊆jM.Y × DN.Y is the external output coupling,
IC ⊆jM.Y × jM.X is the internal coupling,
SELECT: 2M – ϕ → M is the tie-breaking selector.
An overall system consists of a set of component models, either atomic or coupled, thus being in a hierarchical structure.
Each DEVS model, either atomic or coupled, has correspondence to an object in the real-world system to be modeled. Within
the DEVS framework, model design may be performed in a top-down fashion and model implementation in a bottom-up
manner.
The DEVE simulation is based on the action of the atomic models, atomic model for simulation are consist of 4 function
(initial function, external function, output function and internal function), and the simulation step as follows:
1) Initial function: The initial state of the atomic model before running the simulation
2) External function; External function is the operation for receiving the input X. And change the state and time of the
atomic model.
3) Output function: Output Y send to next atomic model.
4) Internal function: Internal function operation after output function.
2.3 Inventory policy
Inventory policy is to prepare for uncertainty in all stages of the supply chain from production to sale. For this purpose,
the method strategically manages remained raw materials and commodities. The ideal amount of inventory is to make close
to 0. However, the wholesaler prepares some reserved stock due to the uncertainty. A shortage problem may occur when the
stock is set to minimum point, and vice versa.
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Inventory policy can be classified into Fixed Order Quantity (FOQ), Economic Order Quantity, Periodic Order Quantity
(POQ), (s,S) and (R,S) according to the strategy for maintaining the optimum stockage level.
FOQ is also referred to Q system. The agent automatically orders specified amounts of products when the inventory is
less than a threshold. FOQ is easy to manage, and suitable for product that is impossible to manage and predict the demand.
However, FOQ may cause an over stock problem due to the increased inventory.
POQ is also referred to P system. The agent orders the shortfall by checking the stock at regular intervals. However,
POQ should secure more safely stock than other methods because it does not consider the stock volatility until the next
inventory.
(s,S) is a combination method of FOQ and POQ. The manager orders amounts "S" when the inventory is less than
threshold "s". S is obtained by subtracting the current inventory from the appropriate quantity.
(R,S) is a periodic policy. The manager checks the stock level at regular ordering period R, and supplements the
predetermined amounts "S". This policy is helpful when the demand is stationary. Otherwise, it is difficult to determine the
amount of orders (Strijbosch, et al., 2006).
2.4 Particle Swarm Optimization
An inventory policy uses PSO (Particle Swarm Optimization) to optimize an inventory cost for global optimization. PSO is
an algorithm that imitate every particle's behavior in the swarm. PSO is faster than the existing genetic algorithm and also
advantageous requiring a long time to calculate the objective method. Besides PSO can approach to the global optimization
because it can optimize a non-linear data. A position of each particle is affected to the optimal position of PSO. PSO
calculates a speed vik+1 of i-th particle in the swarm for k+1-th step. A particle's position xik+1 is determined by the location
in k-th step and the speed in k+1-th step as defined in equation 1. PSO performs an optimization of the prediction model by
searching a particle's optimal point. The optimal point can find from input parameters that is a particle's position in each
step.
(1)
PSO operates particles with a little different in improvements as a swarm. Each particle is improved by a speed and
random value of pbest and gbest. In this paper we propose PSO-(s) to solve trade-off between demands and orders of the
inventory policy model.
3. MODEL DESIGN
3.1 Medicine Supply Chain
We design a modeling for inventory management and overall configuration of medicine supply chain based on analyzing
results of the process. In order to apply the inventory management methods, we must analyze objects and its properties on
the supply chain. Data components for inventory data analysis are consist of maximum and minimum stock, order cycle and
shipping time. And we define sales price, sales amount, deliver fee, order count, average stock count, stock price and net
profit by using data components (Ye et al., 2012). A design of medicine is need to model and simulate the inventory
management. Figure 2 presents our design of medicine supply chain model.
The medicine supply chains include a pharmaceutical company, wholesaler, hospital and pharmacy.
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A pharmaceutical company develops and manufactures new medicine by using raw materials. Produced medicines are
stored in the packaging and labeling conditions according to those types and sizes. The company manages ships requested
amounts of medicines to each wholesaler.
A wholesaler imports medicines from the pharmaceutical company. Imported medicines are stored in its container in
accordance with the type and characteristic. The wholesaler requests the shortfall medicines to the pharmaceutical company.
In order to order proper amounts of medicines, the wholesaler requires the inventory management that considers maintenance
and administrative costs. Due to characteristics of medicine supply chain, both hospital and drugstore are located in the lower
level. The wholesaler receives a request of medicine supply from hospitals and drugstores, and exports the requested amount.
Therefore, it is difficult to predict a demand. A hospital receives medicines from the wholesaler. Medicines can be used
directly through a prescription from the hospital. An unused inventory can be released into a nearby drugstore. This shipment
is caused when the pharmacy requests medicines. A pharmacy is the last step of the supply chain, and directly provides
medicines to customers. Generic medicines can be sold directly to customers. In contrast, specific medicines require a
prescription. Medicines can be supplied from the wholesaler or hospital. An urgent demand is procured via the hospital. A
bulk purchase is a share of the wholesaler.
Figure 2. Medicine Supply Chain Model
3.2 Medicine Model
The supply chain is composed of four steps, including the pharmaceutical company, wholesaler, hospital and drugstore.
Medicines are classified into six types designated as A to J. Prices and demands for product for specific products were refer
to the production results and ranking statistics (KPMA, 2013). There are differences in a lead time, price and demand for
each product. A product margin is 40% of sales. We assume that inventory and shipping cost is same regardless of the product
type. Parameters for medicine model are shown in Table 1.
A lead time is set to one day that reflects a distribution system in South Korea. Inventory and shipping cost is set to 3%
of sales. This setting reflects the data released by the Korea International Trade Association in 2011 (KITA, 2012). Shipping
cost was 8.03%, and storage cost was 28.8% of revenue. We consider the opportunity cost of shortage as triple of the net
profit. This assumption reflects the loss of customer’s trust in the opportunity cost.
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Medicine Name
Price
A
B
C
D
E
F
4,717
2,039
1,732
936
877
3,805
Table 1. Characteristic by Medicine
Demand
Lead Time
Stock /
Delivery
Cost
33.4
1 Day
Price * 3%
14.5
12.3
6.6
6.2
27.0
Damage Cost
Price * 3
3.3 Inventory Policy
In this study, we measure shortage quantity and frequency for product, individual and total inventories in supply chain, net
profits and inventory cost. Costs due to the shortage are only added up in retail stores. In contrast, both shipping and
inventory cost are occurring at all steps. We select FOQ, POW, (s,S) , (R,S) and PSO-(s) to the inventory managing of the
wholesaler.
The proposed PSO-(s) calculates optimal orders at the specific order time (s). PSO-(s) uses current, minimum and
maximum stocks to calculate orders for each medicine. A detailed algorithm is as shown in Figure 3.
Figure 3. PSO Algorithm
PSO-(s) calculates optimal orders for every medicines A to F at the order time (s). We set both local mass and global
math as 0.7 which is most widely used value to find an optimal point. The number of iterations is set to 100. Optimal orders
is calculated after 100th iteration is finished. All calculations are based on the fitness function shown in equation 2.
Fitness Funtion = (Minimum required capacity) < (𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 +
(𝑀𝑎𝑥 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 ∗ 𝑂𝑟𝑑𝑒𝑟 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦(%)))
(2)
This fitness function calculates a current quantity and order quantity. The order quantity must be higher than minimum
required capacity at this calculation. PSO increases a net-profit with maintaining a minimum capacity by using the fitness
function.
Table 2 shows specific configuration of each methods. An order interval is set to four days, and an order time is set to
60% of the maximum stock. Results are calculated separately for each medicine.
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Method
FOQ
POQ
(s,S)
(R,S)
PSO-(s)
Table 2. Detail Method
Note
Order Quantity = Max inventory capacity * 20%
Order time = Max inventory capacity * 60%
Order Quantity = Max inventory capacity – Current inventory
Order time = 4 Day
Order Quantity = Max inventory capacity – Current inventory
Order time = Max inventory capacity * 60%
Order Quantity = Max inventory capacity * 20%
Order time = 4 Day
Order Quantity = PSO result
Order time = Max inventory capacity * 60%
4. DEVS BASED MODEL IMPLEMENTATION
An inventory management problem in supply chain is 0-1 integer programming which is one of the NP-hard problem. A
mixed integer programming can calculate with the practical time by using optimization because that problem uses a relatively
small integer variable. However, our study cannot apply that solution because the calculation time and required memory are
exponentially increased according to the problem's scale. Therefore, this paper analyze the sub-optimal solution with the
proposed PSO-(s) and four inventory policies (FOQ, POS, (S s) and (R, s)) by using DEVS-based modeling and simulation.
4.1 DEVS Model
We build a DEVS-based model to experiment and evaluate the inventory management model. Figure 4 shows a DEVS-based
model for medicine supply chain.
Figure 4. DEVS based Medicine Supply Chain Simulation Model
Each model has its own input and output port that is composed of medicine shipment and medicine order. A designed
model can include several hospital and pharmacy according to the simulation. The pharmaceutical company releases
medicines when the wholesaler sends an order. The wholesaler releases medicines with orders from hospital and pharmacy.
Both hospital and pharmacy prescribe and sell medicines to the customer.
This paper intensively design the model for wholesaler because we have focused on the inventory management of that.
Figure 5 shows a detailed structure of the wholesale model.
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Figure 5. Wholesale Atomic Model
Request manager is the model to receive the order from hospital and pharmacy. Coordinator assigns a task to each site
for providing medicines. Site keeps a medicine with categorized by characteristics and types of medicines. A medicine is
differently stored in Site. Packing is the packaging stage for ordered medicines as its name. Delivery manager sends medicines
to the hospital and pharmacy. Stock is the putting stage for received medicines from pharmaceutical company. A received
medicine stores to each stock according to the characteristics and types. Wholesale order manager sends orders to supplement
the shortfall.
Detailed atomic models of wholesales is as following figure 6.
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Figure 6. Detail Atomic Models in Wholesale Model
Figure 7 shows detailed logics of wholesale order manager model. This model handles a policy for inventory
management with calculating warehouse max capacity (wmax), warehouse minimum capacity (wmin), current quantity and
order quantity at the order time. Inventory Policy function includes FOQ, POQ, (s,S), (R,S) and the proposed optimized S,S.
After the calculation, Order function requests medicines to corresponding pharmaceutical company. We simulate and analyze
the performance and efficiency of the inventory policy model by using a DEVS-based supply chain model.
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Figure 7. Detail of Order Manager Atomic Model
5. SIMULATION
5.1 Scenario
A simulation is to compare and verify the inventory managing of the wholesaler in medicine supply chain. As shown in
figure, a virtual system includes 6 pharmaceutical companies, a wholesale, 5 hospitals and 15 drugstores. Table 4 shows 6
medicine parameters for simulation.
Medicine
A
B
C
D
E
F
Max inventory
capacity
5,000
4,800
4,600
4,400
4,600
4,800
Table 3. Medicine Parameter
Minimum required Inventory
Initial Inventory
capacity
3,000
3,150
2,880
3,500
2,760
3,500
2,640
3,150
2,760
3,360
2,880
3,200
Price
Demand
4,717
2,039
1,732
936
877
3,805
33.4%
14.5%
12.3%
6.6%
6.2%
27.0%
Supply chain simulation was run for 300 virtual days by using each managing method. We have obtained results by
calculating the sum value from total 1,000 runs of simulation. In order to assess each inventory management method, we
have compared sales price, sales account, order count, delivery cost, stock price and net profit. Equation 3 describes
calculations of delivery cost, stock price and net profit.
6
Delivery cost = ∑ sales account 𝑛 ∗ medicine price𝑛 ∗ 0.03
𝑛=1
6
(3)
Stock Price = ∑ 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦𝑛 ∗ 0.288
𝑛=1
net prifit = (Sales Price ∗ 0.4) − 𝐷𝑒𝑙𝑒𝑣𝑒𝑟𝑦 𝑐𝑜𝑠𝑡 − 𝑆𝑡𝑜𝑐𝑘 𝑃𝑟𝑖𝑐𝑒
5.2 Simulation result
Simulation results are shown in table 4.
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Table 4. Simulation result
Sale Price
Sales account
Order count
Delivery cost
Stock Price
Net profit
FOQ
328,279,413
102,218
105,480
9,848,382
5,660,334
115,803,048
POQ
329,322,720
101,405
112,685
9,879,682
8,035,473
113,813,933
(s,S)
325,263,033
101,278
106,181
9,757,891
6,508,974
113,838,348
(R,S)
327,258,522
101,896
113,176
9,817,756
8,035,446
113,050,207
PSO-(s)
326,761,324
101,275
101,362
9,802,840
4,857,568
116,044,121
Total Average
327,377,002
101,614
107,777
9,821,310
6,619,559
114,509,932
A total error of the sales price is 0.05%. FOQ records 0.01003%, POQ records 0.01006%, (s,S) records 0.00994%, (R.S)
records 0.01% and PSO-(s) records 0.00998%. As above, simulation of this study is reliable because there is no significant
difference in the error.
POQ records the highest number of sales (329,322,720). However, this result is not important because it is sale price
for the order. The high-net profit methods are FOQ (115,803,048) and PSO-(s) (116,044,121). Both model shows high net
profit that low sales price. Especially, PSO-(s) records highest net profit than lowest sales price. From this result, PSO-(s) is
suitable for medicine distribution.
Stock price is an indicator of the proper amount of inventory stocks. Figure 4 shows 1,000runs of stock price. The lowcost methods are FOQ (5,660,334) and PSO-(s) (4,857,568) PSO-(s) (4,857). These methods order medicines when the
inventory is less than the specific level. This approach is more useful than a regular order. In particular, PSO-(s) has the
lowest inventory cost.
Next is comparing the order count and sales account as shown in figure 8.
Figure 8. Compare Order count to Sales account
This simulation is to identify the optimal policy with minimizing a difference between the order count and sales account.
Both (R,S) and POQ are not suitable because those models shows highest difference (11,280) between the order count and
sales account. FOQ records 3,262 and (s,S) records 4,903 which is relatively small difference. However, the proposed PSO(s) shows smallest difference (82). We can find that the proposed model is an optimal inventory policy for medicine supply
chain with highest net profit.
By results of the simulation, PSO-(s) is the most effective method for inventory management in medicine supply chain.
PSO-(s) orders predefined amounts according to the inventory. PSO-(s) generally has a problem of excess inventory. However,
there are severe fluctuations in medicine orders. In addition, the medicine distribution should manage multiple items. PSO(s) can be a proper method for these features.
A proposed PSO-(s) provides higher net profit that other models because the model can find optimal orders at the order
time. PSO-(s) finds an optimal cost and current orders by using PSO to represent the profit between orders and consumption.
More simulation will be increase an efficiency of PSO-(s). Because of these characteristics, the proposed model is also
suitable for inventory policy for other domains.
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6. CONCLUSION
An objective of this paper is to analyze the effective inventory control method of the wholesaler in medicine supply chain.
We analyze the medicine supply chain, and perform modeling and simulation.
An inventory policy is a key factor to determine order time and quantity. It is also an important policy to handle an
optimal profit in the supply chain. Therefore, the policy should minimize a trade-off between consumption and orders to
increase the profit. This paper proposes the inventory policy by using PSO. The proposed PSO-(s) calculates optimal orders
from current stocks at the designated regular order times. We compare the FOQ, POQ, (s,S), (R,S) and PSO-(s) for inventory
management method. Simulation results show the effectiveness of remaining stock-based order and specified amounts of
order. PSO-(s) satisfies both conditions, and is a useful method to manage the wholesaler's inventory policy in medicine
supply chain.
Limitations of this study are as follows. It is difficult to consider the number of hospitals and drugstores. Moreover, we
did not reflect the characteristics of the demand.
ACKNOWLEDGE
This work was supported by INHA University Research Grant.
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