- Email: [email protected]
An agent-based model of supply chains with dynamic structures
Applied Mathematical Modelling 37 (2013) 5403–5413
Contents lists available at SciVerse ScienceDirect
Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm
An agent-based model of supply chains with dynamic structures Jing Li a, Felix T.S. Chan b,⇑ a b
School of Engineering, Nanjing Agricultural University, Nanjing, China Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong
a r t i c l e
i n f o
Article history: Received 4 May 2012 Received in revised form 21 September 2012 Accepted 22 October 2012 Available online 8 November 2012 Keywords: Supply chain structures Agent-based model Make-to-order supply chains Make-to-stock supply chains Simulation model
a b s t r a c t This paper proposes a common agent-based model for the simulation of MTS and MTO supply chains with dynamic structures. Based on the model, scholars can model supply chains easily. Basic characters of supply chains are proposed in the model. Agents, who are used to simulate the members of supply chains, produce appropriate products by intelligent choices. The relationships among agents are connected by their products. Different agents’ attributes are presented by their knowledge and actions of agents are introduced in the paper. Experiments are produced to show the availability of the agent-based model. The model should be available as a toolkit for the studying of dynamic supply chains. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Traditionally, companies produce products and stock them as inventory until they are sold (MTS, make-to-stock). However, some products cannot be produced with make-to-stock strategy. For many companies, product’s design in different orders is not same. All companies must produce different products to satisfy different demands. These companies have designed their production systems to produce a product only after it is ordered. Thus, many companies have shifted to ‘‘pull’’, holding no inventory at all and producing to order [1]. This kind of supply chain (consists of former companies) is referred to as MTO (make-to-order) supply chain. Meanwhile, there can be various types of changes to supply chains that may require adaptations. New trading partners and new products are the main causes of structural changes. Structural changes alter the topology of supply chains. Based on the agent-based model of make-to-order supply chain [2], this paper extended the agent-based model to simulate the make-to-stock and make-to-order supply chains with dynamic structures. Based on the model, scholars can research on the management of different supply chains. Since the phenomena were modeled in our paper involved non-linear relationships, it is implausible to make simplifying assumptions until the equation do become solvable. Scholars have completed various perspectives in order to resolve problems of the non-linear system. Computer simulation can be used to model either quantitative theories or qualitative ones. It is particularly good at modeling process and although non-linear relations can generate some methodological problems, there is no difficulty in representing them with a computer program [3]. The breakthrough in computer modeling came with the development of the multi-agent system. Although the agent-based modeling has become an increasingly important tool for scholars studying supply chains, but there are no common models on describing and testing the make-to-order and make-to-stock dynamic supply chains. An agent-based model is proposed in the paper to simulate supply chains with dynamic structures.
⇑ Corresponding author. Tel.: +852 2766 6605; fax: +852 2362 5267. E-mail addresses: [email protected], [email protected] (F.T.S. Chan). 0307-904X/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.apm.2012.10.054
5404
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
The rest of the paper is organized as follows. The related literature is reviewed in Section 2 and then the basic simulation model based on the multi-agent technology is developed in Section 3. The simulation of a foreign trade supply chain is presented in Section 4 to illustrate the validity of the model. Finally, the conclusions and directions for future research are given in Section 5.
2. Review of the related research Since the complexity of supply chains, agent-base technologies were used in many significant works to study the management of supply chains. Tiwari et al. [4] proposed an agent-based model to optimize the scheduling decision in E-manufacturing. For the group decision-making problem, agent-base technology was used to optimize the selection of different technologies [5]. Zheng presented a multi-agent architecture for specifying and analyzing supply chains [6]. Rajagopalan [7] provided insights into the impact of various problem parameters on the make-to-order versus make-to-stock decisions using a computational study. Rajagopalan’s research is beneficial to the study of make-to-order supply chains. The paper’s agent-based model depends on the development of the former artificial model based on multi-agent system. Gilbert et al. [8] built a multi-agent model embodying a theory of innovation networks. A number of policy-relevant conclusions were suggested through experiments with the model’s parameters. Gilbert’s work was a key issue for the building of the multi-agent system. Bhavnani et al. [9] provided a general introduction to an agent-based computational framework for studying the relationship between natural resources, ethnicity, and civil war. The framework in Bhavnani’s work is beneficial for the building of our model. Andronache and Scheutz [10] presented the agent architecture for the design, implementation, and testing of distributed agent architectures. Lei et al. [11] discussed a distributed modeling architecture in a multi-agent-based behavioral economic landscape (MABEL) model that simulated land-use changes over time and space. Graf proposed a multiagent architecture dedicated to model computer vision systems, which provided the vision system with a great degree of flexibility [12]. These structures show significance on the development of our work. A few agent-based models were proposed with different technologies [13,14]. Janssen et al. [15] reported on the establishment of the Open Agent-Based Modelling Consortium, www.openabm.org, a community effort to foster the agent-based modelling development, communication, and dissemination for research, practice and education. Combination of logic-based artificial intelligence with virtual reality is proposed in mVlTAL [16]. These agent-based models show significance to build the model of our paper. Although agent technology has shown its advantages for various collaborative applications, the flexibility of interoperation among heterogeneous agents was restricted [17]. Mishra and Kumar applied agent-based technology to optimize decision in different kind of supply chains [18,19]. With the recent trends of virtual and extended enterprises, one of the key questions in supply chain management was how companies in supply chains could adapt to structural changes [20]. New products, new trading partners, and advancements in IT are the main causes of structural changes. Sinha et al. [21] used multi-agent technology to simulate the complex structure of petroleum supply chain. Susarla et al. [22] researched the impact on supply chains caused by new products. The impact of new suppliers and buyers was studied by Walsh and Wellman [23]. For the reason of advancements in information technologies, the supply chain was reconfigured by new transaction models [24]. The structure of supply chains also could be influence by changes in demand and price [25]. In this regard, researchers have delivered significant outputs. Coronato et al. [26] focused on automatic mechanisms for task distribution and execution in virtual and mobile environments. Dullaert et al. [27] developed an intelligent agent-based communication support platform for multimodal transport. A cooperative multiagent platform was proposed to support the invention process based on the patent document analysis [28]. Chiam et al. [29] considered the multi-objective evolutionary platform of technical trading strategies. Robu et al. [30] described an agentbased platform for the allocation of loads in distributed transportation logistics. Agent technologies were used to improve the management, flexibility and reusability of grid-like parallel computing architectures [31]. An agent-based coordination network was proposed to bring true benefit to drivers and car park operators ]32]. Yeh et al. [33] proposed the intelligent service-integrated platform, which employed the software agent as the framework to construct the integrated information system mechanism. Gatial et al. [34] proposed a platform to achieve trusted data collection from heterogeneous distributed sources including legacy systems and human end users. Tah [35] developed a simulation platform to provide an inexpensive and risk-free environment for organisations to experiment with emerging practices. For the reverse supply chain, Mishra et al. [36] simulated the reverse logistics in a greed supply chain with agent-based technology. Web-based platform improved the development of agent-based technologies. Sabucedo et al. [37] addressed a semantic based philosophy to tackle a holistic platform for the domain taking into account the knowledge of the administrations. Foukarakis et al. [38] proposed a mobile agent platform based on the integration of the mobile agent computing paradigm with Web Services. Sagiroglu and Yilmaz [39] introduced a new vision-based and web-based mobile robot platform for real-time exercises. For the simulation of supply chains, researchers have proposed significant results. Ahn et al. [40] suggested a flexible agent system for supply chains that could adapt to the changes in transactions introduced by new products or new trading partners. Lin and Long [41] presented a multi-agent-based distributed simulation platform to support the extremely complex semiconductor manufacturing analysis. Based on former researches, an agent-based model is proposed in our paper to study the supply chain with dynamic structures. In our paper, the structure of the supply chain’ model depends on the different knowledge of agents and the characteristics of demands. The C2 architecture, which was studied to present a network [42], inspired the structure definition of our
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
5405
paper. Agents are used to simulate the members of make-to-order supply chains. Fuller and Dennis [43] strived to explain how the two major fit appropriation model (FAM) constructs, task-technology fit (TTF) and appropriation, influenced team performance. This work is referenced in our paper to support agents’ actions. Agent-based technologies show significance on the study of supply chains. However, the limitation of existing agent based systems was that it was difficult to make agent based supply chains adapt to new products or new trading partners because agent systems usually used a fixed set of transaction sequences, which was a critical barrier to adaptability [44]. Li and Sheng [2] built a basic model to simulate the make-to-order supply chain. The purpose of this paper is to propose a flexible agent based model, which is adaptable to the dynamic changes of structures in make-to-order and make-to-stock supply chains. 3. The agent-based model The agent-based model is a model containing heterogeneous agents (virtual companies) which act in a virtual environment. In the model, the production of virtual company may be supported by several sub-components which are produced by other virtual companies. Virtual companies accomplish their works with their knowledge. Each virtual company is simulated by an agent in the model. The companies with different knowledge can produce different products. The virtual supply chain is classified as make-to-order and make-to-stock dynamic supply chain. The agent-based model G (G = hV,E,Pi) consists of N agents (V = {v1,v2,v3, . . . ,vN}), where each agent can be considered as a unique node in the virtual supply chain. The relationship in the network is modeled by an adjacency matrix E, where an element of the adjacency matrix eij = 1 if the agent vi uses his knowledge to support vj to satisfy its demand ðM v j Þ and eij = 0 otherwise. The relation among the agents are directed, so eij – eji. The relation between vi and vj is shown in Fig. 1 with an arrow. The arrowed line between vi and vj means vi produces the sub-components of vj’s products. P is attributes of the model. Some parameters of the model’s attribute are stored in the set of P(P = {maxParttimeWork, initialPopulation, requirementCount, subRequirementCount}). How many products can be produced by an agent in same time is decided by the parameter (maxParttimeWork) of the model. This parameter will increase the complexity of supply chains. The initial population of agents is set by the parameter of initialPopulation. The total number of customer requirements (products) and sub-requirements (sub-components) are controlled by parameters requirementCount and subRequirementCount. Fig. 1 shows the model of the agent-based model of supply chains. Agents are assigned to satisfy certain customer requirements according to their knowledge. If an agent produces products of the system, this agent will be set in the supply chains (‘‘Agents with tasks’’). If an agent does not contribute to the system, this agent will be put in the pool of ‘‘Agents without tasks’’. The basic definition of this model is similar with the model in Li and Sheng [2]. 3.1. Customer requirements Customer requirements are decided by environments of the virtual system. The requirements (products) consist of several sub-requirements (sub-components). In the paper, all requirements are defined as AT = {subti, i = 0,1,2 . . . }. Each subrequirement subti has two characteristics fsubti and t subti . fsubti means the field knowledge requirement of subti for the agent who want to satisfy this sub-requirement. tsubti means the requirement of technologies in the field of fsubti . Only if the agent has enough field knowledge and technologies in the special field, the agent is the adaptive candidate to satisfy the
Fig. 1. An overview of the agent-based model.
5406
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
sub-requirement. Rules of choose agents for sub-requirements will be proposed in the following section (Agent actions). The total number of sub-requirements depend on parameters of the model, such as requirementCount and subRequirementCount. A special software interface is proposed to design the requirements based on users’ requirements. One of the most important actions for agents in the model is to find suitable requirements (sub-requirements) according to its’ knowledge and tasks’ characteristics. 3.2. Agent states The state of vi is defined as Sv i ¼ fkv i ; fv i g of make-to-order supply chains, where kv i is the knowledge of the agent, fv i is the fitness of the agent. If fv i 6 fdead ; v i will be deleted from the model. In the model, the agent is a member with an individual nn o n o n oo F T F T F T kv i ; kv i ; kv i ; kv i ; . . . ; kv i ; kv i , where knowledge base. This knowledge of vi is represented as kv i ¼ h i h i F F F T T T F is the research field, kv i kv i 2 1; kv i max is the special technology in the field of kv i . The length of kv i kv i 2 1; kv i max min
kv i is between klv i
max
and klv i .
The agent’s performance in the model is presented as the fitness (fv i Þ. The fitness can be explained by the sum of rewards in the all last periods. In the paper, all revenues and costs are in fitness units. Each new agent’s fitness is finitial. For the make-to-stock supply chain, the state of vi is defined as Sv i ¼ fkv i ; fv i ; stockv i g, where stockv i is the state of v 0i s stocks. stockv i ðstockv i ¼ fstrategy; count; S; T; s; Q gÞ consists of stock strategy (strategy), current stock (count), maximal stock (S), replenishment period (T), safe stock (s), and optimal order count (Q). Different parameters are used when vi chooses one strategy from the four strategies of (S, s), (Q, s), (T, S), and (T, S, s). Other states in the make-to-stock supply chain are same with the states of make-to-order supply chains. 3.3. Agent actions A finite set of actions for agent vi is defined as Av i ¼ faav i ; abv i ; acv i ; atv i g of make-to-order supply chains. aav i means the action of vi to compute his attributes, such as fields, technologies and work qualities. abv i means the bid action of vi. acv i means the action of vi to call for bids and choose adaptive agents as his suppliers. atv i is used to pay taxes of agent vi at each period of simulations. Tax rate in the model is trate. Taxes of vi at each simulation period is fv i trate . The relation among these four actions at a simulation period is shown in Fig. 2. At the beginning of each period, agent will check their work plans. If agent vi gives offer to other agents to buy some subcomponents in last periods, vi will purchase these sub-components only if the sub-components is produced by sub-components’ manufacturers. If vi has no purchasing mission at this period, vi will bid the requirements according his abilities. If no agent wins the offer, vi will bid again with new price until one of agents gets the offer. If vi wins the offer, vi will choose the suppliers of sub-components. Actions of vi are proposed in the following. 1. Actions of computing attributions For the first action aav i ; v i will compute his work fields ðav i Þ, technologies ðbv i Þ and qualities (qv i Þ of work results. The fields of vi is calculated by Formula (1) and (2).
amin vi ¼
klv i X F kv i j c klv i :
ð1Þ
j¼1
amax vi ¼
klv i X F kv i j þ c klv i :
ð2Þ
j¼1
Fig. 2. Actions of
vi at simulation period t of make-to-order supply chains.
5407
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
amin v i is the minimal value of av i ðav i is the field of vi). klv i is the length of kv i . c(c 2 [0,1]) is a system parameter to control the min influence of agents’ different research fields. amax v i is the maximal value of av i . The fields of vi is the value between av i and
h
i
max max . This means the product fields between amin amax av i 2 amin vi v i ; av i v i and av i may be produced by vi.
Based on the model of Gilbert et al. [8], this paper proposed the following model to quantify agents’ technologies. The technologies of
bmin vi
vi is calculated by Formula (3) and (4) where N is the maximal value of kTv . i
0 1 klv i X F T ¼ @ kv i j kv i j A ð1 kÞ=N:
ð3Þ
j¼1
bmax vi
0 1 klv i X F T ¼ @ kv i j kv i j A ð1 þ kÞ=N:
ð4Þ
j¼1
bmin v i is the minimal value of bv i (bv i is the technologies of vi). k (k 2 [0,1]) is a system parameter to enlarge the scale of tech h i min max max . bv i 2 bmin nologies. bmax v i is the maximal value of bv i . The technologies of vi is the value between bv i and bv i v i ; bv i min max max If amin v i 6 fsubti 6 av i and bv i 6 t subti 6 bv i , agent vi is an adaptive candidate (the agent has enough field knowledge and technologies in the special field) of sub-requirement subti. This rule is used at the process of ‘‘Find demands’’ in Fig. 2. The quality of agents’ work depends on the knowledge of agents. The quality ðqv i Þ is calculated by Formula (5) in the model.
0 1, klv i X kFv j A T @ klv i : qv i ¼ kv i j 1 e i
ð5Þ
j¼1
2. Actions of bidding ðabv i Þ subt i min max max for If agent vi is adaptive to do task subt i ðamin v i 6 fsubti 6 av i and bv i 6 t subti 6 bv i Þ; v i calculates his bid price bpv i subti. subti
bpv i
¼ ½g ðav i þ bv i Þ þ ð1 gÞ ðfsubti þ t subti Þ ð1 þ iprÞ nsubt subti :
ð6Þ
subti
is calculated by Formula (6) where g(g 2 [0,1]) is system parameter to show the influence of purchase costs, ipr is the T T T of kv i initial profit rate, nsubt subti is the number of suppliers of subti. If vi accomplishes subti successfully, all kv i ¼ kv i 1 þ Dkv i
bpv i
T
subt i
will be improved (Dkv i is the step of improvements). If vi cannot win the offer, vi will decrease bpv i
with a minor step in next
bid period. 3. Actions of choosing agents ðacv i Þ When vi bid subti successfully, vi needs to choose adaptive agents (suppliers) to satisfy the sub-components ðsubt subti Þ of subti. Since all candidates of subtsubti propose their bid prices and work quality information, vi uses the decision tree (shown in Fig. 3) to choose agents. 1
Supposed there are two candidates (v1,v2) of subtsubti . The bid information of v1 consists of pv 1 (bid price) and qv 1 (quality of v1’s products). v2 proposes pv 2 and qv 2 . u is the high quality prefer of agents. vi uses Fig. 3 to choose agent between v1 and v2. For this scenario, the conditions in arcs can be used to choose v1 or v2. If the relationship between v1 and v2 is same with
Fig. 3. The decision tree of choosing agent.
5408
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413 1
the condition in one arc, then the leaf node of the arc is selected. If there is only one candidate to bid subtsubti , then choose this candidate. If there are more than two candidates, vi uses Fig. 3 iterated to choose agent. For the make-to-stock supply chain, a finite set of actions for agent vi is defined as Av i ¼ faav i ; abv i ; acv i ; atv i ; acsv i ; assv i g, where aav i ; abv i , and acv i are same with actions of make-to-order supply chain. Since there are stocks in the supply chain, subt atv i is defined as fv i ¼ fv i fv i t rate þ stockv i srate bpv i i in make-to-stock supply chains. stockv i is the current stock of vi, and srate is a system parameter of stock taxes. Meanwhile, acsv i means the action of check stock strategy. assv i is the action of selling products with stocks. The relation among these six actions at a simulation period is shown in Fig. 4. For the action of acsv i ; v i chooses strategy from the four strategies ((S, s), (Q, s), (T, S), and (T, S, s)). The process of acsv i is proposed in Fig. 5. Fig. 5 shows vi check the count of replenishment with different stock strategies. For the strategies of (T, S) and (T, S, s), if the result of current period t modeled T is not zero, vi will not replenish at period t. If the result is zero, vi replenish S-count or zero at period t with different current stock (count). For the strategies of (S, s) and (Q, s), vi replenish S-count, Q-count, or zero at period t.
Fig. 4. Actions of
vi at simulation period t of make-to-stock supply chains.
Fig. 5. Actions of acsv i .
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
5409
4. The implementation This paper simulates the supply chain of down coats to show the validity of the multi-agent model. The foreign trade company has down coat suppliers in china. In the last years, this company deals with down coats orders with different category of designs. Since the design of foreign customer’s coat is not same in different orders, all companies in the supply chain produce the products only after it is ordered (make-to-order supply chain). Since it is similar for all suppliers, this paper simulates the supply chain with one down coat supplier. This supply chain consists of one Down-Plant called DP, one FabricPlant called FCP, one Fastener-Plant called FRP, one Down-Coat-Plant called DCP, and one Foreign-Trade-Company called FTC. DP supplies the pure down, FCP supplies the fabric, and FRP supplies various fasteners. DCP is a down coat producer. FTC is a special foreign trade company. The adjacencies of companies for the supply chain are summarized in Fig. 6. In the reminder of the paper the company network made by five node-companies is considered (surrounded by the dashed line in Fig. 6). The agent-based model is programmed by JAVA based on RePast. The program is run on WinXP. In order to simulate the supply chain in Fig. 6, the parametric settings for the model are proposed in Table 1. Most parts of the setting are used in the following three experiments. For the convenience of applying the model for different cases, this paper uses XML to describe the cases’ parameters. A major part of XML file is used to describe the BOM (bill of material) of the product. The BOM of the down coat is shown in the following part of XML files. < Supplychain type=‘‘MTO’’/ > < product code=‘‘111’’ > < parameter father-code=‘‘ 1’’/ > < parameter field-requirement=‘‘90’’/ > < parameter technology-requirement=‘‘90’’/ > < /product > < product code=‘‘111222’’ > < parameter father-code=‘‘111’’/ > < parameter field-requirement=‘‘80’’/ > < parameter technology-requirement=‘‘80’’/ > < /product > < product code=‘‘111222111’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘70’’/ > < parameter technology-requirement=‘‘70’’/ > < /product > < product code=‘‘111222222’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘60’’/ > < parameter technology-requirement=‘‘60’’/ > < /product > < product code=‘‘111222333’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘50’’/ > < parameter technology-requirement=‘‘50’’/ > < /product >
Fig. 6. Foreign down coat supply chain architecture.
5410
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413 Table 1 Parametric settings. maxParttimeWork
initialPopulation
requirementCount
subRequirementCount
1
5 max klv i
1
4
kv i max
kv i max
100 0.1
100 k 0.1
g
30 fdead 100 ipr
0.7 trate 0.005
0.1 srate 0.0001
DkTv i 0
0.8
min
klv i
3 finitial 3000
F
c
T
u
In the XML file, ‘‘code’’ is the unique index of the part (product) in the model. For the final product, it’s ‘‘father-code’’ is ‘‘1’’. For instance, the product ‘‘111222333’’ is used to product ‘‘111222’’, the ‘‘father-code’’ of ‘‘111222333’’ is ‘‘111222’’. h i max The parameter of ‘‘field-requirement’’ means the part’s requirement of producer’s research fields av i 2 amin . The v i ; av i h i max parameter of ‘‘technology-requirement’’ is used to define the requirement of producer’s technologies bv i 2 bmin . v i ; bv i Different case numbers of ‘‘field-requirement’’ and ‘‘technology-requirement’’ show different requirements of products. In this paper, the bigger number means the product needs higher ability of the producer. For instance, product ‘‘111’’ needs the highest number of ‘‘field-requirement’’ and ‘‘technology-requirement’’. This means FTC has the highest ability to control the market in this case supply chain. FTC is the leader of this supply chain. The knowledge of nn o n o n oo is supposed as random numbers according to the requirement of the BOM in v i kv i ¼ kFv i ; kTv i ; kFv i ; kTv i ; . . . kFv i ; kTv i the XML file. Different settings of parameters will influence the running of the model. However, the validity of the model is not depending on the parametric settings. Different supply chains can be modeled by different parameters in the model. In order to represent BOM, product structure and their link with the supply chain, Fig. 7 is proposed to show the relationship of the case. Fig. 8 shows the running of the model which is run with the parametric settings of Table 1. Each agent is shown as a point in the figure. The commercial relationship between two agents is described with the line between agents. The model will run iterated with different customers’ demands. In the model of the supply chain, the agent (virtual FTC) finds demands firstly (step i). Virtual FTC will give offer to the agent (virtual DCP) with the special coat designs (step i + 1). Virtual DCP give offers to three agents (virtual DP, virtual FCP, and virtual FRP) (step i + 2). All virtual companies in the model produce products only after it is ordered (step i + 3). When the virtual FTC finds new demands, the model runs again with different coat designs. Researchers can carry out studying on the supply chain management based on this model. If customers need new products, the supply chain will be changed by FTC with new line of parts or material. This means new suppliers is introduced and the structure of the supply chain is changed according to the BOM of the new product. For
Fig. 7. The relationship between BOM and supply chain architecture.
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
5411
Fig. 8. Simulation of the supply chain by the model.
instance, supposed the new product is raincoat in the paper. The BOM of this raincoat is described in the parts of the following XML files. < Supplychain type=‘‘MTO’’/ > < product code=‘‘111’’ > < parameter father-code=‘‘1’’/ > < parameter field-requirement=‘‘90’’/ > < parameter technology-requirement=‘‘90’’/ > < /product > < product code=‘‘111222’’ > < parameter father-code=‘‘111’’/ > < parameter field-requirement=‘‘80’’/ > < parameter technology-requirement=‘‘80’’/ > < /product > < product code=‘‘111222111’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘70’’/ > < parameter technology-requirement=‘‘70’’/ > < /product >
According to the requirement of the raincoat’s BOM, the supply chain consists of three companies. Three of qualified virtual companies in the model produce this product. From the down coat to the raincoat, only the XML file is changed. If the customer has long-term demands on the raincoat, the supply chain uses the MTS strategy. The XML file is changed as following in the model.
Fig. 9. Stocks of the make-to-stock supply chain.
5412
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
< Supplychain type=‘‘MTS’’/ > < product code=‘‘111’’ > < parameter father-code=‘‘1’’/ > < parameter field-requirement=‘‘90’’/ > < parameter technology-requirement=‘‘90’’/ > < parameter stock-strategy=‘‘TS’’ > < parameter max-stock=‘‘2000’’/ > < parameter safe-stock=‘‘1000’’/ > < parameter check-period=‘‘20’’/ > < /product > < product code=‘‘111222’’ > < parameter father-code=‘‘111’’/ > < parameter field-requirement=‘‘80’’/ > < parameter technology-requirement=‘‘80’’/ > < parameter stock-strategy=‘‘TS’’ > < parameter max-stock=‘‘4000’’/ > < parameter safe-stock=‘‘2000’’/ > < parameter check-period=‘‘20’’/ > < /product > < product code=‘‘111222111’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘70’’/ > < parameter technology-requirement=‘‘70’’/ > < parameter stock-strategy=‘‘TS’’ > < parameter max-stock=‘‘5500’’/ > < parameter safe-stock=‘‘3000’’/ > < parameter check-period=‘‘30’’/ > < /product >
The parameter of ‘‘stock-strategy’’ means which stock strategy is used by the producer. The producer checks his stock after ‘‘check-period’’ periods. If his stock is less than ‘‘safe-stock’’, the producer orders products to replenish his stock to ‘‘max-stock’’. Based on the simulation of the model, the stocks of the three companies are shown in Fig. 9. Fig. 9 shows the stocks of companies in 200 simulation period. It is found that virtual companies can replenish their stocks with their strategy in the model. These three experiments show the validity of the model for the simulation of flexible supply chains. 5. Conclusion An agent-based model is proposed in the paper to simulate the make-to-order and make-to-stock supply chains with dynamic structures. This model is an attempt to improve our understanding of the complex processes going on in dynamic supply chains. The validity of the model is shown by the simulation of the three experiments. Agents are used to simulate the members of the supply chain. Agents’ attributes are presented by their knowledge kv i . Different knowledge means the agent produces different products. Actions of agents are defined to support the decision of agents. The purpose of the paper is to propose a common agent-based model to simulate make-to-order and make-to-stock supply chains with dynamic structures. The virtual supply chains can be modeled in the model easily. The model also can be extended with different model for the action of agents. Researchers can update the learning algorithm with new model. Virtual company’s behaviors can be defined according to the requirement of researches. Although the initial focus of the model is on scholars who develop agentbased models of supply chains, the model can be expanded to other application domains if the essence of the domains is the supplying relationships. Acknowledgments This research was supported in part by: (i) Natural Science Foundation of Jiangsu (China) under Grant BK2011652; (ii) National Natural Science Foundation of China under Grant 71101072; and (iii) The Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 510311).
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
5413
References [1] P. Kaminsky, O. Kaya, Combined make-to-order/make-to-stock supply chains, IIE Trans. 41 (2) (2009) 103–119. [2] J. Li, Z.H. Sheng, An agent-based model of make-to-order supply chains, in: Y. Tan, Y. Shi, K.C. Tan (Eds.), Proceedings of International Conference on Swarm Intelligence 2010, Lecture Notes in Computer Science 6146 (2010) 108–115. [3] N. Gilbert, P. Terna, How to build and use agent-based models in social science, Mind Soc. 1 (1) (2000) 57–72. [4] M.K. Tiwari, Jha Sujit Kumar, Anand Raj Bardhan, Operation allocation and part type selection in E-manufacturing: an auction based heuristic supported by agent technology, Rob. Computer Integr. Manuf. 26 (4) (2010) 312–324. [5] A.K. Choudhury, R. Shankar, M.K. Tiwari, Consensus-based intelligent group decision-making model for the selection of advanced technology, Decision Support Syst. 42 (3) (2006) 1776–1799. [6] Y. Zheng, J. Wang, J. Xue, A-team based supply chain management agent architecture, Int. J. Artif. Intell. Tools 18 (6) (2009) 801–823. [7] S. Rajagopalan, Make to order or make to stock: model and application, Manage. Sci. 48 (2) (2002) 241–256. [8] N. Gilbert, A. Pyka, P. Ahrweiler, Innovation networks – a simulation approach, J. Artif. Soc. Soc. Simulat. 4 (3) (2001). jasss.soc.surrey.ac.uk/4/3/8.html. [9] R. Bhavnani, D. Miodownik, J. Nart, REsCape: an agent-based model for modeling resources, ethnicity, and conflict, J. Artif. Soc. Soc. Simulat. 11 (2) (2008). jasss.soc.surrey.ac.uk/11/2/7.html. [10] V. Andronache, M. Scheutz, ADE – an architecture development environment for virtual and robotic agents, Int. J. Artif. Intell. Tools 15 (2) (2006) 251– 285. [11] Z. Lei, C.B. Pijanowski, J. Olson, Distributed modeling architecture of a multi-agent-based behavioral economic landscape (MABEL) model, Simulation 81 (7) (2005) 503–515. [12] T. Graf, A. Knoll, A multi-agent system architecture for distributed computer vision, Int. J. Artif. Intell. Tools 9 (2) (2000) 305–319. [13] B.J. Dunham, An agent-based spatially explicit epidemiological model in MASON, J. Artif. Soc. Soc. Simulat. 9 (1) (2005). http://jasss.soc.surrey.ac.uk/9/ 1/3.html. [14] K. Shibuya, A framework of multi-agent-based modeling, simulation, and computational assistance in an ubiquitous environment, Simulation 80 (7) (2004) 367–380. [15] A.M. Janssen, L.N. Alessa, M. Barton, S. Bergin, A. Lee, Towards a community framework for agent-based modelling, J. Artif. Soc. Soc. Simulat. 11 (2) (2008). http://jasss.soc.surrey.ac.uk/11/2/6.html. [16] G. Anastassakis, T. Panayiotopoulos, A system for logic-based intelligent virtual agents, Int. J. Artif. Intell. Tools 13 (3) (2004) 593–621. [17] M.T. Kone, A. Shimazu, T. Nakajima, The state of the art in agent communication languages, Knowledge Inform. Syst. 2 (2) (2000) 259–284. [18] V. Kumar, N. Mishra, A multi-agent self correcting architecture for distributed manufacturing supply chain, IEEE Syst. J. 5 (1) (2011) 6–15. [19] N. Mishra, V. Kumar, F.T.S. Chan, A multi-agent framework for agile outsourced supply chain, Enterprise Networks and Logistics for Agile Manufacturing-Edited by Lihui Wang and S.C. Lenny Koh (2010) 207–223 (Chapter 10). [20] K.L. Choy, W.B. Lee, L. Victor, An intelligent supplier management tool for benchmarking suppliers in outsource manufacturing, Expert Syst. Appl. 22 (3) (2002) 213–224. [21] A.K. Sinha, H.K. Aditya, M.K. Tiwari, F.T.S. Chan, Agent oriented petroleum supply chain coordination: co-evolutionary particle swarm optimization based approach, Expert Syst. Appl. 38 (5) (2011) 6132–6145. [22] A. Susarla, M. Parameswaran, A.B. Whinston, Emerging market structures in the digital supply chain, IT Professional 2 (5) (2000) 33–39. [23] W.E. Walsh, M.P. Wellman, Modeling supply chain formation in multiagent systems, in: Proceedings of the Agent Mediated Electronic Commerce Workshop (IJCAI-99), 1999, pp. 94–101. [24] K.A. Patterson, C.M. Grimm, T.M. Corsi, Adopting new technologies for supply chain management, Transp. Res. Part E 39 (2003) 95–121. [25] M.S. Fox, M. Barbuceanu, R. Teigen, Agent-oriented supply chain management, Int. J. Flexible Manuf. Syst. 12 (2/3) (2000) 165–188. [26] A. Coronato, G. De Pietro, L. Gallo, An agent based platform for task distribution in virtual environments, J. Syst. Archit. 54 (9) (2008) 877–882. [27] W. Dullaert, T. Neutens, et al, MamMoe: an intelligent agent-based communication support platform for multimodal transport, Expert Syst. Appl. 36 (7) (2009) 10280–10287. [28] V. Soo, S. Lin, et al, A cooperative multi-agent platform for invention based on patent document analysis and ontology, Expert Syst. Appl. 31 (4) (2006) 766–775. [29] S.C. Chiam, K.C. Tan, A.A. Mamun, Investigating technical trading strategy via an multi-objective evolutionary platform, Expert Syst. Appl. 36 (7) (2009) 10408–10423. [30] V. Robu, H. Noot, et al, A multi-agent platform for auction-based allocation of loads in transportation logistics, Expert Syst. Appl. 38 (4) (2011) 3483– 3491. [31] D. Sánchez, D. Isern, et al, Agent-based platform to support the execution of parallel tasks, Expert Syst. Appl. 38 (6) (2011) 6644–6656. [32] S. Chou, S. Lin, C. Li, Dynamic parking negotiation and guidance using an agent-based platform, Expert Syst. Appl. 35 (3) (2008) 805–817. [33] K. Yeh, R. Chen, C. Chen, Intelligent service-integrated platform based on the RFID technology and software agent system, Expert Syst. Appl. 38 (4) (2011) 3058–3068. [34] E. Gatial, Z. Balogh, L. Hluchy´, Platform for distributed execution of agents for trusted data collection, Procedia Comput. Sci. 1 (1) (2010) 2023–2032. [35] J.H.M. Tah, Towards an agent-based construction supply network modeling and simulation platform, Autom. Constr. 14 (3) (2005) 353–359. [36] N. Mishra, V. Kumar, F.T.S. Chan, A multi-agent architecture for reverse logistics in a green supply chain, Int. J. Prod. Res. 50 (9) (2012) 2396–2406. [37] L.Á. Sabucedo, L.E. Anido-Rifón, et al, Knowledge-based platform for eGovernment agents: a web-based solution using semantic technologies, Expert Syst. Appl. 37 (5) (2010) 3647–3656. [38] I.E. Foukarakis, A.I. Kostaridis, et al, Webmages: an agent platform based on web services, Comput. Commun. 30 (3) (2007) 538–545. [39] S. Sagiroglu, N. Yilmaz, Web-based mobile robot platform for real-time exercises, Expert Syst. Appl. 36 (2) (2009) 3153–3166. [40] H.J. Ahn, H. Lee, S.J. Park, A flexible agent system for change adaptation in supply chains, Expert Syst. Appl. 25 (4) (2003) 603–618. [41] J. Lin, Q. Long, Development of a multi-agent-based distributed simulation platform for semiconductor manufacturing, Expert Syst. Appl. 38 (5) (2011) 5231–5239. [42] D. Krackhardt, M.K. Carley, A PCANS model of structure in organization, in: Proceedings of the 1998 International Symposium on Command and Control Research and Technology, Evidence Based Research, Vienna, VA, 1998, pp. 113–119. [43] M.R. Fuller, R.A. Dennis, Does fit matter? The impact of TTF and appropriation on team performance in repeated tasks, Inform. Syst. Res. 20 (1) (2009) 2–17. [44] J. Freire, L. Botelho, Executing explicitly represented protocols, Proceedings of the AAMAS Workshop on Agentcities: Challenges in Open Agent Systems (2002) 37–40.
Contents lists available at SciVerse ScienceDirect
Applied Mathematical Modelling journal homepage: www.elsevier.com/locate/apm
An agent-based model of supply chains with dynamic structures Jing Li a, Felix T.S. Chan b,⇑ a b
School of Engineering, Nanjing Agricultural University, Nanjing, China Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong
a r t i c l e
i n f o
Article history: Received 4 May 2012 Received in revised form 21 September 2012 Accepted 22 October 2012 Available online 8 November 2012 Keywords: Supply chain structures Agent-based model Make-to-order supply chains Make-to-stock supply chains Simulation model
a b s t r a c t This paper proposes a common agent-based model for the simulation of MTS and MTO supply chains with dynamic structures. Based on the model, scholars can model supply chains easily. Basic characters of supply chains are proposed in the model. Agents, who are used to simulate the members of supply chains, produce appropriate products by intelligent choices. The relationships among agents are connected by their products. Different agents’ attributes are presented by their knowledge and actions of agents are introduced in the paper. Experiments are produced to show the availability of the agent-based model. The model should be available as a toolkit for the studying of dynamic supply chains. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Traditionally, companies produce products and stock them as inventory until they are sold (MTS, make-to-stock). However, some products cannot be produced with make-to-stock strategy. For many companies, product’s design in different orders is not same. All companies must produce different products to satisfy different demands. These companies have designed their production systems to produce a product only after it is ordered. Thus, many companies have shifted to ‘‘pull’’, holding no inventory at all and producing to order [1]. This kind of supply chain (consists of former companies) is referred to as MTO (make-to-order) supply chain. Meanwhile, there can be various types of changes to supply chains that may require adaptations. New trading partners and new products are the main causes of structural changes. Structural changes alter the topology of supply chains. Based on the agent-based model of make-to-order supply chain [2], this paper extended the agent-based model to simulate the make-to-stock and make-to-order supply chains with dynamic structures. Based on the model, scholars can research on the management of different supply chains. Since the phenomena were modeled in our paper involved non-linear relationships, it is implausible to make simplifying assumptions until the equation do become solvable. Scholars have completed various perspectives in order to resolve problems of the non-linear system. Computer simulation can be used to model either quantitative theories or qualitative ones. It is particularly good at modeling process and although non-linear relations can generate some methodological problems, there is no difficulty in representing them with a computer program [3]. The breakthrough in computer modeling came with the development of the multi-agent system. Although the agent-based modeling has become an increasingly important tool for scholars studying supply chains, but there are no common models on describing and testing the make-to-order and make-to-stock dynamic supply chains. An agent-based model is proposed in the paper to simulate supply chains with dynamic structures.
⇑ Corresponding author. Tel.: +852 2766 6605; fax: +852 2362 5267. E-mail addresses: [email protected], [email protected] (F.T.S. Chan). 0307-904X/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.apm.2012.10.054
5404
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
The rest of the paper is organized as follows. The related literature is reviewed in Section 2 and then the basic simulation model based on the multi-agent technology is developed in Section 3. The simulation of a foreign trade supply chain is presented in Section 4 to illustrate the validity of the model. Finally, the conclusions and directions for future research are given in Section 5.
2. Review of the related research Since the complexity of supply chains, agent-base technologies were used in many significant works to study the management of supply chains. Tiwari et al. [4] proposed an agent-based model to optimize the scheduling decision in E-manufacturing. For the group decision-making problem, agent-base technology was used to optimize the selection of different technologies [5]. Zheng presented a multi-agent architecture for specifying and analyzing supply chains [6]. Rajagopalan [7] provided insights into the impact of various problem parameters on the make-to-order versus make-to-stock decisions using a computational study. Rajagopalan’s research is beneficial to the study of make-to-order supply chains. The paper’s agent-based model depends on the development of the former artificial model based on multi-agent system. Gilbert et al. [8] built a multi-agent model embodying a theory of innovation networks. A number of policy-relevant conclusions were suggested through experiments with the model’s parameters. Gilbert’s work was a key issue for the building of the multi-agent system. Bhavnani et al. [9] provided a general introduction to an agent-based computational framework for studying the relationship between natural resources, ethnicity, and civil war. The framework in Bhavnani’s work is beneficial for the building of our model. Andronache and Scheutz [10] presented the agent architecture for the design, implementation, and testing of distributed agent architectures. Lei et al. [11] discussed a distributed modeling architecture in a multi-agent-based behavioral economic landscape (MABEL) model that simulated land-use changes over time and space. Graf proposed a multiagent architecture dedicated to model computer vision systems, which provided the vision system with a great degree of flexibility [12]. These structures show significance on the development of our work. A few agent-based models were proposed with different technologies [13,14]. Janssen et al. [15] reported on the establishment of the Open Agent-Based Modelling Consortium, www.openabm.org, a community effort to foster the agent-based modelling development, communication, and dissemination for research, practice and education. Combination of logic-based artificial intelligence with virtual reality is proposed in mVlTAL [16]. These agent-based models show significance to build the model of our paper. Although agent technology has shown its advantages for various collaborative applications, the flexibility of interoperation among heterogeneous agents was restricted [17]. Mishra and Kumar applied agent-based technology to optimize decision in different kind of supply chains [18,19]. With the recent trends of virtual and extended enterprises, one of the key questions in supply chain management was how companies in supply chains could adapt to structural changes [20]. New products, new trading partners, and advancements in IT are the main causes of structural changes. Sinha et al. [21] used multi-agent technology to simulate the complex structure of petroleum supply chain. Susarla et al. [22] researched the impact on supply chains caused by new products. The impact of new suppliers and buyers was studied by Walsh and Wellman [23]. For the reason of advancements in information technologies, the supply chain was reconfigured by new transaction models [24]. The structure of supply chains also could be influence by changes in demand and price [25]. In this regard, researchers have delivered significant outputs. Coronato et al. [26] focused on automatic mechanisms for task distribution and execution in virtual and mobile environments. Dullaert et al. [27] developed an intelligent agent-based communication support platform for multimodal transport. A cooperative multiagent platform was proposed to support the invention process based on the patent document analysis [28]. Chiam et al. [29] considered the multi-objective evolutionary platform of technical trading strategies. Robu et al. [30] described an agentbased platform for the allocation of loads in distributed transportation logistics. Agent technologies were used to improve the management, flexibility and reusability of grid-like parallel computing architectures [31]. An agent-based coordination network was proposed to bring true benefit to drivers and car park operators ]32]. Yeh et al. [33] proposed the intelligent service-integrated platform, which employed the software agent as the framework to construct the integrated information system mechanism. Gatial et al. [34] proposed a platform to achieve trusted data collection from heterogeneous distributed sources including legacy systems and human end users. Tah [35] developed a simulation platform to provide an inexpensive and risk-free environment for organisations to experiment with emerging practices. For the reverse supply chain, Mishra et al. [36] simulated the reverse logistics in a greed supply chain with agent-based technology. Web-based platform improved the development of agent-based technologies. Sabucedo et al. [37] addressed a semantic based philosophy to tackle a holistic platform for the domain taking into account the knowledge of the administrations. Foukarakis et al. [38] proposed a mobile agent platform based on the integration of the mobile agent computing paradigm with Web Services. Sagiroglu and Yilmaz [39] introduced a new vision-based and web-based mobile robot platform for real-time exercises. For the simulation of supply chains, researchers have proposed significant results. Ahn et al. [40] suggested a flexible agent system for supply chains that could adapt to the changes in transactions introduced by new products or new trading partners. Lin and Long [41] presented a multi-agent-based distributed simulation platform to support the extremely complex semiconductor manufacturing analysis. Based on former researches, an agent-based model is proposed in our paper to study the supply chain with dynamic structures. In our paper, the structure of the supply chain’ model depends on the different knowledge of agents and the characteristics of demands. The C2 architecture, which was studied to present a network [42], inspired the structure definition of our
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
5405
paper. Agents are used to simulate the members of make-to-order supply chains. Fuller and Dennis [43] strived to explain how the two major fit appropriation model (FAM) constructs, task-technology fit (TTF) and appropriation, influenced team performance. This work is referenced in our paper to support agents’ actions. Agent-based technologies show significance on the study of supply chains. However, the limitation of existing agent based systems was that it was difficult to make agent based supply chains adapt to new products or new trading partners because agent systems usually used a fixed set of transaction sequences, which was a critical barrier to adaptability [44]. Li and Sheng [2] built a basic model to simulate the make-to-order supply chain. The purpose of this paper is to propose a flexible agent based model, which is adaptable to the dynamic changes of structures in make-to-order and make-to-stock supply chains. 3. The agent-based model The agent-based model is a model containing heterogeneous agents (virtual companies) which act in a virtual environment. In the model, the production of virtual company may be supported by several sub-components which are produced by other virtual companies. Virtual companies accomplish their works with their knowledge. Each virtual company is simulated by an agent in the model. The companies with different knowledge can produce different products. The virtual supply chain is classified as make-to-order and make-to-stock dynamic supply chain. The agent-based model G (G = hV,E,Pi) consists of N agents (V = {v1,v2,v3, . . . ,vN}), where each agent can be considered as a unique node in the virtual supply chain. The relationship in the network is modeled by an adjacency matrix E, where an element of the adjacency matrix eij = 1 if the agent vi uses his knowledge to support vj to satisfy its demand ðM v j Þ and eij = 0 otherwise. The relation among the agents are directed, so eij – eji. The relation between vi and vj is shown in Fig. 1 with an arrow. The arrowed line between vi and vj means vi produces the sub-components of vj’s products. P is attributes of the model. Some parameters of the model’s attribute are stored in the set of P(P = {maxParttimeWork, initialPopulation, requirementCount, subRequirementCount}). How many products can be produced by an agent in same time is decided by the parameter (maxParttimeWork) of the model. This parameter will increase the complexity of supply chains. The initial population of agents is set by the parameter of initialPopulation. The total number of customer requirements (products) and sub-requirements (sub-components) are controlled by parameters requirementCount and subRequirementCount. Fig. 1 shows the model of the agent-based model of supply chains. Agents are assigned to satisfy certain customer requirements according to their knowledge. If an agent produces products of the system, this agent will be set in the supply chains (‘‘Agents with tasks’’). If an agent does not contribute to the system, this agent will be put in the pool of ‘‘Agents without tasks’’. The basic definition of this model is similar with the model in Li and Sheng [2]. 3.1. Customer requirements Customer requirements are decided by environments of the virtual system. The requirements (products) consist of several sub-requirements (sub-components). In the paper, all requirements are defined as AT = {subti, i = 0,1,2 . . . }. Each subrequirement subti has two characteristics fsubti and t subti . fsubti means the field knowledge requirement of subti for the agent who want to satisfy this sub-requirement. tsubti means the requirement of technologies in the field of fsubti . Only if the agent has enough field knowledge and technologies in the special field, the agent is the adaptive candidate to satisfy the
Fig. 1. An overview of the agent-based model.
5406
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
sub-requirement. Rules of choose agents for sub-requirements will be proposed in the following section (Agent actions). The total number of sub-requirements depend on parameters of the model, such as requirementCount and subRequirementCount. A special software interface is proposed to design the requirements based on users’ requirements. One of the most important actions for agents in the model is to find suitable requirements (sub-requirements) according to its’ knowledge and tasks’ characteristics. 3.2. Agent states The state of vi is defined as Sv i ¼ fkv i ; fv i g of make-to-order supply chains, where kv i is the knowledge of the agent, fv i is the fitness of the agent. If fv i 6 fdead ; v i will be deleted from the model. In the model, the agent is a member with an individual nn o n o n oo F T F T F T kv i ; kv i ; kv i ; kv i ; . . . ; kv i ; kv i , where knowledge base. This knowledge of vi is represented as kv i ¼ h i h i F F F T T T F is the research field, kv i kv i 2 1; kv i max is the special technology in the field of kv i . The length of kv i kv i 2 1; kv i max min
kv i is between klv i
max
and klv i .
The agent’s performance in the model is presented as the fitness (fv i Þ. The fitness can be explained by the sum of rewards in the all last periods. In the paper, all revenues and costs are in fitness units. Each new agent’s fitness is finitial. For the make-to-stock supply chain, the state of vi is defined as Sv i ¼ fkv i ; fv i ; stockv i g, where stockv i is the state of v 0i s stocks. stockv i ðstockv i ¼ fstrategy; count; S; T; s; Q gÞ consists of stock strategy (strategy), current stock (count), maximal stock (S), replenishment period (T), safe stock (s), and optimal order count (Q). Different parameters are used when vi chooses one strategy from the four strategies of (S, s), (Q, s), (T, S), and (T, S, s). Other states in the make-to-stock supply chain are same with the states of make-to-order supply chains. 3.3. Agent actions A finite set of actions for agent vi is defined as Av i ¼ faav i ; abv i ; acv i ; atv i g of make-to-order supply chains. aav i means the action of vi to compute his attributes, such as fields, technologies and work qualities. abv i means the bid action of vi. acv i means the action of vi to call for bids and choose adaptive agents as his suppliers. atv i is used to pay taxes of agent vi at each period of simulations. Tax rate in the model is trate. Taxes of vi at each simulation period is fv i trate . The relation among these four actions at a simulation period is shown in Fig. 2. At the beginning of each period, agent will check their work plans. If agent vi gives offer to other agents to buy some subcomponents in last periods, vi will purchase these sub-components only if the sub-components is produced by sub-components’ manufacturers. If vi has no purchasing mission at this period, vi will bid the requirements according his abilities. If no agent wins the offer, vi will bid again with new price until one of agents gets the offer. If vi wins the offer, vi will choose the suppliers of sub-components. Actions of vi are proposed in the following. 1. Actions of computing attributions For the first action aav i ; v i will compute his work fields ðav i Þ, technologies ðbv i Þ and qualities (qv i Þ of work results. The fields of vi is calculated by Formula (1) and (2).
amin vi ¼
klv i X F kv i j c klv i :
ð1Þ
j¼1
amax vi ¼
klv i X F kv i j þ c klv i :
ð2Þ
j¼1
Fig. 2. Actions of
vi at simulation period t of make-to-order supply chains.
5407
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
amin v i is the minimal value of av i ðav i is the field of vi). klv i is the length of kv i . c(c 2 [0,1]) is a system parameter to control the min influence of agents’ different research fields. amax v i is the maximal value of av i . The fields of vi is the value between av i and
h
i
max max . This means the product fields between amin amax av i 2 amin vi v i ; av i v i and av i may be produced by vi.
Based on the model of Gilbert et al. [8], this paper proposed the following model to quantify agents’ technologies. The technologies of
bmin vi
vi is calculated by Formula (3) and (4) where N is the maximal value of kTv . i
0 1 klv i X F T ¼ @ kv i j kv i j A ð1 kÞ=N:
ð3Þ
j¼1
bmax vi
0 1 klv i X F T ¼ @ kv i j kv i j A ð1 þ kÞ=N:
ð4Þ
j¼1
bmin v i is the minimal value of bv i (bv i is the technologies of vi). k (k 2 [0,1]) is a system parameter to enlarge the scale of tech h i min max max . bv i 2 bmin nologies. bmax v i is the maximal value of bv i . The technologies of vi is the value between bv i and bv i v i ; bv i min max max If amin v i 6 fsubti 6 av i and bv i 6 t subti 6 bv i , agent vi is an adaptive candidate (the agent has enough field knowledge and technologies in the special field) of sub-requirement subti. This rule is used at the process of ‘‘Find demands’’ in Fig. 2. The quality of agents’ work depends on the knowledge of agents. The quality ðqv i Þ is calculated by Formula (5) in the model.
0 1, klv i X kFv j A T @ klv i : qv i ¼ kv i j 1 e i
ð5Þ
j¼1
2. Actions of bidding ðabv i Þ subt i min max max for If agent vi is adaptive to do task subt i ðamin v i 6 fsubti 6 av i and bv i 6 t subti 6 bv i Þ; v i calculates his bid price bpv i subti. subti
bpv i
¼ ½g ðav i þ bv i Þ þ ð1 gÞ ðfsubti þ t subti Þ ð1 þ iprÞ nsubt subti :
ð6Þ
subti
is calculated by Formula (6) where g(g 2 [0,1]) is system parameter to show the influence of purchase costs, ipr is the T T T of kv i initial profit rate, nsubt subti is the number of suppliers of subti. If vi accomplishes subti successfully, all kv i ¼ kv i 1 þ Dkv i
bpv i
T
subt i
will be improved (Dkv i is the step of improvements). If vi cannot win the offer, vi will decrease bpv i
with a minor step in next
bid period. 3. Actions of choosing agents ðacv i Þ When vi bid subti successfully, vi needs to choose adaptive agents (suppliers) to satisfy the sub-components ðsubt subti Þ of subti. Since all candidates of subtsubti propose their bid prices and work quality information, vi uses the decision tree (shown in Fig. 3) to choose agents. 1
Supposed there are two candidates (v1,v2) of subtsubti . The bid information of v1 consists of pv 1 (bid price) and qv 1 (quality of v1’s products). v2 proposes pv 2 and qv 2 . u is the high quality prefer of agents. vi uses Fig. 3 to choose agent between v1 and v2. For this scenario, the conditions in arcs can be used to choose v1 or v2. If the relationship between v1 and v2 is same with
Fig. 3. The decision tree of choosing agent.
5408
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413 1
the condition in one arc, then the leaf node of the arc is selected. If there is only one candidate to bid subtsubti , then choose this candidate. If there are more than two candidates, vi uses Fig. 3 iterated to choose agent. For the make-to-stock supply chain, a finite set of actions for agent vi is defined as Av i ¼ faav i ; abv i ; acv i ; atv i ; acsv i ; assv i g, where aav i ; abv i , and acv i are same with actions of make-to-order supply chain. Since there are stocks in the supply chain, subt atv i is defined as fv i ¼ fv i fv i t rate þ stockv i srate bpv i i in make-to-stock supply chains. stockv i is the current stock of vi, and srate is a system parameter of stock taxes. Meanwhile, acsv i means the action of check stock strategy. assv i is the action of selling products with stocks. The relation among these six actions at a simulation period is shown in Fig. 4. For the action of acsv i ; v i chooses strategy from the four strategies ((S, s), (Q, s), (T, S), and (T, S, s)). The process of acsv i is proposed in Fig. 5. Fig. 5 shows vi check the count of replenishment with different stock strategies. For the strategies of (T, S) and (T, S, s), if the result of current period t modeled T is not zero, vi will not replenish at period t. If the result is zero, vi replenish S-count or zero at period t with different current stock (count). For the strategies of (S, s) and (Q, s), vi replenish S-count, Q-count, or zero at period t.
Fig. 4. Actions of
vi at simulation period t of make-to-stock supply chains.
Fig. 5. Actions of acsv i .
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
5409
4. The implementation This paper simulates the supply chain of down coats to show the validity of the multi-agent model. The foreign trade company has down coat suppliers in china. In the last years, this company deals with down coats orders with different category of designs. Since the design of foreign customer’s coat is not same in different orders, all companies in the supply chain produce the products only after it is ordered (make-to-order supply chain). Since it is similar for all suppliers, this paper simulates the supply chain with one down coat supplier. This supply chain consists of one Down-Plant called DP, one FabricPlant called FCP, one Fastener-Plant called FRP, one Down-Coat-Plant called DCP, and one Foreign-Trade-Company called FTC. DP supplies the pure down, FCP supplies the fabric, and FRP supplies various fasteners. DCP is a down coat producer. FTC is a special foreign trade company. The adjacencies of companies for the supply chain are summarized in Fig. 6. In the reminder of the paper the company network made by five node-companies is considered (surrounded by the dashed line in Fig. 6). The agent-based model is programmed by JAVA based on RePast. The program is run on WinXP. In order to simulate the supply chain in Fig. 6, the parametric settings for the model are proposed in Table 1. Most parts of the setting are used in the following three experiments. For the convenience of applying the model for different cases, this paper uses XML to describe the cases’ parameters. A major part of XML file is used to describe the BOM (bill of material) of the product. The BOM of the down coat is shown in the following part of XML files. < Supplychain type=‘‘MTO’’/ > < product code=‘‘111’’ > < parameter father-code=‘‘ 1’’/ > < parameter field-requirement=‘‘90’’/ > < parameter technology-requirement=‘‘90’’/ > < /product > < product code=‘‘111222’’ > < parameter father-code=‘‘111’’/ > < parameter field-requirement=‘‘80’’/ > < parameter technology-requirement=‘‘80’’/ > < /product > < product code=‘‘111222111’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘70’’/ > < parameter technology-requirement=‘‘70’’/ > < /product > < product code=‘‘111222222’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘60’’/ > < parameter technology-requirement=‘‘60’’/ > < /product > < product code=‘‘111222333’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘50’’/ > < parameter technology-requirement=‘‘50’’/ > < /product >
Fig. 6. Foreign down coat supply chain architecture.
5410
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413 Table 1 Parametric settings. maxParttimeWork
initialPopulation
requirementCount
subRequirementCount
1
5 max klv i
1
4
kv i max
kv i max
100 0.1
100 k 0.1
g
30 fdead 100 ipr
0.7 trate 0.005
0.1 srate 0.0001
DkTv i 0
0.8
min
klv i
3 finitial 3000
F
c
T
u
In the XML file, ‘‘code’’ is the unique index of the part (product) in the model. For the final product, it’s ‘‘father-code’’ is ‘‘1’’. For instance, the product ‘‘111222333’’ is used to product ‘‘111222’’, the ‘‘father-code’’ of ‘‘111222333’’ is ‘‘111222’’. h i max The parameter of ‘‘field-requirement’’ means the part’s requirement of producer’s research fields av i 2 amin . The v i ; av i h i max parameter of ‘‘technology-requirement’’ is used to define the requirement of producer’s technologies bv i 2 bmin . v i ; bv i Different case numbers of ‘‘field-requirement’’ and ‘‘technology-requirement’’ show different requirements of products. In this paper, the bigger number means the product needs higher ability of the producer. For instance, product ‘‘111’’ needs the highest number of ‘‘field-requirement’’ and ‘‘technology-requirement’’. This means FTC has the highest ability to control the market in this case supply chain. FTC is the leader of this supply chain. The knowledge of nn o n o n oo is supposed as random numbers according to the requirement of the BOM in v i kv i ¼ kFv i ; kTv i ; kFv i ; kTv i ; . . . kFv i ; kTv i the XML file. Different settings of parameters will influence the running of the model. However, the validity of the model is not depending on the parametric settings. Different supply chains can be modeled by different parameters in the model. In order to represent BOM, product structure and their link with the supply chain, Fig. 7 is proposed to show the relationship of the case. Fig. 8 shows the running of the model which is run with the parametric settings of Table 1. Each agent is shown as a point in the figure. The commercial relationship between two agents is described with the line between agents. The model will run iterated with different customers’ demands. In the model of the supply chain, the agent (virtual FTC) finds demands firstly (step i). Virtual FTC will give offer to the agent (virtual DCP) with the special coat designs (step i + 1). Virtual DCP give offers to three agents (virtual DP, virtual FCP, and virtual FRP) (step i + 2). All virtual companies in the model produce products only after it is ordered (step i + 3). When the virtual FTC finds new demands, the model runs again with different coat designs. Researchers can carry out studying on the supply chain management based on this model. If customers need new products, the supply chain will be changed by FTC with new line of parts or material. This means new suppliers is introduced and the structure of the supply chain is changed according to the BOM of the new product. For
Fig. 7. The relationship between BOM and supply chain architecture.
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
5411
Fig. 8. Simulation of the supply chain by the model.
instance, supposed the new product is raincoat in the paper. The BOM of this raincoat is described in the parts of the following XML files. < Supplychain type=‘‘MTO’’/ > < product code=‘‘111’’ > < parameter father-code=‘‘1’’/ > < parameter field-requirement=‘‘90’’/ > < parameter technology-requirement=‘‘90’’/ > < /product > < product code=‘‘111222’’ > < parameter father-code=‘‘111’’/ > < parameter field-requirement=‘‘80’’/ > < parameter technology-requirement=‘‘80’’/ > < /product > < product code=‘‘111222111’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘70’’/ > < parameter technology-requirement=‘‘70’’/ > < /product >
According to the requirement of the raincoat’s BOM, the supply chain consists of three companies. Three of qualified virtual companies in the model produce this product. From the down coat to the raincoat, only the XML file is changed. If the customer has long-term demands on the raincoat, the supply chain uses the MTS strategy. The XML file is changed as following in the model.
Fig. 9. Stocks of the make-to-stock supply chain.
5412
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
< Supplychain type=‘‘MTS’’/ > < product code=‘‘111’’ > < parameter father-code=‘‘1’’/ > < parameter field-requirement=‘‘90’’/ > < parameter technology-requirement=‘‘90’’/ > < parameter stock-strategy=‘‘TS’’ > < parameter max-stock=‘‘2000’’/ > < parameter safe-stock=‘‘1000’’/ > < parameter check-period=‘‘20’’/ > < /product > < product code=‘‘111222’’ > < parameter father-code=‘‘111’’/ > < parameter field-requirement=‘‘80’’/ > < parameter technology-requirement=‘‘80’’/ > < parameter stock-strategy=‘‘TS’’ > < parameter max-stock=‘‘4000’’/ > < parameter safe-stock=‘‘2000’’/ > < parameter check-period=‘‘20’’/ > < /product > < product code=‘‘111222111’’ > < parameter father-code=‘‘111222’’/ > < parameter field-requirement=‘‘70’’/ > < parameter technology-requirement=‘‘70’’/ > < parameter stock-strategy=‘‘TS’’ > < parameter max-stock=‘‘5500’’/ > < parameter safe-stock=‘‘3000’’/ > < parameter check-period=‘‘30’’/ > < /product >
The parameter of ‘‘stock-strategy’’ means which stock strategy is used by the producer. The producer checks his stock after ‘‘check-period’’ periods. If his stock is less than ‘‘safe-stock’’, the producer orders products to replenish his stock to ‘‘max-stock’’. Based on the simulation of the model, the stocks of the three companies are shown in Fig. 9. Fig. 9 shows the stocks of companies in 200 simulation period. It is found that virtual companies can replenish their stocks with their strategy in the model. These three experiments show the validity of the model for the simulation of flexible supply chains. 5. Conclusion An agent-based model is proposed in the paper to simulate the make-to-order and make-to-stock supply chains with dynamic structures. This model is an attempt to improve our understanding of the complex processes going on in dynamic supply chains. The validity of the model is shown by the simulation of the three experiments. Agents are used to simulate the members of the supply chain. Agents’ attributes are presented by their knowledge kv i . Different knowledge means the agent produces different products. Actions of agents are defined to support the decision of agents. The purpose of the paper is to propose a common agent-based model to simulate make-to-order and make-to-stock supply chains with dynamic structures. The virtual supply chains can be modeled in the model easily. The model also can be extended with different model for the action of agents. Researchers can update the learning algorithm with new model. Virtual company’s behaviors can be defined according to the requirement of researches. Although the initial focus of the model is on scholars who develop agentbased models of supply chains, the model can be expanded to other application domains if the essence of the domains is the supplying relationships. Acknowledgments This research was supported in part by: (i) Natural Science Foundation of Jiangsu (China) under Grant BK2011652; (ii) National Natural Science Foundation of China under Grant 71101072; and (iii) The Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 510311).
J. Li, F.T.S. Chan / Applied Mathematical Modelling 37 (2013) 5403–5413
5413
References [1] P. Kaminsky, O. Kaya, Combined make-to-order/make-to-stock supply chains, IIE Trans. 41 (2) (2009) 103–119. [2] J. Li, Z.H. Sheng, An agent-based model of make-to-order supply chains, in: Y. Tan, Y. Shi, K.C. Tan (Eds.), Proceedings of International Conference on Swarm Intelligence 2010, Lecture Notes in Computer Science 6146 (2010) 108–115. [3] N. Gilbert, P. Terna, How to build and use agent-based models in social science, Mind Soc. 1 (1) (2000) 57–72. [4] M.K. Tiwari, Jha Sujit Kumar, Anand Raj Bardhan, Operation allocation and part type selection in E-manufacturing: an auction based heuristic supported by agent technology, Rob. Computer Integr. Manuf. 26 (4) (2010) 312–324. [5] A.K. Choudhury, R. Shankar, M.K. Tiwari, Consensus-based intelligent group decision-making model for the selection of advanced technology, Decision Support Syst. 42 (3) (2006) 1776–1799. [6] Y. Zheng, J. Wang, J. Xue, A-team based supply chain management agent architecture, Int. J. Artif. Intell. Tools 18 (6) (2009) 801–823. [7] S. Rajagopalan, Make to order or make to stock: model and application, Manage. Sci. 48 (2) (2002) 241–256. [8] N. Gilbert, A. Pyka, P. Ahrweiler, Innovation networks – a simulation approach, J. Artif. Soc. Soc. Simulat. 4 (3) (2001). jasss.soc.surrey.ac.uk/4/3/8.html. [9] R. Bhavnani, D. Miodownik, J. Nart, REsCape: an agent-based model for modeling resources, ethnicity, and conflict, J. Artif. Soc. Soc. Simulat. 11 (2) (2008). jasss.soc.surrey.ac.uk/11/2/7.html. [10] V. Andronache, M. Scheutz, ADE – an architecture development environment for virtual and robotic agents, Int. J. Artif. Intell. Tools 15 (2) (2006) 251– 285. [11] Z. Lei, C.B. Pijanowski, J. Olson, Distributed modeling architecture of a multi-agent-based behavioral economic landscape (MABEL) model, Simulation 81 (7) (2005) 503–515. [12] T. Graf, A. Knoll, A multi-agent system architecture for distributed computer vision, Int. J. Artif. Intell. Tools 9 (2) (2000) 305–319. [13] B.J. Dunham, An agent-based spatially explicit epidemiological model in MASON, J. Artif. Soc. Soc. Simulat. 9 (1) (2005). http://jasss.soc.surrey.ac.uk/9/ 1/3.html. [14] K. Shibuya, A framework of multi-agent-based modeling, simulation, and computational assistance in an ubiquitous environment, Simulation 80 (7) (2004) 367–380. [15] A.M. Janssen, L.N. Alessa, M. Barton, S. Bergin, A. Lee, Towards a community framework for agent-based modelling, J. Artif. Soc. Soc. Simulat. 11 (2) (2008). http://jasss.soc.surrey.ac.uk/11/2/6.html. [16] G. Anastassakis, T. Panayiotopoulos, A system for logic-based intelligent virtual agents, Int. J. Artif. Intell. Tools 13 (3) (2004) 593–621. [17] M.T. Kone, A. Shimazu, T. Nakajima, The state of the art in agent communication languages, Knowledge Inform. Syst. 2 (2) (2000) 259–284. [18] V. Kumar, N. Mishra, A multi-agent self correcting architecture for distributed manufacturing supply chain, IEEE Syst. J. 5 (1) (2011) 6–15. [19] N. Mishra, V. Kumar, F.T.S. Chan, A multi-agent framework for agile outsourced supply chain, Enterprise Networks and Logistics for Agile Manufacturing-Edited by Lihui Wang and S.C. Lenny Koh (2010) 207–223 (Chapter 10). [20] K.L. Choy, W.B. Lee, L. Victor, An intelligent supplier management tool for benchmarking suppliers in outsource manufacturing, Expert Syst. Appl. 22 (3) (2002) 213–224. [21] A.K. Sinha, H.K. Aditya, M.K. Tiwari, F.T.S. Chan, Agent oriented petroleum supply chain coordination: co-evolutionary particle swarm optimization based approach, Expert Syst. Appl. 38 (5) (2011) 6132–6145. [22] A. Susarla, M. Parameswaran, A.B. Whinston, Emerging market structures in the digital supply chain, IT Professional 2 (5) (2000) 33–39. [23] W.E. Walsh, M.P. Wellman, Modeling supply chain formation in multiagent systems, in: Proceedings of the Agent Mediated Electronic Commerce Workshop (IJCAI-99), 1999, pp. 94–101. [24] K.A. Patterson, C.M. Grimm, T.M. Corsi, Adopting new technologies for supply chain management, Transp. Res. Part E 39 (2003) 95–121. [25] M.S. Fox, M. Barbuceanu, R. Teigen, Agent-oriented supply chain management, Int. J. Flexible Manuf. Syst. 12 (2/3) (2000) 165–188. [26] A. Coronato, G. De Pietro, L. Gallo, An agent based platform for task distribution in virtual environments, J. Syst. Archit. 54 (9) (2008) 877–882. [27] W. Dullaert, T. Neutens, et al, MamMoe: an intelligent agent-based communication support platform for multimodal transport, Expert Syst. Appl. 36 (7) (2009) 10280–10287. [28] V. Soo, S. Lin, et al, A cooperative multi-agent platform for invention based on patent document analysis and ontology, Expert Syst. Appl. 31 (4) (2006) 766–775. [29] S.C. Chiam, K.C. Tan, A.A. Mamun, Investigating technical trading strategy via an multi-objective evolutionary platform, Expert Syst. Appl. 36 (7) (2009) 10408–10423. [30] V. Robu, H. Noot, et al, A multi-agent platform for auction-based allocation of loads in transportation logistics, Expert Syst. Appl. 38 (4) (2011) 3483– 3491. [31] D. Sánchez, D. Isern, et al, Agent-based platform to support the execution of parallel tasks, Expert Syst. Appl. 38 (6) (2011) 6644–6656. [32] S. Chou, S. Lin, C. Li, Dynamic parking negotiation and guidance using an agent-based platform, Expert Syst. Appl. 35 (3) (2008) 805–817. [33] K. Yeh, R. Chen, C. Chen, Intelligent service-integrated platform based on the RFID technology and software agent system, Expert Syst. Appl. 38 (4) (2011) 3058–3068. [34] E. Gatial, Z. Balogh, L. Hluchy´, Platform for distributed execution of agents for trusted data collection, Procedia Comput. Sci. 1 (1) (2010) 2023–2032. [35] J.H.M. Tah, Towards an agent-based construction supply network modeling and simulation platform, Autom. Constr. 14 (3) (2005) 353–359. [36] N. Mishra, V. Kumar, F.T.S. Chan, A multi-agent architecture for reverse logistics in a green supply chain, Int. J. Prod. Res. 50 (9) (2012) 2396–2406. [37] L.Á. Sabucedo, L.E. Anido-Rifón, et al, Knowledge-based platform for eGovernment agents: a web-based solution using semantic technologies, Expert Syst. Appl. 37 (5) (2010) 3647–3656. [38] I.E. Foukarakis, A.I. Kostaridis, et al, Webmages: an agent platform based on web services, Comput. Commun. 30 (3) (2007) 538–545. [39] S. Sagiroglu, N. Yilmaz, Web-based mobile robot platform for real-time exercises, Expert Syst. Appl. 36 (2) (2009) 3153–3166. [40] H.J. Ahn, H. Lee, S.J. Park, A flexible agent system for change adaptation in supply chains, Expert Syst. Appl. 25 (4) (2003) 603–618. [41] J. Lin, Q. Long, Development of a multi-agent-based distributed simulation platform for semiconductor manufacturing, Expert Syst. Appl. 38 (5) (2011) 5231–5239. [42] D. Krackhardt, M.K. Carley, A PCANS model of structure in organization, in: Proceedings of the 1998 International Symposium on Command and Control Research and Technology, Evidence Based Research, Vienna, VA, 1998, pp. 113–119. [43] M.R. Fuller, R.A. Dennis, Does fit matter? The impact of TTF and appropriation on team performance in repeated tasks, Inform. Syst. Res. 20 (1) (2009) 2–17. [44] J. Freire, L. Botelho, Executing explicitly represented protocols, Proceedings of the AAMAS Workshop on Agentcities: Challenges in Open Agent Systems (2002) 37–40.