Shu-fang ZHOU, Yi ZHENG, Yu-hua MA

(Mechanical & Electronic Engineering College， Qingdao Huanghai University， Qingdao 266427, China)

Abstract: Service selection problem is one important research content in cloud manufacturing (CMfg). Most service selection mathematical models considered manufacturing task, and few studies considered design task, but no mathematical models considered the product task. The mathematical model of manufacturing service selection process or design service selection process is part of product service selection process. The mathematical model of product-oriented service selection process is more realistic and it needs to be comprehensively studied. Besides, most studies solved the mathematical models by heuristic algorithms, which can obtain the solution but cannot guarantee that the solution is the best. In this paper, the problems in product-oriented service selection process are described and the mathematical model of product-oriented service selection process is established. A new optimization algorithm is proposed in this paper and two experiments show that the mathematical model and optimization algorithm is correct and efficient.

Key words: CMfg， IMDP， Product-oriented service selection process

1 Introduction

Cloud manufacturing (CMfg) is one research direction of “Made in China 2025”, which was firstly proposed by Li et al. [3-6] in 2009. Based on the “Internet +”, cloud computing and big data, aiming at resources horizontal integration (industrial chain integration) [7], CMfg is one trend of intelligent manufacturing. Therefore, it attracts a lot of attention, and has made a series of achievements. However, since CMfg is still one new manufacture paradigm, the researches mostly studied on the content and features of CMfg [8-9], the core technology [10-11], integrated technology [12], application modes [7,13-17], and service selection [12,18-33].

The service selection problem is one critical problem in CMfg. The essence of this problem is to find the proper service providers for consumer. Usually, the purposes of consumers will maximize the quality of parts best or others, so the objective functions are QoS (quality of service)-based [18-21], TQCS (time, quality, cost, and service)-based [22], etc. The train thought of service selection problems is firstly used to build the mathematical model, and then proper algorithm is used to solve the mathematical model.

Due to cloud services was previously defined as manufacturing resources and manufacturing capabilities [23-24], so the researches about service selection problems were focusing on manu facturing resources service selection. Huang et al. [25] generally provided the building idea of objective functions and constraints of cloud service composition optimal-selection (CSCOS), and designed a new chaos control optimization algorithm (CCOA). To effectively address manufacturing resources service selection problem, Zhou et al. [26] proposed a context-aware artificial bee colony (caABC) algorithm based on the principle of ABC and service features in the cloud environment. Cao et al. [22] focused on manufacturing task and built A TQCS (time, quality, cost, and service) -based service selection and scheduling method, and presented ant colony optimization (ACO) algorithm. Liu et al. [27] presented a cloud manufacturing multi-task scheduling method based on task workload in order to achieve better solution of multiple manufacturing tasks scheduling problem in a cloud manufacturing system. Zhou et al. [28] built aggregation function for QoS computation of composite services according to four basic methods for a composite service executive path [29]: sequence, parallel, selective, and circular, and presented hybrid artificial bee colony (HABC) algorithm to solve the problem. Wang et al. [30] proposed a manufacturing resource selection strategy based on an improved distributed genetic algorithm (DGA) for manufacturing resource combinatorial optimization (MRCO) in CMfg.

Recently, the research of service selection problem has extended. Mai et al. [31] built mathematical model for customized product-oriented based on distributed 3D printing services in cloud manufacturing. In order to design process of product-oriented, Zheng et al. [32] presented a QoS computation method based on fuzzy theory and adopted particle swarm optimization (PSO) algorithm to solve the problem. Considering logistics problems, Wang et al. [12] provided an improved particle swarm optimization (IPSO) algorithm as one selection strategy of machining equipment in cloud manufacturing. Chen et al. [33] proposed a flexible and efficient Web service selection method by multi-objective optimization to provide users enhanced information to choose appropriate services.

To sum up, there are two questions in current studies of service selection:

1) The mathematical models focused on manufacturing task or design task of product. But the product-oriented service selection process contains design service selection process and manufacturing service selection process. The mathematical model of product-oriented service selection process should be built.

2) In current studies, mathematical models are solved by heuristic algorithms. But most heuristic algorithms need to set proper parameters to get the solution, and they cannot guarantee the solution is the best. Thus, the algorithms should be improved.

In order to solve the above problems, the mathematical model of product-oriented service selection process is established and a new optimization algorithm is proposed to solve the mathematical model.

The rest of this paper is organized as follows. Problem description of product-oriented service selection on CMfg platform will be discussed in section 2. Mathematical model of design service selection process, mathematical model of manufacturing service selection process, and mathematical model of product-oriented service selection process are presented in section 3, section 4, and section 5, respectively. To solve the mathematical model, a new optimization algorithm is designed in section 6. Two experiments are carried out and the results shown in section 7. Finally, section 8 summarizes this paper.

2 Problem description

For design process on CMfg platform, firstly, consumers provide product-oriented design demands; Secondly, CMfg platform will decompose the demands into several sub-tasks, and provides available design service providers for every sub-task. Then the consumers will choose the proper design service providers. The manufacturing process on CMfg platform is just the same as design process. So, the product-oriented service selection problem is to select the proper service providers. In this paper, the service selection strategy is that with the condition of quality, minimize the total cost and total processing time.

The service selection problem can be simplified as follows: ① after all design service providers done, manufacturing process can start. If there is no design process, the problem becomes manufacturing service selection problem; if there is no manufacturing process, the problem becomes design service selection problem. ② One design order can be separated into several design sub-tasks, and all design sub-tasks are series connection, which means the design sub-task should be designed one by one and it cannot be designed at the same time. ③ During manufacturing process, assemblies should be considered. And only all of the manufacturing sub-tasks (parts) for one assembly is ready, this assembly can be manufactured. ④ There are several available service providers on the platform for one sub-task.

3 Mathematical model of design service selection process

Because the transport objects from one design service provider to another is product-oriented data, there is no need to consider logistics cost and logistics time. Firstly, the number of total like people could be calculated.

The total cost will be discussed. The assumption is that the design process consistsnsub-tasks, and each part haskservice providers. Each sub-task needs only one service provider. Hence, the cost is the summation of all the selected design service providers, which could be evaluated in Eq. (1).

(1)

Where,

The total design time could be analyzed. Because the assumption is that all the sub-tasks are designed one by one, the total design time is the summation of selected design service providers (as shown in Eq. (2)).

(2)

The mathematical model of design service selection process is built. In this paper, the condition of quality is that the qualified rate or favorable rate is greater or equal to one setting number. According to the service selection strategy, the mathematical model of design service selection process is as follows (Eq. (3)):

(3)

4 Mathematical model of manufacturing service selection process

In this section, the manufacturing process including the processes of assembly is firstly introduced, and then the mathematical model could be established.

4.1 Manufacturing process including assemblies

Discrete manufacturing often contains many parts and assemblies and the manufacturing process of simple product is one simple case of complication products. In this paper, the manufacturing process of complication product is analyzed: every assembly is made of several parts, and assemblies are manufactured by sequence. Fig.1 shows one example of three assemblies. As can be seen, only all of parts 1 tonare done, can first assembly be proceed. Only first assembly and parts 2 tonare done, can second assembly be manufactured. So does the final assembly until the product is finished.

Fig.1 Manufacturing process of three assemblies

4.2 Mathematical model of manufacturing service selection process

On CMfg platform, every part and assembly may have several available service providers. Every service provider will provide its own manufacturing cost, manufacturing time, evaluation people and the favorable rating. Parts can be manufactured by available service providers, and will be transported to the next available service provider who provides the assembly function, until the manufacturing process is done. Thus, the cost contains manufacturing cost and logistic cost. The total processing time contains manufacturing time and logistic time.

The total manufacturing cost is the summation of all selected part service providers and the selected assembly service providers, and all the transportation cost from parts to assemblies and the cost from the assembly to the next assembly, and the transportation cost from the final assembly to consumer could be evaluated as follows (i.e., Eq. (4)).

(4)

The total manufacturing time is analyzed. According to the manufacturing process, when thejth assembly is done, the assembly time equals summation of the following time: maximum parts manufacturing time for every assembly before thejth assembly, which includes thejth assembly, and all the assemblies time, which includes thejth assembly, and all the transportation time from parts to assemblies. For thejth assembly, the total processing time is as follows (Eq. (5)):

(5)

The total processing time of manufacturing is the summation of final assembly processing time and the transportation time from the final assembly to consumer, then the Eq. (5) could be changed to Eq. (6).

(6)

The mathematical model of manufacturing service selection process aims at minimizing manufacturing cost and time, with the condition of quality. For parts and assemblies, the condition of quality is that the number of total like people is greater or equal to one number. The mathematical model of manufacturing process is shown in Eq. (7).

(7)

5 Mathematical model of product-oriented service selection process

The product-oriented service selection process includes design service selection process and manufacturing service selection process, so the total cost is the summation of them (i.e., Eq. (8)). In the same way, the processing time is the summation of design time and manufacturing time as shown in Eq. (9).

(8)

T=(Td+Tm)

(9)

According to the service selection strategy, the mathematical model can be represented as follows (Eq. (10)):

(10)

Normally, there are three approaches about multi-objective problem [34]. The most efficient one is to transform the multi-objective problem to a mono-objective problem by assigning different weight coefficients for each objective. This section this approach will be adopted. In this paper, the weight of cost and time are defined asm% andn%, respectively. Then the objective function will be changed to Eq. (11). The weight can be reset and can be different according to the real requirement of consumers.

f=m%C+n%T

(11)

6 The new optimization algorithm

This product-oriented producing process consists two parts: design process and manufacturing process, so this paper will divide the optimization algorithm into two parts: optimization algorithm of design service provider and optimization algorithm of manufacturing service provider.

6.1 Optimization algorithm of design service provider

For design service provider selection, the objective function is denoted asfd. Firstly, the objective function will be computed according to Eq. (11). Then the minimumfdwill be selected as the optimization design service provider.

6.2 Optimization algorithm of manufacturing service

provider

(1) An improved MDP

Markov decision process (MDP) is one algorithm which is based on reinforcement learning. Classical MDP can efficiently solve the shortest route problem, in which every step is stationary. But every step has several available service providers in the mathematical model which is built in section 5. Therefore, the MDP and value iteration algorithm need to be improved.

In order to solve the mathematical model, the description of problem is changed firstly. Fig.2 shows an example of three parts for the first assembly (i.e.,J1,1,J1,2andJ1,3). And there are two available manufacturing service providers for each part. The original question is shown in the left figure of Fig.2. As can be seen in this figure, there are four path for one part, and there are three parts that operate at the same time. The number of combinations is 43=64. Thus, the best solution probability is 1/64=1.56%. If there are n providers for one part, and there are m parts, the best solution probability is 1/mn. Apparently, with the increase of providers’ number and parts’ number, the best solution probability gets decreased. In this paper, the situation could be transformed to the right two figures of Fig.2. For one assembly provider, firstly, the shorted path of every part will be selected; secondly, the longest path as the solution of assembly provider will be chose; thirdly, compare the solutions of providers, and the shorted one will be selected as the best solution. There are two assembly providers in Fig.2, thus there are two solutions. The best solution probability is 1/2=50%. Normally, if there are k assembly providers in this situation, the best solution probability is 1/k. Without doubt, the algorithm of the right two figures are simpler and easier than the left figure.

Fig.2 An example of manufacturing section process

After transform the manifestation of the manufacturing section process, the MDP is improved to adapt to the situation. The definition of IMDP parameters are as follows:

①S: state of operations.A11the parts, which prepare for one assembly and the last assembly, are defined as one S, and then in the right two figures of Fig.2,J1,1,J1,2andJ1,3isS1. The first assemblyA1, and the parts for the second assembly (J2,1andJ2,2) isS2.

②A: direction ofS. In this paper,Ais the direction of parts to assembly.

③Psa: the state transition probabilities. In this paper,Psais defined as the probability to every available assembly service providers, and every assembly service providers have the same value ofPsa.

④γ∈[0,1]: damping coefficient; In this paper,γ=0.99.

⑤R(s,a): reward function of S with direction A. To calculate the reward, the problem is transformed to the shortest route problem by adding the manufacturing time to the logistic time. Thus, for one part,

(12)

(13)

(2) Value iteration algorithm

Normally, the purpose of MDP is to find the proper path to make R maximum, but this paper will aim to look for the minimumf, so the value function for a policyπis as follows:

Vπ(s,a)=E[R(s0,a0)+γR(s1,a1)+

γ2R(s2,a2)+…|s0,a0=s,a,π]

(14)

The optimization value function is as follows:

(15)

Then, according to the value iteration algorithm, the optimization value function could be evaluated. The pseudo code of value iteration algorithm is shown as follows:

② Repeat until convergence {

For every state, update

}

7 Experiments

7.1 Experiment 1

This section computed the data from literature [12]. The results are the same as those in literature [12] (i.e., the best selection is S14-S22-S31-S43-S53; the cost is 516; the processing time is 49 and the average qualified rate is 95%). But as compared to the improved particle swarm optimization algorithm (IPSO) from literature [12], the optimization algorithm has two advantages.

(1) Literature [12] conducted 40 times experiments to obtain the best results, while the present optimization algorithm only takes one time to get the results. In order to further prove the correction of the optimization algorithm, we computed it by IPSO and the optimization algorithm 100 times each. Fig.3 shows the results of computation time of IPSO and the optimization algorithm.T1represents computation time of IPSO, andT2represents computation time of the optimization algorithm. The average computation time of IPSO and the optimization algorithm with 100 times is 0.571 and 0.073, respectively. Therefore, the present optimization algorithm is more efficient.

Fig.3 Computation time of IPSO and IMDP with 100 times

(2) Literature [12] needs proper parameters to get the correct results, while the optimization algorithm does not need setting parameters.

7.2 Experiment 2

Experiment 1 is about parts’ service selection process. The assembly service selection process and design service selection process are not included, which does not fit the realistic product-oriented service selection process. The product-oriented service selection process is considered in experiment 2.

The parameters of design process are shown in Table 1. The manufacturing time, cost, favorable rating and numbers of evaluations of parts and assemblies are shown in Table 2, in which the cost, favorable rating and numbers of evaluations of parts and assemblies are all from Tianmao Mall. The logistic time and cost are shown in Table 3. In this experiment, the first assembly contains part 1 and part 2, and the second (final) assembly contains assembly 1, part 3 and part 4. The base line of qualified rate is 90%.

Table 1 Parameters of available design service providers

ParametersCostTimeqkd,n/%D112004898D213002099D312505591D412801089

Table 2 Parameters of parts and assemblies

Parts/assembliesTi,km, j/Tk′A, jCi,km, j/Ck′A, jRi,km, j/Rk′A, jPart 1M1,11206598%M1,21276496%M1,31188098%M1,41307092%Part 2M2,11593991%M2,21375096%M2,31465798%M2,41634593%Assembly 1A11487090%A21286086%A31376698%A41503090%

Continue table 2

Parts/assembliesTi,km, j/Tk′A, jCi,km, j/Ck′A, jRi,km, j/Rk′A, jPart 3M1,12493894%M1,22365688%M1,32607893%M1,42486087%Part 4M2,12384890%M2,22458592%M2,32607084%M2,32458095%Assembly 2A12564496%A22595088%A32405797%A42554095%

Table 3 The logistic time and cost

Ti,k→k′m, j→A, j/Tk′→k′A, j-1→A, j1234Ci,k→k′m, j→A, j/Ck′→k′A, j-1→A, j1234M1,11→Ak′102112764M1,21→Ak′112125767M1,31→Ak′101112464M1,41→Ak′120028137M2,11→Ak′110125167M2,21→Ak′121208491M2,31→Ak′101022437M2,41→Ak′122118764A11→Ak′220218194A21→Ak′212015734A31→Ak′210125167A41→Ak′201212494M1,12→Ak′221028437M1,22→Ak′202112764M1,32→Ak′211015434M1,42→Ak210225197M2,12→Ak′221128467M2,22→Ak′210225197M2,32→Ak′202022737M2,42→Ak′220128167Ak′2→consumer02122767

Table 4 The results of the optimization algorithm and IPSO

the optimization algorithmIPSOService providersD41?M1,11M2,11}?M1,12A41M2,12}?A12D41?M1,21M2,31}?M1,12A41M2,32}?A42C575615T193214

8 Conclusion

In this paper, after analyzed the product-oriented service selection problem, the mathematical model of product-oriented service selection process is established. The mathematical model of product-oriented service selection process contains two parts: mathematical model of design service selection process and mathematical model of manufacturing service selection process. In the mathematical model of manufacturing service selection process, assembly processes are considered. The optimization algorithm contains optimization algorithm of design service provider and optimization algorithm of manufacturing service provider. In the optimization algorithm of manufacturing service provider, after the manifestation of the manufacturing section process are transformed, the MDP could be improved to solve the mathematical model. At last, two experiments are used to prove that the mathematical model and the optimization algorithm are correct and efficient.

There are three roles in CMfg: platform, consumer and service provider. Recently, most researches considered the service selection problem in the perspective of consumers. The researches based on service providers’ perspective are relatively rarely. As a future research direction, we believe that the service selection problem is worth to explore based on the perspective of service provider.

Acknowledgment

This work supported by Shandong University of science and technology plan projects (No.J16LB58) and Graduate science and technology innovation project (No.SDKDYC170221).

Nomenclature

k: the sequence number of service providers for one design process or manufacturing process,k={1,2,3,…,s};

j: the sequence number of design process or assemblies,j={1,2,3,…,n};

i: the sequence number of parts,i={1,2,3,…,l};

k′: the sequence number of service providers for one assembly process,k′={1,2,3,…,s′};

Cm: the total cost of manufacturing;

Tm: the total processing time of manufacturing;