Utility modelling,equilibrium,and coordination of resource service transaction in service-oriented manufacturing system

Abstract

The resource service transaction in service-oriented manufacturing systems is one of the key issues in deciding its practical implementation and application. In order to enhance the benefit of the three sides or users (i.e. resource service provider, resource service demander, and resource service agent or operator (agent)) using service-oriented manufacturing systems, the comprehensive utility models consider the revenue, time, and reliability for the three sides in the resource service-transaction process faced with uncertain factors under decentralized decision-making conditions are established first. Then the related comprehensive utility model for the resource service transaction chain of ‘multiple resource service providers – one agent – multiple resource service demanders’ under a centralized decision-making condition is proposed and discussed. The existence of utility equilibrium between resource service provider and agent is studied and proved. As is the optimal decision of a resource service transaction chain under the decentralized decision-making condition, as well as the utility equilibrium between agent and resource service demander. A utility coordination method is proposed, with the aim of improving the comprehensive utility of the resource service transaction chain under a decentralized decision-making condition. The case study illustrates that the proposed approach is practicable and effective.

Keywords

Service-oriented manufacturing resource service transaction chain utility modelling utility equilibrium utility coordination service-oriented technology

Introduction

The idea of service-oriented architecture (SOA) has been widely researched and applied in the whole process of production in order to realize the manufacturing resource sharing and cooperation work within an enterprise or among different enterprises. Many service-oriented manufacturing (SOM) modes and technologies have been proposed, such as networked manufacturing (NM),^1–2 application service provider (ASP),^3–5 manufacturing grid (MGrid),^6–11 production-service system (PSS)¹² or industrial production-service system (IPS²),¹³ wireless manufacturing (WM),¹⁴ crowd sourcing, cloud manufacturing (CMfg),^15–17 and so on. These advanced manufacturing models and technologies have played very important roles for the development of modern manufacturing, and SOM has been one of the key developing trends for the manufacturing industry.

The basic principle for the SOM model is illustrated in Figure 1. There are primarily three classes of users in a SOM system, resource service provider (RSP), resource service demander (RSD) or consumer,¹⁷ and resource service agent (expressed as agent hereafter) or operator.

The RSP owns the manufacturing resources and abilities involved in the whole life-cycle of the manufacturing process. It publishes and registers their idle resource, product, manufacturing ability, etc., to the SOM platform, and provides a manufacturing resource and ability service on-demand. The RSP can be a person, an organization, an enterprise, or a third party.

The RSDs are the subscribers of the resource service and ability available in a SOM system or platform. They search the optimal manufacturing resource service and ability and purchase the use of the service and ability from the operator on an operational-expense basis, according to their needs.

The agent operates the SOM platform to deliver service and functions to providers, consumers and the third parties. They deal with the organization, sale, licensing, consulting of the manufacturing service and ability; and provide, update and maintain the technologies and services involved in the operations to the SOM system or platform.¹⁷

Figure 1.

Abstract architecture of SOM.

The SOM system, aims to realize the full sharing and circulation, high utilization, and on-demand use of various manufacturing resources and capabilities by providing safe and reliable, high quality, cheap and on-demand use of manufacturing services for the whole life-cycle of manufacturing.¹⁷ According to the above three classes of users, RSPs publish their services to the agent, and the RSDs invoke the services on-demand from the agent after submitting the service requirements to the agent. The platform of the agent realizes the search and match with registered services of RSPs and the service requirements of RSDs based on this knowledge. Then RSPs and RSDs make the cooperative work through the agent platform. In the resource service transaction flow of SOM, after RSPs publish their available resource and ability services, RSDs submit their service requirements to the agent and search the suitable services of multiple RSPs through the agent platform, then RSPs provide their services to execute the requirements of RSDs under the agent’s scheduling.

Apparently, before a SOM model or system can be fully accepted and used by the three types of users and enterprises, and be successfully and widely applied in the manufacturing industry, the profit and other performance indicators using the SOM system for each side, should be fully considered and guaranteed, especially for the RSP and RSD. However, the existing works and research emphasis for the above proposed SOM model or system (e.g. ASP, NM, and MGrid) are, primarily:

the architectures;^18–19

manufacturing resource modelling, virtualization, service encapsulation,^20–22 digital description,²³ scheduling, and allocation;^24–26

task and workflow management,²⁷ and so on.²⁸

Little work has been emphasized on resource service and ability transaction management, such as:

manufacturing resource service cost management;^29–30

method for payments;^31–32

resource service transaction process monitoring management;^33–34

benefit guaranteeing mechanisms and optimal-allocation methods for RSP and RSD;^35–36

utility equilibrium among RSD, RSP, and agent,^37–38 and so on.

As a result the interest of RSP is not effectively guaranteed, and many RSPs do not want to provide and contribute their idle manufacturing resource and ability to the SOM system or platform, or they have no positive motivation to provide high-quality and reliable resource services. Consequently, without the adequate and available, high-quality and reliable manufacturing services, RSD’s requirements cannot be met and their tasks cannot be well fulfilled via the SOM system. Both RSP and RSD lose their interest and enthusiasm to use the SOM system, and the development and wider practice application of the above mentioned proposed advanced manufacturing modes, are hindered.

Therefore, more attention should be paid to the resource service and ability transaction management in the SOM system. In this article, in order to promote the three types of users’ (i.e. RSP, agent, and RSD) comprehensive utility in the SOM system, so as to enable the SOM system to be accepted and used in practice, and resource service transaction chains (RSTCs) are studied. Three key issues, including utility modelling, utility equilibriums, and utility coordination are emphasized. The main innovative works and contributions of this article are as follows.

The comprehensive utility models considering the revenue, time, and reliability for the three sides, i.e. RSP, RSD, and agent, in the resource service transaction process in a SOM system faced with uncertain factors under decentralized decision-making conditions, are established.

The related comprehensive utility model for the RSTC of ‘multiple RSPs–one agent–multiple RSDs’ under a centralized decision-making condition is investigated and discussed.

The existence of utility equilibriums between RSP and agent, and agent and RSD are proved in the optimal decision of a RSTC under the decentralized decision-making condition.

A utility coordination method is proposed in order to enhance the comprehensive utility for the three type users in the SOM system.

A case study is given out to illustrate the proposed method in this article.

The article is organized as follows. The related works are investigated, and the innovative works of this article are highlighted. The motivation of this article is then defined. The related definitions of resource service utility and the parameters used in this article are presented. The utility modes for RSD, agent, and RSD under decentralized decision-making conditions are then studied, as well as the comprehensive utility mode for the RSTC, i.e. RSD–agent–RSP, in a SOM system. The utility equilibrium between RSP and agent, under decentralized decision-making conditions is investigated, as well as the utility equilibrium between RSD and agent. A utility coordination method is studied with the aim of improving the comprehensive utility of the RSTC under decentralized decision-making conditions. A case study is given before this study is then concluded.

Related works

The immediate quantitative works on the utility of a RSTC in the SOM system are seldom. Some related work can be found in the research field of NM and MGrid. Other related works can be found in the fields of supply chain management (SCM) and the computing grid system.

In the field of the MGrid, a lot of qualitative works about the resource service management system and model,³⁹ architecture of the cooperation service for transaction chain,^40–41 benefit allocation mechanism,^42–44 resource service discovery and scheduling mechanism and algorithm,⁶ resource service composition,⁶ and so forth, have been done, as shown in Table 1. In the field of NM, related works primarily are about the model of multi-agent-based consultation system or model,⁴⁵ and operation model for the transaction chain.⁴⁶ The operation of a two-level supply chain is investigated from the aspects of revenue and performance evaluation of a resource service transaction in NM.^47–48 The concept of utility equilibrium in SOM is expanded from the game theory in economics. Each economic entity makes a decision to get itself maximal utility. The utility equilibrium decision is the optimal decision that makes the utilities of the entities maximal at the same time. If it is not the equilibrium decision, the resource service transaction will be dynamic and unstable so that the entities change their decision to obtain their own maximal utilities. However, how to achieve the utility equilibrium between RSP and RSD while maximizing the utilities for RSP, RSD and the transaction are not fully considered and effectively researched.

Table 1.

Related works in MGrid and NM.

	Reference	Brief summary of the content
MGrid	39	Resource management architecture for MGrid based on computing economy was presented, which can provide service for application with different QoS requirements. The resource discovering and trading model in the architecture were discussed.
	40	A trading-supported manufacturing resources sharing model was presented, as well as the resource selection process in the model (including resource discovering and resource trading).
	41	Resource trading techniques and methods were discussed and studied, and the economic roles were introduced in the trading process. A resource trading model and service match and negotiation mechanism were investigated.
	42	An economic structure of MGrid resource allocation was constructed, the feasible Pareto optimal resource-allocation conditions under complete competition market was studied, the competitive equilibrium of Pareto optimal resource-allocation as well.
	43	The benefit distribution for each manufacturing resource node in MGrid was studied based on the Nash negotiation model.
	44	A benefit-oriented and agent-based MGrid resource management model was proposed using a cell organization management modelling method.
NM	45	A multi-agent negotiation system model was presented for adapting the frequent changes of the members in the supply chain, the negotiation protocol and negotiation process were designed to reach mutually beneficial agreements.
	46	A supply chain operation model based on NM was discussed in order to enhance the information cooperation among enterprises, and an evaluation system of the supply chain was established.
	47	A two-stage supply chain (i.e. manufacture and retailer) coordination model was established based on revenue-sharing contract. The game strategy between the manufacturer and retailer was analysed, and the profit influence of related parameters to enterprises was discussed.
	48	A supply chain operation model was proposed based on NM, and a two-stage supply chain coordination model was established by analysing the process of supply chain using a object-oriented Petri Net and revenue-sharing contract method. The coordination strategies, with order quantity and wholesale price, were found through the Stackelberg game analysis.

MGrid: manufacturing grid; QoS: quality of service; NM: networked manufacturing.

In the field of SCM, the research works are primarily concentrating on coordination and optimization of the supply chain under supply uncertainty or demand uncertainty environments, as shown in Table 2. The studied supply chain modes primarily are ‘one-to-one’^{49–50,52,54–56} models (i.e. one manufacture/supplier and one distributor), or ‘multiple–one’ models.^{51,53,57–58} As an uncertain environment, including supply uncertain, demand uncertain, and supply and demand uncertain, there is not much research about supply chain modes under supply and demand uncertain.^49–51,53 However, in a SOM system, the RSTC is a complex model, i.e. multiple RSPs, single agent, and multiple RSDs. The RSTC is under the uncertain supply and demand environment. Therefore, the RSTC model is much more difficult and complex than the literatures of supply chain models in Table 2, the related method and approached in the supply chain models cannot simply and directly be used in the RSTC of a SOM system.

Table 2.

Related works in SCM.

Reference	Methods and contents	Uncertain environment		Structure of supply chain
		Supply	Demand	O–O	M–O
49	A global supply chain production planning model including fuzzy demands and stochastic throughput was proposed, and the model was mapped into a fuzzy opportunity constraint planning model. The optimal solution was achieved using a hybrid algorithm (i.e. genetic algorithm combined with fuzzy simulation technology).	√	√	√
50	A dynamic robust operating model of multiple-products and multiple-stage SCM with uncertain demands and supplies that satisfies several conflict objectives, such as coordination operation, maximizing profit of all participants, robustness of decision to uncertain demands and supplies, was investigated.	√	√	√
51	An investigation on two levels – VM and suppliers – was conducted, and the results of the case studies illustrated an increased level of customization that would create more uncertainty to the extant supply chains.	√	√		√
52	The coordination problem of supply chain contract under the uncertain demand based on inventory management was investigated. The necessary condition of obtaining the coordination of supply chain and the specific impact were discussed to achieve the Pareto optimization and the best overall performance of supply chain.		√	√
53	A decentralized assembly system under the random demand and the yield of supplier was considered. The concavity of expected supply chain profit was established and the qualitative insights based on a numerical illustration of centralized and decentralized solutions were provided.	√	√		√
54	A computer model was developed to simulate the complex multi-level supply-chain model based on the effectiveness of information sharing under demand uncertainty scenarios. The simulation results obtained by using the proposed new supply chain performance measure mechanism illustrated that, both distributors and suppliers gained significantly from information sharing, except retailers.		√	√
55	A supply-chain model comprising of one supplier and one retailer was studied, and the members of the supply chain interacted at the beginning of each period, the retailer orders, and at the end of each period, the salvage value of the remaining products being zero. In the established model, the demands were uncertain but correlated or non-correlated across the two periods.		√	√
56	A two stages logistics supply chain, with one logistics service integrator and one functional logistics service provider, was studied. The mathematical modes of three coordination strategies (i.e. centralized coordination, Stackelberg game coordination and competitive aligned coordination) were investigated based on the market that was characterized by a price sensitive random demand, and the realization conditions for optimal solution under different coordination strategies were introduced.		√	√
57	A supply chain composed of competing multi-manufacturers and an independent and common retailer based on contract negotiations was studied, and a Stackelberg game model was constructed in which manufacturers were leaders while the retailer was the follower.				√
58	A supply chain, composed of two suppliers and one manufacturer, with random yield was studied. The optimal lot sizing was analysed under a centralized decision, and the optimal lot sizing decision under overflow inventory cost was constructed for suppliers and manufacturers. Nash equilibrium was proved to exist between suppliers and manufacturer when overflow inventory cost was considered. It proved that the profit of supply chain under Nash equilibrium was no more than that under a centralized decision.	√			√

O–O: one-to-one model; M–O: multiple-to-one model; SCM: supply chain management; VM: vehicle manufacturers.

In the field of grid computing systems, some works have been conducted on utility-based resource scheduling and allocation, and the factors considered in the utility are primarily time, quality of service, and budget.^59–64 Related works are illustrated in Table 3. Because many grid systems are developed for a community or an organization and aim to share computational resources, such as processor resources, network resources, and storage resources, the benefit among computational resource providers and users are not paid too much attention. As a result, few works can be found about the resource or service transaction chain. As well as the grid computing system, the SOM system also pays attention to both cost and system performance. However, different from the utility of grid computing system, it is much more important to consider reliability and time in the SOM system.

Table 3.

Related works in computing grid system.

References	Methods and contents
59	The grid scheduling problem from a business perspective was discussed, the managerial insights for all three entities (job owners, resource owners, and the scheduler) were provided, and the heuristics for different variants of the problem is proposed.
60	Both energy minimization for mobile devices and grid utility optimization problem were investigated. The energy aware scheduling was formalized using a nonlinear optimization theory under constraints of energy budget and deadline. A distributed pricing-based algorithm was employed to trade off energy and deadline so as to achieve a system-wide optimization based on the preference of the grid user.
61	The ATCS-MCT scheduling algorithm was proposed in which execution time, weight, due date, communication delay time, and other factors were considered. The experimental results demonstrated that the proposed ATCS-MCT scheduling algorithm outperforms the Min–min heuristics algorithms in terms of makespan and costs.
62	A utility function was proposed as a promising method for grid resource allocation, and the optimal solution was obtained by finding the equilibrium point of resource price. The experimental results run on Java-based discrete GridSim illustrated that utility optimization under budget constraint outperforms deadline constraint in terms of time spent, whereas deadline constraint outperforms budget constraint in terms of cost spent.
63	A continuous double auction method for grid resource allocation was presented in which resources were considered as provider agents and users as consumer agents, and the method was investigated in terms of economic efficiency and system performance.
64	A utility model for resource allocation on computational grid was introduced and the allocation problem was formulated as a variant of the 0–1 multi-choice knapsack problem.

ATCS-MCT: Apparent Tardiness Cost Setups-Minimum Completion Time.

Therefore, in order to promote the three user types (i.e. RSP, agent, and RSD) comprehensive utility in the SOM system, so as to enable the SOM system to be accepted and used in practice, RSTC under uncertain supply and demand environments are studied in this article. Three key issues, including utility modelling, utility equilibriums, and utility coordination are emphasized in this study. According to the utility equilibriums and utility coordination research, the comprehensive utilities of RSTC, RSP and RSD under decentralized decision making are improved. Compared with the current related approaches researches, this article will realize the optimal result of RSTC in SOM with higher revenue, higher reliability, and lower time.

Motivation

According to the abstract architecture of SOM, there are RSPs, agent, and RSDs in these three classes of users in the SOM system. Assuming that there are lots and lots of manufacturing resource services of multiple RSPs published on the agent platform, the RSTC is defined as shown in Figure 2. At first, RSDs with multiple manufacturing requirement tasks submit the service request to the agent platform. The agent then makes the service search and match work for the published services and the requested services based on knowledge. After searching and matching the suitable services, the agent will do the utility evaluation of the services transaction to guide the resource service transaction among RSPs, agent, and RSDs. As to the manufacturing enterprises, they can be the economical entities not only to RSP but also to RSD. The SOM system can be widely practiced under the best service utility evaluation of the agent. The manufacturing enterprises attain many more utilities than the without the SOM system. That is to say, the manufacturing enterprises will all be more willing to share their resource services. The utility equilibrium and utility coordination under the service utility evaluation is much more necessary and important to the system of SOM.

Figure 2.

The flow of RSTC in a SOM system.

Related definition

Parameter definition

As the SOM system has the characteristics of being complex, dynamic, and heterogeneous, the whole RSTC is facing many uncertain factors. This article primarily emphasizes:

how to maximize the comprehensive utility for each side (e.g. RSD, RSP, and agent) or the whole system in RSTC;

how to determine their own demand quantity (or supply quantity) of resource service for the RSD and agent (or the RSP and agent), which involves the uncertain supply of the RSP and the uncertain demand of the RSD.

The used symbols in this article are defined in the Appendix.

It is assumed that the demanded quantity of the resource service that RSD_i submits to the agent via a SOM system or platform is d_j⁰, the agent issues the request q_i⁰ to RSP_i, and the quantity that RSP_i can provide to the agent is q_i. For the consideration of maximizing their respective utilities, the comparison results of d_j⁰, q_i⁰, and q_i is uncertain in the transaction. Furthermore, the amount of resource service that RSP_i can provide is dynamic and uncertain. Therefore, the actual quantity that $RS P_{i}$ provides to the agent is min(q_i, q_i⁰), and the actual amount of resource service that the agent provides to RSD_i is min(d_j, d_j⁰). In this study, only two RSPs, one agent, and two RSDs, i.e. the RSTC ‘two RSP–one Agent–two RSD’ model, are considered in the RSTC.

Definition of utility

In economics, utility is used to describe the degree of consumers’ satisfaction that buying or using something provides. Expanded to the SOM system, the concept of utility evaluat is proposed to describe both the economic efficiency and the comprehensive system performance to provide, use, or transact resource service for RSP, RSD, and agent. In the SOM system, the system of utility evaluation contains many evaluating parameters such as time, cost, reliability, function similarity, security, maintainability, and satisfaction, etc.²⁸ As to the three sides in the SOM system, they all pay much more attention to solve this problem which is how to get the highest revenue in least time with best reliability. For the consideration of reducing the complexity and ease for computing, only time, cost and reliability are considered in this article, i.e. the comprehensive utility models consist of three parts, the revenue utility, the time utility, and the reliability utility, which is in order to make normalization processing for utility evaluation. They are defined as follows.

The revenue utility: $U^{B} = U_{0} (1 - e^{- bB})$ , where $U_{0}$ is the base utility, b is the coefficient, and the revenue B is a function of $d_{j}^{0}, d_{j}, q_{i}^{0}, q_{i}$ , and $B \geq 0$ .

The time utility: $U^{T} = U_{0} + u (T_{D} - T)^{+} - v (T - T_{D})^{+}$ , where $T_{D}$ is the given deadline, u and v are the impact coefficients of the time utility when the task is completed before or after $T_{D}$ , and $0 \leq u, v \leq 1$ , T is the time spent on each subject or the whole RSTC to complete the task, and T is a function of $d_{j}^{0}, d_{j}, q_{i}^{0}, q_{i}$ . Where, if A≥0, then (A)⁺= A, otherwise, (A)⁺=0.

The reliability utility: $U^{R} = U_{0} (1 - 1 / R)$ , where the reliability R is also a function of $d_{j}^{0}, d_{j}, q_{i}^{0}, q_{i}$ .

Therefore, the comprehensive utility model considering revenue, time, and reliability of each side in the RSTC is formulated as

U = α U^{B} + β U^{T} + γ U^{R} = (\begin{matrix} U_{0} - α U_{0} e^{- bB} \\ + β u (T_{D} - T)^{+} - \\ β v (T - T_{D})^{+} - γ U_{0} 1 / R \end{matrix})

(1)

Where $α$ , $β$ , and $γ$ ( $0 \leq α, β, γ \leq 1$ and $α + β + γ = 1$ ) are the weighing coefficients of the revenue utility, the time utility, and the reliability utility, respectively.

The objective function for maximizing the utility for each side in the RSTC in this article is $max (U)$ . The aim for investigating the utility equilibrium is to find the resource service supply and demand quantity to make the comprehensive utility of each side have the maximum at the same time. The aim for investigating the utility coordination is to realize, not only the optimal comprehensive utility of RSTC, but also the three sides.

Utility modelling

The following utility models are based on one resource service transaction, at some time after a class of resource service requirements of RSDs have been submitted.

Utility model under the decentralized decision-making condition

Under the decentralized decision-making condition, each side will consider the expected utility to be the largest, so as to make the best decision. It is assumed that each side is entirely rational, in order to make sure that the requirement of the resource service of the RSD can be met. The total request quantity of the resource service of the agent is bigger than or equal to that of RSD, and the quantity of the resource service centralized by the agent is bigger than or equal to the total supply quantity that the agent provides for the RSD. It means that ∑q_i⁰_>∑d_j⁰ and ∑min(q_i, q_i⁰)_>∑min(d_j, d_j⁰). Figure 3 is a schematic drawing of the utility modelling under the decentralized decision-making condition. The comprehensive utility models for RSP, agent, and RSD are investigated in the following subsections.

Figure 3.

The schematic drawing of the utility modelling under a decentralized decision-making condition.

The comprehensive utility of the RSP_i

Faced with the agent issues the request q_i⁰ to RSP_i, and the quantity that RSP_i can provide to the agent is q_i, then the actual quantity that RSP_i provides to the agent is min(q_i, q_i⁰).

When providing services to the agent, the revenue of RSP_i is related to the incomes of providing resource services to the agent, and the cost that includes the fixed cost, the variable cost, punishment to the agent of lacking service (q_i < q_i⁰), the overflow cost of service (q_i > q_i⁰), and the service fee paid to the agent. Then the revenue of RSP_i is

B_{pi} = (\begin{matrix} w_{i} min (q_{i}, q_{i}^{0}) - c_{pi}^{0} T_{pi} - c_{pi} q_{i} - \\ s_{i} (q_{i}^{0} - q_{i})^{+} - k_{i} (q_{i} - q_{i}^{0})^{+} - e_{p} \end{matrix})

(2)

The time of RSP_i is consisted of the execution time of providing service and the time of communication to the agent. Then the computing formulate of the time of RSP_i is

T_{pi} = t_{pi} q_{i} + min (q_{i}, q_{i}^{0}) / V

(3)

Considering the communication of RSP_i and the agent, RSP_i and the agent are regarded as two nodes, then the reliability of RSP_i is

R_{pi} = e^{λ_{1 i} min (q_{i}, q_{i}^{0}) / V + θ_{pi} t_{pi} q_{i}}

(4)

According to equation (2)–(4), the comprehensive utility of RSP_i is

U_{pi} = (\begin{matrix} U_{0} - α U_{0} e^{- b (\binom{w_{i} min (q_{i}, q_{i}^{0}) - c_{pi}^{0} T_{pi} - c_{pi} q_{i} -}{s_{i} (q_{i}^{0} - q_{i})^{+} - k_{i} (q_{i} - q_{i}^{0})^{+} - e_{p}})} \\ \begin{matrix} + β u (T_{D}^{pi} - (t_{pi} q_{i} + min (q_{i}, q_{i}^{0}) / V {))}^{+} \\ - β v ((t_{pi} q_{i} + min (q_{i}, q_{i}^{0}) / V) - T_{D}^{pi})^{+} \end{matrix} \\ - γ U_{0} e^{- (λ_{1 i} min (q_{i}, q_{i}^{0}) / V + θ_{pi} t_{pi} q_{i})} \end{matrix})

(5)

After computing, one has $U_{pi}' = 0$ and $U_{pi} < 0$ . It means there is only one optimum solution ${q_{i}}^{*}$ , that can make U_pi be the maximum, and ${q_{i}}^{*}$ satisfies the following requirements from $U_{pi}' = 0$

α bA e^{- b ({Aq}_{i}^{*} + {Dq}_{i}^{0} - e_{p})} + γ C e^{- ({Cq}_{i}^{*} + {Fq}_{i}^{0})} = β uE / U_{0}

(6)

As min(q_i, q_i⁰) has two instances, the constraints of the maximal utility of RSP_i are different under each instance. When $min (q_{i}, q_{i}^{0}) = q_{i}, A = w_{i} + s_{i} - c_{pi}^{0} E - c_{pi},$ then

C = λ_{1 i} / V + θ_{pi} t_{pi}, D = - s_{i}, E = t_{pi} + 1 / V, F = 0

When $min (q_{i}, q_{i}^{0}) = q_{i}^{0}, A = - (c_{pi}^{0} t_{pi} + c_{pi} + k_{i}),$ then

C = θ_{pi} t_{pi}, D = w_{i} + k_{i} - c_{pi}^{0} / V, E = t_{pi}, F = λ_{1 i} / V

The comprehensive utility of the agent

The agent is the linkage of RSP and RSD, RSPs and RSDs pay some service fee to the agent. As the actual quantity that RSP_i provides to the agent is min(q_i, q_i⁰), and the actual amount of resource service that the agent provides to RSD_i is min(d_j, d_j⁰), the revenue, time, and reliability of the agent are much more complex as follows.

When purchasing services from RSPs and providing services to RSDs, the revenue of the agent is related to the incomes of providing resource services to RSDs, the service fee paid by RSPs and RSDs, and the default punishment of RSDs, and the cost of including the fixed cost, the variable cost, the cost of purchasing services form RSPs, punishment to RSDs of lacking service (d_j < d_j⁰), and the overflow cost of service (d_j > d_j⁰). Then the revenue of the agent is

B_{a} = (\begin{matrix} \sum_{j = 1}^{2} p_{j} min (d_{j}, d_{j}^{0}) + 2 (e_{d} + e_{p}) + \sum_{i = 1}^{2} s_{i} {(q_{i}^{0} - q_{i})}^{+} - c_{a}^{0} T_{a} \\ - \sum_{j = 1}^{2} c_{a} d_{j}^{0} - \sum_{i = 1}^{2} w_{i} min (q_{i}, q_{i}^{0}) - \sum_{j = 1}^{2} h_{j} (d_{j}^{0} - d_{j})^{+} + \\ \sum_{j = 1}^{2} l_{j} (d_{j} - d_{j}^{0})^{+} - k_{a} (\sum_{i = 1}^{2} min (q_{i}, q_{i}^{0}) - \sum_{j = 1}^{2} min (d_{j}, d_{j}^{0})) \end{matrix})

(7)

The time of the agent is consisted of the time to communicate with RSPs, the time to communicate with RSDs, and the resource services dealing time of the agent

T_{a} = \sum_{i = 1}^{2} q_{i}^{0} / V + t_{a} \sum_{j = 1}^{2} d_{j}^{0} + \sum_{j = 1}^{2} min (d_{j}, d_{j}^{0}) / V

(8)

As well as the communication with RSPs, the agent and RSDs are also regarded as some nodes. The reliability of the agent is

R_{a} = e^{\sum_{i = 1}^{2} λ_{1 i} q_{i}^{0} / V + \sum_{j = 1}^{2} λ_{2 j} min (d_{j}, d_{j}^{0}) / V + θ_{a} t_{a} \sum_{j = 1}^{2} d_{j}^{0}}

(9)

According to equation (7)–(9), the comprehensive utility of the agent is as

U_{a} = (\begin{matrix} U_{0} - α U_{0} e^{(\binom{- b (\sum_{j = 1}^{2} p_{j} min (d_{j}, d_{j}^{0}) + 2 (e_{d} + e_{p}) + \sum_{i = 1}^{2} s_{i} {(q_{i}^{0} - q_{i})}^{+}}{\binom{- c_{a}^{0} T_{a} - \sum_{j = 1}^{2} c_{a} d_{j}^{0} - \sum_{i = 1}^{2} w_{i} min (q_{i}, q_{i}^{0}) - \sum_{j = 1}^{2} h_{j} (d_{j}^{0} - d_{j})^{+}}{+ \sum_{j = 1}^{2} l_{j} (d_{j} - d_{j}^{0})^{+} - k_{a} (\sum_{i = 1}^{2} min (q_{i}, q_{i}^{0}) - \sum_{j = 1}^{2} min (d_{j}, d_{j}^{0})))}})} \\ + β u (T_{D}^{a} - (\sum_{i = 1}^{2} q_{i}^{0} / V + t_{a} \sum_{j = 1}^{2} d_{j}^{0} + \sum_{j = 1}^{2} min (d_{j}, d_{j}^{0}) / V {))}^{+} \\ - β v ((\sum_{i = 1}^{2} q_{i}^{0} / V + t_{a} \sum_{j = 1}^{2} d_{j}^{0} + \sum_{j = 1}^{2} min (d_{j}, d_{j}^{0}) / V) - T_{D}^{a})^{+} \\ - γ U_{0} e^{- (\sum_{i = 1}^{2} λ_{1 i} q_{i}^{0} / V + \sum_{j = 1}^{2} λ_{2 j} min (d_{j}, d_{j}^{0}) / V + θ_{a} t_{a} \sum_{j = 1}^{2} d_{j}^{0})} \end{matrix})

(10)

Based on the comprehensive utility model of the agent, the only extrenal solution $(q_{i}^{0 *}, {d_{j}}^{*})$ can be obtained, and $q_{i}^{0 *}$ satisfies

\frac{\partial U_{a}}{\partial q_{i}^{0}} = (\begin{matrix} α U_{0} (w_{i} + k_{a}) e^{- b B_{a}} - β u / V \\ + (γ U_{0} λ_{1 i} / V) R_{a}^{- 1} \end{matrix}) = 0

(11)

Where $q_{i}^{0 *} < q_{i}$ and ${d_{j}}^{*}$ satisfies

\frac{\partial U_{a}}{\partial d_{j}} = (\begin{matrix} α U_{0} (p_{i} + h_{i} - c_{a}^{0} / V - k_{a}) e^{- b B_{a}} \\ - β u / V + γ U_{0} (1 / V) R_{a}^{- 1} \end{matrix}) = 0

(12)

Taking the frontier point $(q_{i}^{0} = q_{i}, d_{j}^{*})$ , as $U_{a}^{B}, U_{a}^{T}, U_{a}^{R}$ all grow down along with the increasing of $q_{i}^{0}$ , $U_{a}$ is inversely proportional to $q_{i}^{0}$ and $q_{i}^{0 *} < q_{i}$ , so ${U_{a}}_{(q_{i}^{0 *}, d_{j}^{*})} > {U_{a}}_{(q_{i}, d_{j}^{*})}$ . Therefore, $(q_{i}^{0 *}, {d_{j}}^{*})$ is not the minimum point but the maximum point.

The comprehensive utility of RSD_i

The demanded quantity of the resource service that RSD_i submits to the agent via a SOM system or platform is d_j⁰, and the quantity that the agent can provide to RSD_i is d_j. Then the actual amount of resource service transaction between the agent and RSD_i is min(d_j, d_j⁰).

The revenue of RSD_i is related to the incomes of executing the service on-demand and the punishment from the agent of lacking service, and the cost that includes the fixed cost, the cost of purchasing service from the agent, and the service fee paid to the agent. Then the revenue of RSD_i is

\begin{matrix} B_{dj} = (r_{j} - p_{j}) min (d_{j}, d_{j}^{0}) + h_{j} (d_{j}^{0} - d_{j})^{+} \\ - l_{j} (d_{j} - d_{j}^{0})^{+} - c_{dj}^{0} T_{dj} - e_{d} \end{matrix}

(13)

The time of RSD_i consists of the time to execute service and the waiting time of sending services request

T_{dj} = d_{j}^{0} / V + t_{dj} min (d_{j}, d_{j}^{0})

(14)

Similarly to RSPs and the agent’s reliabilities, the reliability of RSD_i is

R_{dj} = e^{λ_{2 j} d_{j}^{0} / V + θ_{dj} t_{dj} min (d_{j}, d_{j}^{0})}

(15)

According to equation (13)–(15), the comprehensive utility of RSD_i is

U_{dj} = (\begin{matrix} U_{0} - α U_{0} e^{(\binom{- b ((r_{j} - p_{j}) min (d_{j}, d_{j}^{0}) + h_{j} (d_{j}^{0} - d_{j})^{+}}{- l_{j} (d_{j} - d_{j}^{0})^{+} - c_{dj}^{0} T_{dj} - e_{d})})} \\ + β u (T_{D}^{dj} - (d_{j}^{0} / V + t_{dj} min (d_{j}, d_{j}^{0} {)))}^{+} \\ - β v ((d_{j}^{0} / V + t_{dj} min (d_{j}, d_{j}^{0})) - T_{D}^{dj})^{+} \\ - γ U_{0} e^{- (λ_{2 j} d_{j}^{0} / V + θ_{dj} t_{dj} min (d_{j}, d_{j}^{0}))} \end{matrix})

(16)

Similarly to the comprehensive utility of RSP_i, it is subsistent that ${U'}_{dj} = 0$ and ${U ″}_{dj} < 0$ for RSD_i. It means that there is only one optimum solution $d_{j}^{0 *}$ , which makes the comprehensive utility have maximum value, and $d_{j}^{0 *}$ satisfies the following requirement

α bD e^{- b (A' d_{j}^{0 *} + D' d_{j} - e_{d})} + γ C' e^{- (C' d_{j}^{0 *} + F' d_{j})} = β u E' / U_{0}

(17)

As min(d_j, d_j⁰) has two instances, the constrains of the maximal utility of RSD_i are different under each instance. When $min (d_{j}, d_{j}^{0}) = d_{j}^{0}, A' = r_{j} + l_{j} - p_{j} - c_{dj}^{0} (t_{dj} + 1 / V),$ then

C' = λ_{2 j} / V + θ_{dj} t_{dj}, D' = - l_{j}, E' = t_{dj} + 1 / V, F' = 0

When $min (d_{j}, d_{j}^{0}) = d_{j}, A' = l_{j} - c_{dj}^{0} V, C' = λ_{2 j} / V,$ then

D' = r_{j} - p_{j} - h_{j} - c_{dj}^{0} t_{dj}, E' = 1 / V, F' = θ_{dj} t_{dj}

Utility model under the centralized decision-making condition

Under the centralized decision-making condition, the optimal solution must make the utility of the RSTC have the biggest value. RSP, RSD, and the agent discuss together to decide their own demand or supply of resource service, therefore $q_{i} = q_{i}^{0}$ , $d_{j} = d_{j}^{0}$ , and $\sum q_{i}^{0} = \sum d_{j}^{0} = M$ . Figure 4 is the schematic drawing of the utility model under the centralized decision-making condition.

Figure 4.

The schematic drawing of the utility model under a centralized decision-making condition.

Under the centralized decision-making condition, the revenue B_c, the time T_c, and the reliability R_c of the RSTC that comprehensively considering RSPs, the agent, and RSDs of the RSTC in the SOM system are formulated as equations (18), (19), and (20), respectively

\begin{matrix} B_{c} = \sum B_{pi} + B_{a} + \sum B_{dj} \\ = (\begin{matrix} \sum (r_{j} + k_{a} - c_{dj}^{0} t_{dj} - c_{dj}^{0} / V - c_{a}^{0} t_{a} - c_{a} - c_{a}^{0} / V) d_{j}^{0} \\ - \sum (k_{a} + c_{pi}^{0} / V + c_{pi}^{0} t_{pi} + c_{pi} - c_{a}^{0} / V) q_{i} \end{matrix}) \end{matrix}

(18)

\begin{matrix} T_{c} = \sum T_{pi} + T_{a} + \sum T_{dj} \\ = \sum (t_{pi} + 2 / V) q_{i} + \sum (t_{a} + 2 / V + t_{dj}) d_{j}^{0} \end{matrix}

(19)

\begin{matrix} R_{c} = R_{a} Π R_{pi} Π R_{dj} \\ = e^{Σ (2 λ_{1 i} / V + θ_{pi} t_{pi}) q_{i} + Σ (2 λ_{2 j} / V + θ_{dj} t_{dj} + θ_{a} t_{a}) d_{j}^{0}} \end{matrix}

(20)

According to equations (18)–(20), the comprehensive utility model of the RSTC under the centralized decision-making is formulated as

U_{c}^{c} = (\begin{matrix} U_{0} - α U_{0} e^{- b (\binom{(\sum (r_{j} + k_{a} - c_{dj}^{0} t_{dj} - c_{dj}^{0} / V - c_{a}^{0} t_{a} - c_{a} - c_{a}^{0} / V) d_{j}^{0}}{- \sum (k_{a} + c_{pi}^{0} / V + c_{pi}^{0} t_{pi} + c_{pi} - c_{a}^{0} / V) q_{i})})} \\ + β u {(T_{D}^{c} - (\sum (t_{pi} + 2 / V) q_{i} + \sum (t_{a} + 2 / V + t_{dj}) d_{j}^{0}))}^{+} \\ - β v {((\sum (t_{pi} + 2 / V) q_{i} + \sum (t_{a} + 2 / V + t_{dj}) d_{j}^{0}) - T_{D}^{c})}^{+} \\ - γ U_{0} e^{- (\sum (2 λ_{1 i} / V + θ_{pi} t_{pi}) q_{i} + \sum (2 λ_{2 j} / V + θ_{dj} t_{dj} + θ_{a} t_{a}) d_{j}^{0})} \end{matrix})

(21)

Because the resource service demand information is transparent under the centralized decision-making, and M is certain, therefore, there is only one variable, i.e. $q_{i}$ , in equation (21) in fact.

Let $G = (c_{p 1}^{0} / V + c_{p 1}^{0} t_{p 1} + c_{p 1}) - (c_{p 2}^{0} / V + c_{p 2}^{0} t_{p 2} + c_{p 2})$ and $H = (2 λ_{12} / V + θ_{p 2} t_{p 2}) - (2 λ_{11} / V + θ_{p 1} t_{p 1})$ to simplify the utility formulate of RSTC. If the algebraic symbols of $G$ and $H$ are the same, $U_{c}$ is monotone, and the optimum solution is ${q_{i}}^{C *} = 0$ or ${q_{i}}^{C *} = M$ . Otherwise, the optimum solution ${q_{i}}^{C *}$ meets

- α U_{0} G e^{- b B_{c}} - γ U_{0} {HR}_{c}^{- 1} = β u (t_{pi} + 2 / V)

(22)

Utility equilibrium

Under decentralized decision-making, each user of the SOM makes the service provider or requirement quantity for their own maximal utility. However, how to find the optimal result that results in the maximal utilities of RSPs, the agent and RSDs at the same time is much more important, then the utility equilibrium is necessary. There are three sides in the RSTC ‘RSP–Agent–RSD’, i.e. RSD, RSP, and the agent, therefore, the related utility equilibrium study can be divided into two parts: the utility equilibrium between RSP and the agent, and the utility equilibrium between RSD and the agent.

The utility equilibrium between RSP and the agent

According to the previous sections, one can know that the optimal solution of RSP and agent can be solved by getting the derivative or partial derivative under the decentralized decision-making. One can get the equations $d U_{pi} / d q_{i} = 0, \partial U_{a} / \partial q_{i}^{0} = 0$ and make the equilibrium analysis.

According to Ma and Li,⁵⁸ as to the differentiable function $f (x)$ and $g (x)$ , if there always exists $f' (x) - g' (x) < 0$ or $f' (x) - g' (x) > 0$ for all x, there is only one x^* that can meet the function $f (x^{*}) = g (x^{*})$ . Adopting the reduction to absurdity, it is assumed that $d^{2} U_{pi} / d {q_{i}}^{2} = \partial^{2} U_{a} / \partial q_{i}^{02}$ , there is an equation that getting from the above assumption $((w_{i} + k_{a})^{2} e^{- b B_{a}} - A^{2} e^{- b B_{pi}}) / (C^{2} R_{pi}^{- 1} - (λ_{1 i} / V)^{2} R_{a}^{- 1}) = γ / α b^{2}$ . But according to $d U_{pi} / d q_{i} = 0, \partial U_{a} / \partial q_{i}^{0} = 0$ , one can get

\frac{{(w_{i} + k_{a})}^{2} e^{- b B_{a}} - A^{2} e^{- b B_{pi}}}{C^{2} R_{pi}^{- 1} - {(λ_{1 i} / V)}^{2} R_{a}^{- 1}} < \frac{γ}{α b} < \frac{γ}{α b^{2}}

(23)

Therefore the above assumption $d^{2} U_{pi} / d {q_{i}}^{2} = \partial^{2} U_{a} / \partial q_{i}^{02}$ has failed compared with equation (23), then there is only one set of equilibrium solution $({q_{i}}^{* E}, q_{i}^{0 * E})$ for the equations $d U_{pi} / d q_{i} = 0, \partial U_{a} / \partial q_{i}^{0} = 0$ , which can maximize the comprehensive utilities of RSP_i and the agent at the same time.

The utility equilibrium between RSD and the agent

The optimal solution of RSD and the agent can also be solved by derivative or partial derivative under the decentralized decision-making. One can also get the equations $\partial U_{a} / \partial d_{j} = 0, d U_{dj} / {dd}_{j}^{0} = 0$ and make the same equilibrium analysis as follows with the reduction to absurdity. If it is assumed that $d^{2} U_{dj} / {dd}_{j}^{02} = \partial^{2} U_{a} / \partial {d_{j}}^{2}$ , then one can get

\frac{{(p_{i} + h_{i} - c_{a}^{0} / V - k_{a})}^{2} e^{- b B_{a}} - {A'}^{2} e^{- b B_{dj}}}{{C'}^{2} R_{dj}^{- 1} - {(1 / V)}^{2} R_{a}^{- 1}} = \frac{γ}{α b^{2}}

(24)

But according to $\partial U_{a} / \partial d_{j} = 0, d U_{dj} / {dd}_{j}^{0} = 0$ , there exists

\frac{{(p_{i} + h_{i} - c_{a}^{0} / V - k_{a})}^{2} e^{- b B_{a}} - {A'}^{2} e^{- b B_{dj}}}{{C'}^{2} R_{dj}^{- 1} - {(1 / V)}^{2} R_{a}^{- 1}} < \frac{γ}{α b} < \frac{γ}{α b^{2}}

(25)

Therefore, the assumption also fails similarly to the equilibrium analysis of RSP and the agent, and there is only one set of equilibrium solution $(d_{j}^{* E}, d_{j}^{0 * E})$ , which can maximize the comprehensive utilities of RSD and the agent at the same time.

Utility coordination

Under the decentralized decision-making condition, if each side (i.e. RSP, the agent and RSD) decides its demand and supply quantities according to their resource service equilibrium solutions, then each of them will have the biggest utility. However, the comprehensive utility for the whole RSTC under the decentralized decision-making condition would be smaller than (or equal at best) to the maximal utility under the centralized decision-making condition. Therefore, how to improve the comprehensive utility of the RSTC under the decentralized decision-making condition, and enable it close to the maximal or optimal utility of RSTC under the centralized decision-making condition, is a key for realizing added-value of service in the SOM system.

In this article, a coordination method is used to change the single sides comprehensive utility model and break the equilibrium solution under the decentralized decision-making condition, so as to make the comprehensive utility of the whole RSTC close to the maximal utility of the RSTC under the centralized decision-making condition as much as possible, and increase each side’s maximal utility at the same time. The detailed coordination method is that an agreement between RSP_i and the agent is achieved first. In this agreement both RSP_i and the agent agree to adjust their asking price for the resource service, and let the adjusting coefficient be a_i. Furthermore, the cost for the redundant resource service is afforded by RSP_i and the agent together, according to a coordination coefficient, and let the adjusting coefficient be b_i. After the implementation of the above coordination the revenue models for RSP_i and the agent can be updated as equations (26) and (27), respectively.

B_{pi} = (\begin{matrix} (w_{i} + a_{i}) min (q_{i}, q_{i}^{0}) - c_{pi}^{0} T_{pi} - c_{pi} q_{i} - s_{i} (q_{i}^{0} - q_{i})^{+} \\ - k_{i} (q_{i} - q_{i}^{0})^{+} \\ - e_{p} - b_{i} (\sum_{i = 1}^{2} min (q_{i}, q_{i}^{0}) - \sum_{j = 1}^{2} min (d_{j}, d_{j}^{0})) \end{matrix})

(26)

B_{a} = (\begin{matrix} \sum_{j = 1}^{2} p_{j} d_{j} + 2 (e_{d} + e_{p}) + \sum_{i = 1}^{2} s_{i} {(q_{i}^{0} - q_{i})}^{+} - c_{a}^{0} T_{a} - \sum_{j = 1}^{2} c_{a} d_{j}^{0} \\ - \sum_{i = 1}^{2} (w_{i} + a_{i}) min (q_{i}, q_{i}^{0}) - \sum_{j = 1}^{2} h_{j} (d_{j}^{0} - d_{j})^{+} + \sum_{j = 1}^{2} l_{j} (d_{j} - d_{j}^{0})^{+} \\ - (k_{a} - \sum b_{i}) (\sum_{i = 1}^{2} min (q_{i}, q_{i}^{0}) - \sum_{j = 1}^{2} min (d_{j}, d_{j}^{0})) \end{matrix})

(27)

Although the revenue of RSP_i and the agent are changed after coordination, the change only takes place within the RSTC, and the total revenue of the chain will be unchanged. In order to make the comprehensive utility of the whole RSTC arrive at the maximal utility value of the RSTC under the centralized decision-making condition, the providing quantity of resource service should equal the optimal decision value q_i^c* that makes the comprehensive utility under the centralized decision-making condition the maximal value. Therefore, let the demand quantity q_i⁰ the agent asked from the RSP_i be the optimal solution q_i^c* under the centralized decision-making condition, i.e. set q_i⁰ = q_i^c*. There are only four q_i⁰, q_i, a_i and b_i variables, both in the derivation function

\frac{d U_{pi}}{d q_{i}} = 0 and \frac{\partial U_{a}}{\partial q_{i}^{0}} = 0

of the utility models after coordination. If set q_i⁰ = q_i^c* and q_i = q_i^c*, then the two coordination coefficients, i.e. a_i and b_i, can be obtained after calculation according to

{\begin{matrix} \frac{{dU}_{pi}}{d q_{i}} = α U_{0} bA e^{- b (A {q_{i}}^{c *} - s_{i} {q_{i}}^{c *} - e_{p})} - β u (t_{pi} + 1 / V) \\ + γ U_{0} C e^{- C {q_{i}}^{c *}} = 0 \\ \frac{\partial U_{a}}{\partial q_{i}^{0}} = α U_{0} b ((w_{i} + a_{i}) + (k_{a} - \sum b_{i}) e^{- b B_{a}} - \frac{β u}{V} \\ + γ U_{0} \frac{λ_{1 i}}{V} R_{a}^{- 1}) = 0 \end{matrix}}

(28)

where

A = (w_{i} + a_{i}) + s_{i} - c_{pi}^{0} (t_{pi} + 1 / V) - c_{pi} - b_{i}, C = λ_{1 i} / V + θ_{pi} t_{pi}

It means that the agent sets its demand quantity at q_i^c* and sends it to RSP_i first, then RSP_i and the agent adjusts the cooperation coefficients a_i and b_i together so as to make the optimal quantity of RSP_i providing the agent with q_i^c* too. As a result, the equilibrium under the decentralized decision-making condition before coordination is broken down, and the comprehensive utility for the whole RSTC has been improved, while the comprehensive utilities RSP and the agent has not been reduced. It realizes the added value of service in the SOM system.

Case study

It is assumed that there are two manufacturing enterprises, i.e. an aircraft manufacturing enterprise and an automobile manufacturing enterprise (denoted as RSD₁ and RSD₂, respectively), submit their design and simulation analysis service requirements to the resource service operator (denoted as the agent) via a SOM system, such as a MGrid platform, and their demand quantities are 40 and 20 services, respectively. The detailed service requirements of RSD₁ are the optimal design service of the wing’s structure, assembly simulation service of aircraft system, the optimal design service of the aircraft fuselage, etc. And the detailed service requirements of RSD₂ are the optimal design service of the engine’s structure, the optimal design service of the automobile body, the optimal design service of the automobile chassis, etc. It assumed that there are two service providers (denoted as RSP₁ and RSP₂) that can provide the related functional service, and the detailed services that RSPs can provide are the same function class of design and simulation software service such as ANSYS, Pro/E, SolidWorks, UG, CATIA, and so on. The aim of this study is to show how to apply the proposed method to help the three sides (i.e. the agent, the two RSPs and the two RSDs) to determine and adjust their resource service demand and supply quantities so as to maximize their comprehensive utility while improve the comprehensive utility of the RSTC at the same time. The related parameters for the case study as shown in Table 4 and all data analysis are done using MATLAB7.1.

Table 4.

Related parameters in the case study.

	Parameters	RSP₁	RSP₂	Parameters	Agent	Parameters	RSD₁	RSD₂
Proprietary parameters	c_pi ⁰	5	3	c_a ⁰	2	c_dj ⁰	8	10
	c_pi	3	4	c_a	1	e_d	200	200
	e_p	100	100	k_a	20	h_j	0.9	0.8
	k_i	0.3	0.5	t_a	0.1	l_j	0.6	0.7
	s_i	0.5	0.6	T_D ^a	50	p_j	70	60
	t_pi	0.1	0.3	θ_a	0.9	r_j	100	100
	w₁	20	40			t_dj	0.2	0.4
	T_D ^pi	20	20			T_D ^dj	20	20
	λ_1i	0.8	0.6			λ_2j	0.7	0.7
	θ_pi	0.8	0.6			θ_dj	0.7	0.7
Common parameters	b	u	v	U₀	V	α	β	γ
	0.01	3	5	100	5	0.5	0.2	0.3

RSP: resource service provider; RSD: resource service demander.

Utility modelling in the case study

Under the decentralized decision-making condition, facing the resource service request from the agent, the changing curves of the related comprehensive utility for RSP₁ and RSP₂, along with the changes of q_i, are illustrated in Figure 5(a) and (b). Facing the resources provided by the agent, the changing curves of the related comprehensive utility for RSD₁ and RSD₂, along with the changing of d_j⁰, are illustrated in Figure 5(c) and (d). As shown in Figure 5, there exists an optimal solution of the comprehensive utility of both RSP and RSD, which maximize the comprehensive utility of each subject. Besides the comprehensive utility curves, the curves reflecting the revenue utility (U^B_p₁), the time utility U^T_p₁ ), and the reliability utility (U^R_p₁ ), changing along with the q_i, are illustrated in Figure 5(a). As shown in Figure 5(a), when the revenue of RSP₁B_p₁ ≤ 0, its utilities are zero, and when q₁ increases to a certain amount that makes B_p1 > 0, along with the increasing of q₁, U^B_p₁ is increasing first and decreasing late, U^T_p₁ is decreasing and U^R_p₁ is increasing.

Figure 5.

Comprehensive utility curve under a decentralized decision-making condition.

Because there are four variables with wide value ranges involved in U_a, the corresponding values of U_a are calculated by dividing the value ranges into several segments. According to the calculating results, it is found that the U_a decreases along with the increase of q_i⁰ and decreases along with the increase of d_j, and a group solution exists that makes the comprehensive utility of U_a have the maximal value. The maximal values of the comprehensive utilities for each side and the related optimal solutions are shown in Table 5.

Table 5.

The maximal values of the comprehensive utilities and the related optimal solutions.

Decision-making condition	Subject	The optimal solution	The maximum of the comprehensive utility
Under the decentralized decision-making condition	RSP₁	q₁^ =* 31	Max(U_p1) = 102.2382
	RSP₂	q₂^ =* 16	Max(U_p2) = 106.3954
	Agent	(q₁^0,q₂^0,d₁^,d₂^) = (51,0,21,15)	Max(U_a) = 116.5600
	RSD₁	d₁^0 =* 23	Max(U_d1) = 102.6455
	RSD₂	d₂^0 =* 18	Max(U_d2) = 104.6514
Under the centralized decision-making condition	RSTC	(q₁^c,q₂^c) = (50,0)	Max(U_c) = 103.0000

RSP: resource service provider; RSD: resource service demander.

Under the centralized decision-making condition, if set d₁ ⁰ =d₂ ⁰ =25, then $q_{i} = q_{i}^{0}$ , $d_{j} = d_{j}^{0}$ , and $\sum q_{i}^{0} = \sum d_{j}^{0} = M$ =50. The comprehensive utility curve of the RSTC is shown in Figure 6. As illustrated in Figure 6, U_c increases with the increasing of q₁ and U_c has its maximum when q₁ = 50.

Figure 6.

Comprehensive utility curve under a centralized decision-making condition.

Table 5 shows the maximum and the optimal solution of the comprehensive utility for each side (i.e. RSP, RSD, and the agent) under the decentralized decision-making condition and comprehensive utility of the RSTC under the centralized decision-making condition.

Utility equilibrium in the case study

In order to simplify the computation, the equilibrium analysis under the decentralized decision-making condition is divided into the following two steps:

taking the equilibrium analysis of RSP and RSD, and finding out the value ranges of (q_i,q_i⁰) and (d_j,d_j⁰) that make the comprehensive utilities of each side close to, or equal to, the maximal utility values listed in Table 5;

calculating the comprehensive utility of the agent within the value range generated in the last step, finding out the solution that enable the agent’s comprehensive utility close to, or equal to, the maximal utility of the agent listed in Table 5, and the solution point is the target equilibrium solution point.

The value ranges of the eight parameters (q_i, q_i⁰, d_j, d_j⁰) are obtained in the first step; q₁∈(30,32), q₁ ⁰ ∈(30,40), q₂∈(15,16), q₂ ⁰ ∈(15,20), d₁∈(23,25), d₁ ⁰ =23, d₂∈(17,25), and d₂ ⁰ ∈(17,18). The comprehensive utilities equilibrium analysis of RSP and RSD are illustrated in Figure 7. In the second step, the comprehensive utility of the agent are calculated within the values ranges of the eight parameters above. The equilibrium solutions for RSP–agent and RSD–agent under the decentralized decision-making condition when U_a^E = Max(U_a) = 106.5600 are found as well, the equilibrium solution of RSP–agent is (q₁^*E,q₁^0*E, q₂^*E,q₂ ^0*E ) = (30,32,15,20), while the equilibrium solution of RSD–agent is (d₁^*E,d₁^0*E,d₂^*E,d₂ ^0*E ) = (23,23,21,17). According to the equilibrium solution of RSP–agent (q₁^*E,q₁^0*E,q₂^*E,q₂ ^0*E ) and the equilibrium solution of RSD–agent (d₁^*E,d₁^0*E,d₂^*E,d₂ ^0*E ), it will ensure that the comprehensive utilities of RSPs and the agent, and the comprehensive utilities of RSDs and the agent are maximal at the same time in the SOM system mode.

Figure 7.

Equilibrium analysis of RSP and RSD under a decentralized decision-making condition.

Utility coordination in the case study

From Table 5 one can conclude that, when (q₁^c*, q₂^c*) = (50, 0), the comprehensive utility of the RSTC under the centralized decision-making condition has the maximal value and Max(U_c) = 103.0000. In order to improve the comprehensive utility of RSTC under the decentralized decision-making condition and enable it be close to, or equal to, the maximal value under the centralized decision-making condition, the resource service provided quantity must equal the optimal solution value (q₁^c*,q₂^c*) under the centralized decision-making condition. First, the agent sets the demand quantity to RSP₁ and RSP₂, i.e. set (q₁^c*, q₂^c*) = (50, 0). Under this condition, only the coordination between RSP₁ and the agent exists because q₂^c* = 0. According to the coordination method previously mentioned, RSP₁ and the agent, and RSP₂ and the agent, negotiate with each other and fix the coordination coefficients a₁ and b₁. The value ranges of a₁ and b₁ can be calculated according to equation (34). The data in Table 6 are the comprehensive utility values of RSP₁ and the agent after coordination calculated using different a₁ and b₁ within their value ranges. From the results shown in Table 6, the coordination coefficients a₁ and b₁ can help RSPs, RSDs, and the agent to obtain much more maximal utilities with the utility coordination under centralized decision-making than the maximal utilities without the utility coordination under decentralized decision-making.

Table 6.

Comparisons of the maximal comprehensive utility before and after coordination.

Before coordination	a ₁	b ₁	U_p ₁	U_a
	0	0	102.2382	116.56
After coordination	a ₁	b ₁	U_p ₁	U_a	a ₁	b ₁	U_p ₁	U_a
	2	10	102.2612	116.56	13	21	103.3294	116.56
	3	10	102.5654	116.56	14	21	103.3489	116.56
	4	10	102.7885	116.56	15	21	103.3631	116.56
	3	11	102.5137	116.56	14	22	103.3456	116.56
	4	11	102.7506	116.56	15	22	103.3607	116.56
	5	11	102.9243	116.56	16	22	103.3718	116.56
	4	12	102.7102	116.56	15	23	103.3581	116.56
	5	12	102.8947	116.56	16	23	103.3699	116.56
	6	12	103.0301	116.56	17	23	103.3786	116.56
	5	13	102.8633	116.56	16	24	103.3679	116.56
	6	13	103.007	116.56	17	24	103.3771	116.56
	7	13	103.1124	116.56	18	24	103.3838	116.5599
	6	14	102.9826	116.56	17	25	103.3755	116.56
	7	14	103.0945	116.56	18	25	103.3827	116.5599
	8	14	103.1766	116.56	19	25	103.3879	116.5599
	7	15	103.0754	116.56	18	26	103.3815	116.5599
	8	15	103.1626	116.56	19	26	103.3871	116.5599
	9	15	103.2265	116.56	20	26	103.3911	116.5599
	8	16	103.1478	116.56	19	27	103.3861	116.5599
	9	16	103.2156	116.56	20	27	103.3904	116.5598
	10	16	103.2654	116.56	21	27	103.3936	116.5598
	9	17	103.2041	116.56	20	28	103.3897	116.5599
	10	17	103.2569	116.56	21	28	103.3931	116.5598
	11	17	103.2957	116.56	22	28	103.3956	116.5598
	10	18	103.2479	116.56	21	29	103.3925	116.5598
	11	18	103.2891	116.56	22	29	103.3951	116.5598
	12	18	103.3193	116.56	23	29	103.3971	116.5596
	11	19	103.2821	116.56	22	30	103.3947	116.5598
	12	19	103.3142	116.56	23	30	103.3967	116.5597
	13	19	103.3377	116.56	24	30	103.3982	116.5595
	12	20	103.3087	116.56	23	31	103.3964	116.5597
	13	20	103.3337	116.56	24	31	103.398	116.5595
	14	20	103.352	116.56	25	31	103.3992	116.5593

The following conclusions can be obtained from Table 7.

Under the decentralized decision-making condition, without changing the agent’s maximal comprehensive utility (i.e. Max(U_a) = 106.5600), the comprehensive utility of RSP₁ can be improved through adjusting the cooperation coefficient a₁ and b₁ compared with the maximal value of comprehensive utility before coordination.

Within the proper value range, when the cooperation coefficient b₁ is unchanged, the comprehensive utility of RSP₁ increases with the increase of the cooperation coefficient a₁.

Within the proper value range, when the cooperation coefficient a₁ is unchanged, the comprehensive utility of RSP₁ decreases with the increase of the cooperation coefficient b₁.

However, although the comprehensive utility of RSP₁ is increased, the comprehensive utility of the agent still equals the maximal value before coordination under the decentralized decision-making condition. The reason is that the key aim of the agent is not pursuing the profit but the quality of service (QoS) (such as time and reliability). In the guarantee of no loss, the change of revenue has small influence on the revenue utility and the comprehensive utility. The coordination method used in this article is that the finances are transferred within the chain of resource service transaction, therefore, the agent’s comprehensive utility after coordination remains at the level of the maximal comprehensive utility before coordination.

Through the calculation results and the analysis in the case study, the following conclusions can be obtained.

The comprehensive utility curves of RSPs and RSDs (i.e. RSP_i and RSD_j) in Figure 4 demonstrated that the comprehensive utility of RSP and RSD under the decentralized decision-making condition only have one maximal value.

The resource service operator (i.e. the agent) under the decentralized decision-making condition has the maximal value of comprehensive utility.

There is only one maximal value of comprehensive utility for the RSTC under the centralized decision-making condition.

The equilibrium analysis demonstrated that, under the decentralized decision-making condition, there is only one equilibrium solution between RSP and the agent (and RSD and the agent) in the chain of the resource service transaction, which enables each side to have the maximal comprehensive utility at the same time.

The results in Table 6 illustrate that, under the decentralized decision-making condition, by adjusting the cooperation coefficient a₁ and b₁ properly between RSP and the agent:

the comprehensive utility of the chain of resource service transaction (i.e. RSTC) can be improved and it can arrive at the maximal comprehensive utility value under the centralized decision-making condition;

the maximal comprehensive utilities of RSP and the agent can be increased compared with the maximal values before coordination, or equal the maximal values before coordination.

Conclusions and future works

In order to enhance the transformation from production-oriented manufacturing to SOM, many SOM systems and models have been proposed and studied during the past decade. One of the key factors deciding whether these SOM systems or models are widely accepted and applied is the utility of the users, including RSPs, RSDs, and the operator or agent in a SOM system. However, few works have been emphasized on the resource service and ability transaction in SOM systems, which is the research topic of this study. The comprehensive utility for the three user types or sides, i.e. RSP, RSD, and resource service agent or operator (agent), during the resource service transaction (RST) process in the SOM system are investigated. In order to guarantee and enhance the comprehensive utility of the three sides using the SOM system, the comprehensive utility models under the decentralized decision-making condition that considered the revenue, time, and reliability for each side in the RST process in the SOM system, are proposed and discussed. Also discussed is the related comprehensive utility model for the RSTC of ‘multiple RSPs–one agent–multiple RSDs’ under the centralized decision-making condition. The existence of utility equilibriums between RSP and the agent, and the agent and RSD, are proved in the optimal decision of the RSTC under the decentralized decision-making condition. A kind of coordination model is also proposed in order to obtain the maximal utility of the whole chain.

Although the case study illustrates that the proposed method is practicable and effective, only three key factors, i.e. revenue, time, and reliability, are considered in this study (including utility modelling, utility equilibrium, and utility coordination). In future, more factors will be considered the utility modes for each side in the SOM during the transaction process, or a general and extensible mode will be investigated. Furthermore, other coordination methods such as economic theory-based, game-based, auction-based methods will be studied, and comparison among these methods will be conducted. The trust model and evaluation algorithms among different users in the resource service transaction process will be emphasized too.

Footnotes

Appendix

This article is partly supported by the NSFC (National Science Foundation of China) Project (Number 51005012) and the Fundamental Research Funds for the Central Universities in China, and the National Hi-Tech R&D1283 (863) Program (Number 2011AA04 0501) in China.

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Utility modelling,equilibrium,and coordination of resource service transaction in service-oriented manufacturing system

Abstract

Keywords

Introduction

Related works

Motivation

Related definition

Parameter definition

Definition of utility

Utility modelling

Utility model under the decentralized decision-making condition

The comprehensive utility of the RSPi

The comprehensive utility of the agent

The comprehensive utility of RSDi

Utility model under the centralized decision-making condition

Utility equilibrium

The utility equilibrium between RSP and the agent

The utility equilibrium between RSD and the agent

Utility coordination

Case study

Utility modelling in the case study

Utility equilibrium in the case study

Utility coordination in the case study

Conclusions and future works

Footnotes

Appendix

References

The comprehensive utility of the RSP_i

The comprehensive utility of RSD_i