Integrated dynamic scheduling of material flows and distributed information services in collaborative cyber-physical supply networks

1 The paper is an extended version of the conference paper Ivanov D., Sokolov B. (2012c), ‘Structure dynamics control-based service scheduling in collaborative cyber-physical supply networks’, in Camarinha-Matos, L., Xu, L. and Afsarmanesh, H. (Eds.), Proceedings of the IFIP Conference on Virtual Enterprises PRO-VE 2012 IFIP AICT 380, pp. 280–288.

Abstract

An original model for dynamic scheduling of information services and material flows in collaborative cyber-physical supply networks is stated and solved with the help of the structure dynamics control approach. The proposed service-oriented description makes it possible to coordinate the availability of information services and material process schedules simultaneously. It also becomes possible to determine the volume of information services needed for the physical supply processes. In addition, the impact of disruptions in information services on the schedule execution in the physical structure is analysed. The results provide a base for information service scheduling according to an actual physical process execution.

Keywords:

• supply network
• collaborative cyber-physical system
• information services
• scheduling
• reconfiguration
• structure dynamics control
• optimal control

Abbreviations

IR	=	Information resource
IS	=	Information service
IT	=	Information technology
MP	=	Mathematical programming
OPC	=	Optimal program control
SDC	=	Structure dynamics control
SN	=	Supply network

1. Introduction

In recent years, considerable advancements in dynamic scheduling of supply networks (SNs) have been achieved with the help of mathematical optimisation, heuristics, and control theory (Averbakh, 2010; Ivanov & Sokolov, 2012a; Subramanian, Rawlings, Maravelias, Flores-Cerrillo, & Megan, 2013). Those models presume in many cases centralised information technology (IT) and full information availability. Nowadays, companies start adopting the distributed information services (ISs). The increasing role of IS requires service-based approaches to integrated scheduling of both material and information flows (Bardhan, Demirkan, Kannan, Kauffman, & Sougstad, 2010; Li et al., 2010). Such integration can also prevent failures of IT-enabled SNs (Soroor, Tarokh, & Keshtgary, 2009).

In this setting, three issues can be highlighted:

1. How to ensure that the schedule of IS availability corresponds to the schedule of material flows?

2. How to estimate the investments into the IS?

3. How to ensure material flow continuity in the case of disruptions in IT?

These issues become more and more important in practice since the impact of IT on the material processes in SN became crucial in recent years (Camarinha-Matos & Maseda, 2010; Cannella, Framinan, & Barbosa-Póvoa, 2013; Choi, Kim, Park, & Kang, 2002; Giard & Mendy, 2008; Lee, Palekar, & Qualls, 2011). Recent research indicated that an aligning of business processes and IT may potentially provide new quality of decision-making support and an increased SN performance (Dedrick, Xu, & Zhu, 2008; Jain, Wadhwa, & Deshmukh, 2009; Surana, Kumara, Greaves, & Raghavan, 2005).

Most of the new IT share attributes of intelligence. Examples include data mining, cloud computing, physical internet, pattern recognition, and knowledge discovery, to name a few. In addition, the beginning era of Internet of Things and explicit inclusion of wireless sensor networks, machine-to-machine systems, and mobile apps into the SN management require the data-driven business models instead of static information architectures.

That is why it becomes a timely and crucial topic to consider SNs as collaborative cyber-physical systems. Cyber-physical systems incorporate elements from both information and material (physical) subsystems and processes which are integrated and decisions in them are cohesive (Zhuge, 2011). Elements of the physical processes are supported by ISs. In addition, such systems evolve through adaptation and reconfiguration of their structures, i.e. through structure dynamics (Ivanov & Sokolov, 2012b; Ivanov, Sokolov, & Kaeschel, 2010). Such SNs are common not only in manufacturing but also in different cyber-physical systems, e.g. in networks of emergency response units, energy supply, city traffic control, and security control systems.

It can be observed that current concepts and models for SN integration do not provide adequate decision support from intelligent IT; we regard this shortcoming as an opportunity for research and development, which could significantly improve the practice of SN management. On one hand, the alignment of new intelligent elements of IT infrastructures with real material flows can be achieved. On the other hand, investments into IT can be estimated regarding real execution dynamics.

This paper faces these two decision domains on the basis of structure dynamics control (SDC) approach that is built upon tools from optimal program control (OPC) theory (Ivanov, Dolgui, & Sokolov, 2012; Ivanov & Sokolov, 2010). Justification of the choice of the OPC for the methodology of this research has two reasons. First, studies by Ivanov and Sokolov (2012a) and Subramanian et al. (2013) presented approaches on integration of control theory and scheduling methods for SN management. These studies discussed the possibilities to translate mathematical scheduling models into state-space form and design rescheduling algorithms with desired closed-loop properties. Second, OPC allows modelling continuous flows as state variables. This can be favourable regarding the information flows.

Although recent research has extensively dealt with SN scheduling (Chen, 2010) and IT scheduling (see, e.g. works on scheduling in telecommunications) in isolation, the integrated scheduling of both material and information flows still represents a research gap.

In this paper, the problem of coordinated dynamic scheduling of IS availability and material flows in the context of SNs as cyber-physical systems is stated and solved with the help of SDC approach. In addition, specific research contributions are the considerations of IT reconfiguration in a real execution stage and monetary estimation of investments into IT.

The remainder of this paper is organised as follows. In Section 2, the problem statement is given. Section 3 presents the SDC methodology. Sections 4 and 5 develop a mathematical model for scheduling of material flows and ISs. In Section 6, integration and practical applicability of these models are discussed. Section 7 represents the algorithmic realisation. The paper is concluded by summarising the main findings and discussing future research.

2. Problem statement

Consider an example of the interrelations among physical processes, IS, information functions, and information resources (IRs) (see Figure 1).

Figure 1. Interrelations among material flows, IS, functions, and IR (based on Ivanov & Sokolov, 2012c).

Such a framework is based on recent developments in cloud computing, see for example studies by Wang et al. (2010) and Jiang, Xu, Vrieze, Lim, and Jarabo (2012). For material flow scheduling and control, some ISs are needed. They should be available when material flow is scheduled and executed. The ISs are provided by some distributed IRs which may be subject to full or partial unavailability due to planned upgrades or unpredicted disruptions. Therefore, such an open SN has to be considered as a dynamic system.

Let us define a formal scheduling problem for this framework.

2.1. General assumptions

• The jobs in material flows are independent and available for processing at time zero. Each of the jobs has a release date that is known in advance through the SN coordination.

• Precedence constraints exist, i.e. the operations are logically arranged in jobs.

• The material flow operations are executed at one of the enterprises in the SN and are supported by ISs from different IRs.

• Machines and IRs have unequal information processing rates which may also differ for various operations and therefore influence the processing time and processing volume.

• Each IS may be composed of functions from different IRs and is characterised by availability time windows, productivity, and costs (fixed and operation cost).

• Setup times are not considered.

• Initial and the desired end states of the dynamic system are known.

• Transition from the initial state to the end state depends on a control selection in material flow, IS, and IR reconfiguration scheduling models.

• Transition from the initial state to the end state can be affected by disruptions in the IRs (for simplification we do not introduce perturbation functions into the material flow scheduling model; these functions may be included there without changing model structural properties).

2.2. Notations

Denote A = {A_ν; ν = 1, …, n} as jobs in a material flow.

Each of the jobs A_v is composed of the operations D^(ν) = {D^(ν)_i; i = 1, …, k_ν}.

• a_i is the planned processing volume (e.g. lot-size) of the operation D^(ν)_i.

• Consider a set of enterprises (machines) B = {B_j; j = 1, …, m}.

• Denote B^{(ν, i)} = {B^{(ν, i)}_r; r = 1, …, ρ_ν} as a set of IRs.

• Denote a_i as processing volume of the operation D^(ν)_i.

• Denote e⁽ⁱ⁾_r, V_r⁽ⁱ⁾, Φ⁽ⁱ⁾_r as maximal processing intensity of the operation D^(ν)_i at the IR B^{(ν, i)}_r, maximal capacity of the IR B^{(ν, i)}_r, and maximal productivity of the IR B^{(ν, i)}_r before the reconfiguration correspondingly; are given variables characterising the same domains but after a disruption-based reconfiguration.

• Let t be current instant of time, T = (t₀, t_f] the scheduling horizon, and t₀ (t_f) the start (end) instant of time for the scheduling horizon, respectively.

• Denote ϵ(t) as an element of the matrix of time-spatial constraints (ϵ(t) = 1, if t^k₀ < t ⩽ t_f^k, ϵ(t) = 0 otherwise), where k are the numbers of time windows available for operation execution (e.g. subject to maintenance).

• Denote S^(ν) = {S^(ν)_l; l = 1, …, d_j} as a set of ISs to execute operations D^(ν).

• Denote F^{(ν, l)} = {F^{(ν, l)}_χ; χ = 1, …, S_l} as a set of functions of IR to implement an IS.

• Denote costs fixed cost as c^{(ν, 1)}_il(t) and operation cost asc^{(ν, 2)}_il(t).

• Denote g^(ν)_l as a number of operations D^(ν)_i which may be processed by a service S^(ν)_l.

• Denote h^(ν)_i as a given number of services S^(ν)_l which may be simultaneously used by execution of the operation D^(ν)_i.

• Denote as operations of IR (e.g. information processing, storage, transmission, and protection).

• Denote as operations in the jobs for reconfiguration of the IR B^{(ν, i)}_r.

• Denote V^(ν)_χ as the online storage capacity of the IR B^{(ν, i)}_r to execute the operation D^{(ν, i)}_{< l, χ >} and δ^{(ν, l)}_χ r(τ) as a quality function to estimate the execution results.

• Denote c^{(l, 1)}_χ r(τ), c^{(l, 2)}_χ r(τ) as given time functions of fixed and operation cost of an IR B^{(ν, i)}_r used for the operation D^{(ν, i)}_{< l, χ >} by realisation of the function F^{(ν, l)}_χ.

• Denote η^(ν)_il(t) as a given time function which characterises the idle time costs of IS for the operation D^(ν)_i.

• y^(ν)_il denotes the value of current idle cost due to a backlog in the operation D^(ν)_i caused by unavailability of the service S^(ν)_l.

In order to describe the execution of operations, let us introduce the state variables:

• x^(ν)_il(t) characterises the execution of the operation D^(ν)_i with the use of the service S^(ν)_l.

• x^{(ν, 1)}_il(t) is an auxiliary variable characterising the current state of the operation D^(ν)_i. Its value is numerically equal to the time interval that has elapsed since the beginning of the scheduling interval and the execution start of the operation D^(ν)_i.

• x^{(ν, 2)}_il(t) is an auxiliary variable characterising the current state of the processing operation. Its value is numerically equal to the time interval that has elapsed since the end of the execution of the operation D^(ν)_i and the end of the scheduling interval.

• x^{(ν, l)}_r is an auxiliary variable characterising the employment time of the IR B^{(ν, j)}_r.

• x^{(ν, l)}_χ is an auxiliary variable which characterises the execution of the operation .

• is an auxiliary variable characterising the current state of the information processing operation. Its value is numerically equal to the time interval that has elapsed since the end of the execution of the operation and the instant of time t.

2.3. Decision variables and goals

• u^(ν)_il(t) is a control that is equal to 1 if the operation D^(ν)_i is assigned to the service S^(ν)_l at the moment t; otherwise u^(ν)_il(t) = 0.

• ϑ^{(ν, 1)}_il(t)(ϑ_il^{(ν, 2)}(t)) are auxiliary control variables that are equal to 1 if the operation D^(ν)_i has not started and is equal to 0 otherwise.

• w^{(ν, l)}_χ r is a control that is equal to 1 if the operation is assigned to the IR B^{(ν, i)}_r and is equal to 0 otherwise.

• is auxiliary control that is equal to 1 if all the operations in the function F^{(ν, l)}_χ are completed and is equal to 0 otherwise.

• ϑ^{(p, 2)}_r(t) is auxiliary control that is equal to 1 if the reconfiguration from old parameters e⁽ⁱ⁾_r, V_r⁽ⁱ⁾, Φ⁽ⁱ⁾_r to new ones is completed and is 0 otherwise.

The problem is to find a joint schedule for dynamic execution of IS and physical flows, i.e. two schedules should be generated in a coordinated manner, i.e.

• an OPC (schedule) for the integrated execution of material flows and ISs(model M1), and

• an OPC (schedule) for the execution of ISs within the IRs (model M2).

The jobs are to be scheduled subject to maximal customer service level (i.e. minimal lateness), minimal backlogs, minimal idle time of ISs, and minimal costs of IT (including fixed, operation, and idle cost).

3. Methodology

In this section, we describe both general methodology and method for formulation of the integrated scheduling model in particular.

3.1. Structure dynamics control methodology

The SN dynamic characteristics are distributed upon different structures, i.e.:

• organisational structure dynamics (i.e. agile supply structure),

• functional structure dynamics (i.e. flexible competencies),

• information structure dynamics (i.e. fluctuating information availability), and

• financial structure dynamics (i.e. cost and profit sharing).

This multi-dimensional dynamic space along with the coordinated and distributed decision-making leads us to the understanding of the SNs as multi-structural systems with structure dynamics. In the works Ivanov et al. (2010) and Ivanov and Sokolov (2012b), basics of the SN SDC have been presented. In this study, we present the SDC ides briefly. The basic ideas of the SC representation as multi-structural dynamic systems are the dynamic decomposition in each of the structure based on the intervals of structural constancy and multi-structural view in each of these intervals.

The SDC-based models build on the dynamic representation where the decisions on SN planning are taken for certain intervals of structural constancy and regarding problems of significantly smaller dimensionality. For each interval, a static optimisation problem of a smaller dimensionality can be solved with the help of mathematical programming (MP). The transitions between the intervals are modelled in the dynamic OPC model. Besides, a-priori knowledge of the SN structure, and moreover, structure dynamics, is no more necessary – the structures and corresponding functions are optimised simultaneously as the control becomes a function of both states and structures. The splitting of the planning period into the intervals occurs according to the natural logic of time and events. As the SDC is based on control theory, it is a convenient approach to describe intangible ISs due to abstract nature of state variables which can be interpreted as abstract service volumes.

3.2. Formulation of the integrated scheduling model

The basic technical idea of our approach, which extends the previous application of maximum principle to production and logistics, is to apply the methods of discrete optimisation for combinatorial tasks within certain time intervals and to use the OPC with all its advantages (i.e. accuracy of continuous time, integration of planning and control, and the operation execution parameters as time functions) for (1) flow control within the operations and (2) interlinking the partial (decomposed) solutions into the optimal schedule.

The SN is modelled as a networked controlled system described through a dynamic interpretation of the operations’ execution. The execution of operations is characterised by (1) results (e.g. processed volume, completion time, etc.), (2) intensity consumption of the machines, and (3) supply and information flows resulting from the schedule execution. The operations control model (M1) is first used to assign and sequence ISs to operations in material flows, and then a flow control model (M2) is employed to assign and schedule jobs at IRs subject to the requirements on the ISs availability. The basic interaction of these two models is that after solving M1, the found control variables are used in the constraints of M2. Note that in the calculation procedure, the models M1 and M2 will be solved simultaneously, i.e. the scheduling problems in all the structures (i.e. material flows, ISs, and IRs) will be integrated.

4. Mathematical model M1

The model of operation execution dynamics can be expressed as follows: (1) (2) (3) Equation (1) describes the operation execution dynamics subject to the IS availability described in the matrix function ϵ_il(t). u^(ν)_il(t) = 1 if service S^(ν)_l is assigned to the operation D^(ν)_i, u^(ν)_il(t) = 0 otherwise. Equation (2) represents idle time in the material flow caused by an unavailability of the IS S^(ν)_l. Equation (3) represents the dynamics of operation's execution according to precedence constraints.

The control actions are constrained as follows: (4) (5) (6) (7) Constraints (4) are assignment problem constraints. They define possibilities of parallel use of many services for one operation and for parallel processing of many operations at one IS. Constraints (5) determine the precedence relations. Constraints (6) interconnect main and auxiliary controls. In Equation (7), control variables are constrained to be Boolean variables.

Remark 1:

Note that constraints (4)–(7) are identical to those in MP models. However, at each t-point of time, the number of variables is determined by the operations which are currently in the ‘scheduling window’. Therefore, the tendency will be to have small-size instances and to apply known methods for the solution of MP models (e.g. Hungarian or branch-and-bound methods) subject to the problem (1)–(12).

The end conditions are defined as follows: (8) (9) Equations (8) and (9) define initial and end values of the variables x^(v)_i(t), y^(v)_il(t), x^(v)_il(t) at the moments t^(j)₀ and t^(j)_f.

Remark 2:

End conditions in OPC models play the role of demand variables in MP models. Conditions (9) reflect the desired end state. The right parts of equations are predetermined at the planning stage subject to the planned demand for each job.

The goals are defined as follows: (10) (11) (12) Equation (10) minimises losses from the IS idle time. Equation (11) estimates the service level by the volume of on-time completed jobs in the material flow. Equation (12) minimises total costs of IS.

5. Mathematical model M2

The model of operation execution dynamics in the IRs can be expressed as follows: (13) Equation (13) describes operation's execution dynamics in the IRs subject to operations of the IRs and recovery operations in the case of disruptions in the information structure.

The control actions are constrained as follows: (14) (15) (16) (17) (18) (19) (20) With the help of functions 0 ⩽ ξ^{(j, 1)}_r(t) ⩽ 1 и 0 ⩽ ξ^{(j, 2)}_r(t) ⩽ 1, perturbation impacts on the IR B^{(ν, j)}_r can be modelled. Equations (14)–(16) are constraints for information processing at B^{(ν, j)}_r before and after the reconfiguration. Constraints (17) set precedence relations on information processing operation similar to Equation (5). Constraints (18) are related to assignment problem and are similar to (4). Equation (19) determines the conditions of processing completion.

The end conditions are defined as follows: (21) (22)

The goals are defined as follows: (23) (24) (25) (26) Equation (23) estimates the uniformity of the use of the IRs B^{(ν, j)}_r и ; r, r₁ ∈ {1, …, ρ_ν}. Equation (24) estimates amount of completed operations D^{(ν, j)}_{< l, χ >}. Equation (25) takes into account losses from non-fulfilled operations. Equation (26) assesses total cost of ownership (TCO) for the IR B^{(ν, j)}_r.

6. Model integration and analysis

In this section, we discuss model integration, analyse model properties, and discuss its practical implications.

6.1. Model integration

The developed modelling complex is composed of the dynamic models of IS and IR control, subject to execution of material flows. It also includes elements of IR reconfiguration (e.g. in Equations (14)–(16) and (20)). Full consideration of the reconfiguration model can be found in Ivanov and Sokolov (2013).

The presented models M1 and M2 are interconnected with the help of Equation (6) where elements from M2 are used in M1. In its turn, M1 influences M2 through the Equations (14) and (20).

The proposed models and algorithms have been validated in a developed prototype based on C++ and XML. The OPC calculation is based on the Hamiltonian function. In integrating the main and the conjunctive equation systems, the values of variables in both of the systems can be obtained at each point of time. The maximum principle guarantees that the optimal solutions (i.e. the solution with maximal values) of the instantaneous problems (i.e. at each point of time) give the optimal solution to the overall problem. For these sub-problems, optimal solutions can be found, e.g. with the help of MP. Then these solutions are linked into an OPC.

6.2. Model analysis

Let us discuss optimality and sufficiency properties that have been proved theoretically and experimentally. The formulated scheduling model satisfies the conditions of the existence theorem in Lee and Markus (1967, Theorem 4, Corollary 2), which allows us to assert the existence of the optimal solution in the appropriate class of admissible controls. The formulated scheduling problem is the standard problem of OPC with mixed constraints and its optimal solution and relaxed system can be obtained with the help of local cut method based modification of the continuous maximum principle. An analysis of constraints in M1 and M2 shows that both state and control variables are constrained, i.e. the mixed state-control constraints exist (Arada & Raymond, 2000; Boltyanskiy, 1973) and form therefore a dynamic system with a variable control domain. To obtain necessary conditions of control optimality, Boltyanskiy's method of local sections can be used. Then the necessary conditions can be formulated in the form of the Boltyanskiy's theorem (maximum principle) (1973).

Corollary 1:

Analysis of Boltyanskiy (1973) and Moiseev (1974) shows that for the linear non-stationary finite-dimensional systems (models M1 and M2) with the convex area of admissible control Q(x) and performance indicators (10)–(12) and (23)–(26), the stated necessary conditions of optimality are also the conditions of sufficiency.

6.3. Practical implications

With the developed model, three schedules can be gained simultaneously, i.e. material flows schedule, schedule of IS availability, and schedule of IR functioning in the planned and disrupted modes. ISs should be available when material flow is scheduled and executed. The ISs are provided by some distributed IRs which may be subject to full or partial unavailability due to planned upgrades or unpredicted disruptions. Through the schedule coordination, IS availability can be matched with the material processes (e.g. manufacturing, stocking, and shipping). On the other hand, an upgrade or recovery of IRs can be brought into correspondence with the IS availability needs.

The proposed approach can be used as a quantitative tool in order to align IR structures with material flows that are scheduled integrated with ISs. Additional application of the developed method is that it can be used at the control stage in order to reconfigure IR structure subject to the continuity of the material flows.

Finally, the investments into IS and IR can be analysed subject to a real dynamics of execution. Equation (12) minimises fixed and operation costs of ISs while Equation (26) assesses TCO for the IRs. According to Equation (12), it can be analysed how purchased ISs are actually used. It can be revealed that in some cases idle costs in material flows are too high because of unavailability of some critical ISs. In some cases, it can be shown that too high and unnecessary investments into ISs have been made; this indicates an excessiveness of ISs. Similarly, according to Equation (26) it can be shown that capacities of some IRs may be insufficient or excessive.

7. Algorithmic realisation

Theorem 1:

Let Γ be a relaxed problem for the basic OPC problem. Then

1. If the problemΓdoes not have allowable solutions, then this is true for the problem PS as well.

2. If the OPC of the problemΓis allowable, then it is the OPC for the problem PS as well.

Proof:

1. If the problem Γ does not have allowable solutions, then a control u(t) transferring dynamic system (1)–(3) and (13) from a given initial state to a given final state does not exist. The same end conditions are violated in the OPC problem.

2. Let u*(t), ∀ t ∈ (T₀, T_f] be an OPC in Γ and x(t) be a solution to models M1 and M2 subject to u(t) = u*(t). Then u*(t) meets the requirements of the local cut method and maximises Hamiltonian for the OPC problem. Hence, vectors u*(t) and x*(t) return minimum to performance indicators (10)–(12) and (23)–(26). The proof is complete.

As the dynamics of state and conjunctive variables is described by differential equations, it becomes possible to calculate these variables at any instant of time subject to given initial conditions. Therefore, the Hamiltonian becomes the function of only one variable u that can be calculated at any t subject to allowable control from u∈G_u. Therefore the OPC problem can be reduced to a boundary problem with the help of the local cut method.

Let us consider the algorithmic realisation of the above-described modified maximum principle. After transforming to the boundary problem, a relaxed problem can be solved to receive OPC for the schedule of the model M1, for computation of which the main and conjunctive systems are integrated, i.e. the OPC vector u*(t) and the state trajectory x*(t) are obtained. The OPC vector at time t = T₀ and for the given value of ψ(t) should return maximum criteria indicators (10)–(12) and (23)–(26) which have been transformed to a general performance index and expressed in a scalar form J_G.

The basic peculiarity of the considered boundary problem is that the initial conditions for the conjunctive variables ψ(t₀) are not given. At the same time, an OPC should be calculated subject to end conditions (8)–(9) and (21)–(22). To obtain the conjunctive system vector, we use the Krylov–Chernousko method for OPC problem with free right end that is based on joint use of modified successive approximations method and branch-and-bound method. We propose to use a heuristics schedule to obtain the initial conditions for ψ(t₀). Then, the algorithm DYN can be stated as follows:

Step 1:	An initial solution is calculated and iteration step r = 0.
Step 2:	The parameters of the gained schedule are put into Equations (1)–(3) and (13) and integrated. As a result of the dynamic model run, a new trajectory of operation states x(r)(t) is received. Besides, if t = Tf then the record value JG = J(r)G can be calculated.
Step 3:	Then, the transversality conditions are evaluated. The conjugate system is integrated subject to and over the interval from t = Tf to t = T0. For t = T0, the first approximation ψ(r)l(T0) is received as a result. Here, the iteration number r = 0 is completed.
Step 4:	The control u(r)(t) is searched for subject to maximisation of the Hamiltonian function. The iterative process of the optimal schedule search is terminated as follows: either the allowable solution is determined, or at the fourth step no significant improvement is achieved.

Analogously, the OPC for the schedule of the model M2 can be obtained through the integration of corresponding conjunctive systems. Subsequently, through the reverse integration of the main equation systems, the mutual interrelation of the models M1 and M2 is realised.

8. Discussion of results and conclusions

New intelligent IT result from decentralised service-oriented infrastructures. This forces changes in decision support systems for SN which may become cyber-physical systems. If so, a new challenge of joint scheduling the material flows and IS will be faced in practice in next years. In these settings, two questions may be raised: (1) how these ISs shall be scheduled at the planning stage and adapted in dynamics at the execution control stage and (2) what is the optimal volume of ISs that is needed to ensure continuity of physical systems. Conventionally, the above-described two problems have been solved step by step. With the help of the SDC, a special dynamic representation of multi-structural networks is proposed where such problems can be solved simultaneously.

The proposed service-oriented description makes it possible to coordinate IS availability and material process schedules simultaneously. It also becomes possible to determine the volume of ISs needed for physical supply processes. In addition, impact of disruptions ISs on the schedule execution in the physical structure is analysed.

The results provide a base for IS scheduling according to actual physical process execution. In addition to the existing models on the scheduling of material processes in SNs, this study has added models for integrated IS, IR, and IR modernisation scheduling. This study is among the first to explicitly formulate and solve, in a dynamic manner, the stated integrated scheduling problem. The proposed service-oriented concept allows explicitly to incorporate material and information processes in the SN and take into account modern trends of decentralised IS, e.g. cloud computing. In addition to the scheduling, the proposed approach makes it possible simultaneously to (1) determine the volume of ISs needed for physical supply processes (Equations (10) and (11)) and (2) determine this volume in monetary form (Equation (12)).

Further analysis may include an explicit incorporation of reconfiguration processes and stability into the scheduling model. This paper can also be extended in future by application to concrete case studies. The proposed models are implemented in software prototype where numerical experiments have already been performed to validate hybrid scheduling algorithms on the basis of OPC and MP. In future, IR modernisation and adaptation can be further investigated with developed models and algorithms.

Acknowledgements

We would like to thank the anonymous referees for their comments and suggestions which contributed to the progress of this paper invaluably.

Additional information

Funding

The research described in this paper is partially supported by the Russian Foundation for Basic Research [grant number 13-07-00279], [grant number 12-07-13119], [grant number 12-07-00302], [grant number 13-08-00702], [grant number 13-08-01250], [grant number 13-07-12120]; Department of Nanotechnologies and Information Technologies of the RAS (project 2.11); by ESTLATRUS projects 1.2./ELRI-121/2011/13 (Baltic ICT Platform) and 2.1/ELRI-184/2011/14 (Integrated Intelligent Platform for Monitoring the Cross-Border Natural-Technological Systems).

Notes on contributors

Dmitry Ivanov

Dmitry Ivanov is full professor of international supply chain management at Berlin School of Economics and Law (BSEL). His research explores supply chain dynamics control and disruption management, with an emphasis on supply chain design and scheduling. His academic background includes industrial engineering, operations research, and applied control theory. He gained his PhD (Dr.rer.pol.), Doctor of Science, and Habilitation degrees in 2006, 2008, and 2011 from TU Chemnitz and University of Saint Petersburg, respectively. In 2005, he was awarded a German Chancellor Scholarship. Prior to becoming an academic he was mainly engaged in industry and consulting, especially for ERP systems. He is the co-author of more than 200 scientific works, including the monograph ‘Adaptive Supply Chain Management’. He has co-authored 8 books, edited 8 conference proceedings, and published 23 papers in refereed journals, 22 book chapters and over 100 papers in conference proceedings. His works have been published in various academic journals, including International Journal of Production Research, European Journal of Operational Research, Journal of Scheduling, etc. He has been guest editor of special issues in different journals. He is an associate editor of International Journal of Systems Science, chair of the IFAC TC 5.2 Working group, ‘Supply Network Engineering’.

Boris Sokolov

Boris Sokolov is professor and a deputy director for research at the Saint-Petersburg Institute of Informatics and Automation (SPIIRAS) of the Russian Academy of Science. He is the author of a new scientific lead: optimal control theory for structure dynamics of complex systems. His research interests include basic and applied research in mathematical modelling, optimal control theory, mathematical models and methods of support and multi-criteria decision-making in complex organisation-technical systems under uncertainties. He has co-authored 5 books on systems and control theory and more than 270 scientific papers. Professor B. Sokolov supervised more than 50 research and engineering projects. His works have been published in various academic journals, including European Journal of Operational Research, Journal of Scheduling, etc.

Evelio Antonio Dilou Raguinia

Evelio Antonio Dilou Raguinia is PhD student at the Saint-Petersburg Institute of Informatics and Automation (SPIIRAS) of the Russian Academy of Science.

Notes

1 The paper is an extended version of the conference paper Ivanov D., Sokolov B. (2012c), ‘Structure dynamics control-based service scheduling in collaborative cyber-physical supply networks’, in Camarinha-Matos, L., Xu, L. and Afsarmanesh, H. (Eds.), Proceedings of the IFIP Conference on Virtual Enterprises PRO-VE 2012 IFIP AICT 380, pp. 280–288.