Two Effective Strategies to Support Cross-Organization Emergency Resource Allocation Optimization

Gao, Ying; Liu, Cong; Zeng, Qingtian; Duan, Hua

doi:https://doi.org/10.1155/2021/7965935

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Abstract Introduction Related Work Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2021 | Article ID 7965935 | https://doi.org/10.1155/2021/7965935

Two Effective Strategies to Support Cross-Organization Emergency Resource Allocation Optimization

Ying Gao,¹Cong Liu,²Qingtian Zeng,¹and Hua Duan¹

Academic Editor: Carlos T. Calafate

Received20 Feb 2020

Revised08 May 2020

Accepted25 Nov 2020

Published04 Jan 2021

Abstract

Cross-organization emergency resource allocation optimization problem is essential to guarantee a successful emergency disposal, and it has become a research focus of modern emergency management. Generally speaking, there are two possible types of resource allocation scenarios: (1) if the emergency resources are overallocated, on the one hand, parallel execution of independent emergency activities can be supported and the emergency disposal time is reduced; on the other hand, too many idle resources may cause low resource utilization rate, high scheduling overhead, and high cost; and (2) if emergency resources are underallocated, this may lead to resource conflicts and the need for some emergency activities to wait for others to complete, and finally the emergency disposal time may increase. Therefore, reasonable emergency resource allocation strategies are highly desired. To the best of our knowledge, there is no formal approach to support the cross-organization emergency resource allocation issue. To handle this problem, we propose a two-layered framework to facilitate the allocation of limited emergency resources to meet its time constraints with high efficiency. More specifically, a kind of Petri net extended with time, resource, and message information, denoted as CE-net, is presented to model cross-organization emergency response processes. Based on the obtained CE-net, the minimum resource requirements are obtained with corresponding algorithms. Then, Minimum Execution Time (MET) strategy and Minimum Resource Consumption (MRC) strategy with their corresponding estimated execution intervals are introduced to facilitate the stakeholder to determine which strategy is suitable according to the timing requirements. A cross-organization fire emergency case is applied to validate the proposed approaches throughout the whole paper.

1. Introduction

The allocation of distributed emergency resources has been a challenging issue in the cross-organization emergency management area. An emergency is defined as a situation that imposes immediate risk to life, property, and environment, which requires urgent disposal and intervention to prevent its worsening [1, 2]. These disposals are normally organized as a group of collaborated emergency response processes charged by an emergency command center and several subordinate emergency organizations that need to work together to accomplish the whole emergency mission [3].

Generally speaking, cross-organization emergency response processes usually exhibit the following features (or requirements) that differentiate themselves from traditional business processes [1, 4–6]: (1) There are close relations between emergency activities and resources. During the execution of an emergency response process, large quantities of resources, for example, ambulances, fire trucks, medicines, tents, food, and clothing, are badly needed. On the one hand, if the emergency resources are overallocated, parallel execution of independent emergency activities can be enabled to reduce the execution time; however, too many idle resources may lead to low resource utilization rate, high scheduling overhead, and even high cost. On the other hand, if the emergency resources are underallocated, this may lead to resource conflicts and the need for some activities to wait for others to complete, and finally the execution time of the emergency response process may increase. Consequently, reasonable emergency resource allocation strategies are highly desired. (2) There are a lot of collaborations that need either messages sent by other organizations or resources shared among different organizations. Hence, effective collaboration modeling for this case is required. (3) Cross-organization emergency response processes are a real-time service where timeliness is critical to its mission success. Therefore, time performance evaluation and optimization strategies are needed.

Modeling across-organization emergency response processes is a complicated and time-consuming work. In addition, optimized emergency resource allocation will benefit both successful emergency response process execution with high time performance and high resource utilization rate. Therefore, emergency resources should be optimized and allocated properly at least from the two following perspectives: (1) minimizing emergency resource requirement as much as possible to achieve a high resource utilization rate and (2) shortening emergency response time as much as possible to achieve its crucial timing constraints. Note that this problem is different from conventional workflow resource scheduling [7–12], which aims at minimizing the application’s runtime on a limited resource set. Differently, we try to propose effective strategies to support cross-organization emergency resource allocation optimization. To this end, we introduce a kind of Petri net [13–15] extended with time, resource, and message information, CE-net for short, to model cross-organization emergency response processes. Actually, the CE-net is an extension of our previous E-net model [1] to suit cross-organization scenario. Accurately, a time interval is used to predict the uncertain execution time of an emergency activity. In addition, emergency resources are divided as reusable and consumable ones; that is, the reusable resources can be reused by other emergency activities when released, while the consumable ones can be used only once and cannot be reused any more.

The main contributions of this paper are summarized as follows: (1) a kind of Petri net extended with time, resource, and message information, CE-net for short, is proposed to model cross-organization emergency response processes; (2) a two-layered framework is proposed to support cross-organization emergency resource allocation; and (3) we present two effective resource allocation strategies, that is, the minimum execution time strategy and the minimum resource consumption strategy, to support the efficient emergency resource allocation decision-making based on the resource requirements analysis results.

The remainder of this paper is structured as follows. Section 2 discusses the related work. In Section 3, a cross-organization fire emergency response scenario is given as a case to validate our proposed approaches. Section 4 investigates the modeling approaches for cross-organization emergency response processes using CE-net. Then, minimum emergency resource requirements analysis is investigated based on the CE-net in Section 5. Section 6 introduces two effective resource allocation strategies to support the emergency resource allocation decision-making. Finally, Section 7 draws concluding remarks.

In this section, we mainly review existing work related to (1) workflow resource allocation as well as emergency resource scheduling and (2) modeling of cross-organizational workflow and emergency response processes.

2.1. Workflow Resource Allocation and Emergency Resource Scheduling

Workflow scheduling is a well-known problem whose main objective is to minimize the completion time of a workflow using a given (or limited) set of resources. Deelman proposes one of the most popular algorithms, called Pegasus, to schedule workflows on distributed systems [7]. It is built on top of the list scheduling approach and considers both communication and computation cost. Based on experimental evaluation, it is demonstrated that Pegasus achieves relatively good performance for most cases. Besides the list scheduling approach, other techniques, such as DAG-based scheduling [8], greedy randomized adaptive search [9], and critical path first [10], have also been investigated. More recently, Byun proposes a new algorithm named BTS for estimating the minimum number of hosts that are needed to execute a workflow within a given deadline to bridge the gap between workflow management systems and resource provisioning systems [11, 12].

As authoritative emergency management experts, Tufekci and Wallace [16] consider emergency management as a complex multiobjective optimization problem and utilizing limited resources compromisingly is the best way to be adopted. Following their thoughts, emergency resource allocation optimization has been studied by many researchers in the past decades. A dynamic optimization model is used to find the best assignment of available resources to operational areas by Fiedrichet et al. [17]. In [18], by considering multiple disaster places and multiple resource suppliers, an optimized algorithm is proposed to solve resource collision problem for large-scale public emergency response. In [19], the problem of allocating multiple emergency service resources to protect critical transportation infrastructures is studied. Different modeling approaches, including deterministic, stochastic programming and robust optimization, are used to model various risk preferences in decision-making under uncertain service availability and accessibility. To find an optimal solution for resource deployment and dispatching, Kondaveti and Ganz [20] introduce a decision support framework built on rapid information collection and resource tracking functionalities. The equipment control structure presented in [21] enables decentralized and collective decision-making for equipment prioritization and distribution in response to disasters. More recently, by considering time performance, Wang et al. [22] discuss a negotiation strategy and a compromised resources allocation model for emergency response. The negotiation strategy can facilitate requesters to find out the demanded resources efficiently. In addition, a mathematical model is presented to compute the earliest start time of emergency response on condition of continuous requirement for resources.

2.2. Modeling of Cross-Organizational Workflow and Emergency Response Processes

Van der Aalst first considers workflows distributed over a number of organizations in [23, 24], where two important questions are addressed: (1) the minimal requirements of interorganizational workflow and (2) how to decide if an interorganizational workflow, modeled with Petri nets, is consistent with an interaction structure specified through a message sequence. In [25], Liu et al. propose a kind of interactive Petri net to model the message channels between different process-oriented systems, and the compatibility preservation of an integrated system with message interaction is revealed. Differently, Schulz and Orlowska focus on three aspects to support the execution of cross-organizational workflows that have been modeled with a process-view approach in [26]: (1) communication between the entities, (2) their impact on an extended workflow engine, and (3) the design of cross-organizational workflow architecture. A Petri net-based state transition approach that binds states of private workflow tasks to their adjacent workflow view is introduced. Its concepts are demonstrated by a scenario involving two workflow management systems. Jiang et al. [27] describe a timed colored Petri net and process-view combined approach to construct cross-organizational workflows, and a three-layered framework is proposed to realize the interoperability of cross-organizational workflows.

In [28], we investigate the application of process mining for workflow integration using a type of Petri nets extended with resource and message factors. A process integration-based approach is presented to obtain the model for a cross-organization workflow based on the model mined for each organization and the coordination patterns among different organizations. More recently, we formally define several collaboration patterns, including message interaction pattern, resource interaction pattern, task collaboration pattern, and service outsourcing pattern, in [29]. Modeling and analysis of a cross-department medical workflow are effectively supported, and the correctness is verified by building the reachability graph. To cope with the cross-organizational characteristics of emergency response, we conduct the formal modeling and analysis of cross-organizational emergency response system in [4]. This work first introduces the formal model of emergency activities and identifies five kinds of interactivity relations during the cross-organizational coordination process. Then, OTRM_Net, a kind of Petri nets extended with time, resource message, and organization information, is presented to model the emergency response processes. Also, we further study its timing performance, resource conflict detection, and the reduction or concealment of inner emergency activities. More recently, we propose a top-down approach for model construction and correctness verification of cross-organization emergency response processes in [3]. For the resource conflict and resolution issue during the execution of cross-organization emergency response process, a novel controller design method is given in [5]. In addition, the privacy issue during the modeling of cross-organization emergency response processes is handled by a package reduction-based privacy protection approach in [6].

2.3. Summary

Based on the above literature review, we can see that researches into (1) modeling and analysis of cross-organizational emergency response processes and (2) emergency resource allocation and optimization issue have drawn much public attention. However, the existing works have at least the following limitations: (1) emergency resources are not fully quantified (e.g., [2–6]); that is, emergency resource quantity is not investigated during the modeling and allocation process, which will inevitably lead to an inaccurate resource allocation; and (2) there is a lack of time description for emergency activities, based on which we can estimate the time performance of cross-organization emergency response processes when using a specific resource allocation strategy. To deal with these limitations, this work provides a two-layered framework to support optimized resource allocation for cross-organizational emergency response processes.

3. A Two-Layered Framework to Support Emergency Resource Allocation

In this section, we introduce a cross-organization fire emergency scenario that will be used as an illustrating example for the paper. Then, we propose our emergency resource allocation mechanism.

3.1. A Cross-Organization Fire Emergency Scenario

In this paper, a fire emergency scenario in [3] is adopted as a typical scenario. It involves the following organizations: police station, emergency command center (ECC), explosive ordnance disposal (EOD) team, fire brigade, and hospital. Some of the critical missions in this scenario are rescue of victims and disposal of the moving fire. This scenario includes the following steps:(1)The police station first receives the fire emergency call and then reports the emergency information to ECC.(2)The police rushes to the emergency site to perform its detailed disposal missions and then reports the site conditions to ECC.(3)After receiving the emergency information, ECC first establishes a temporary emergency command group and then makes and issues emergency plans to its collaborative organizations, that is, medical rescue instruction to a hospital, search EOD instruction to an EOD team, and fire rescue instruction to the fire brigade.(4)The EOD team rushes to the site upon receiving the search EOD instruction from ECC and conducts its specific disposal activities according to its emergency handling requirements and finally reports the EOD search results to ECC.(5)The fire brigade rushes to the site upon receiving the fire rescue instruction from ECC and conducts its specific disposal activities according to its emergency handling requirements and finally reports the fire rescue results to ECC.(6)The hospital personnel rush to the site upon receiving the medical rescue instruction from ECC and conduct their specific disposal activities according to their emergency handling requirements and finally report the medical rescue results to ECC.(7)After receiving all the feedback information from the hospital, EOD team, and fire brigade, ECC makes emergency summary and evaluation and finally does the file archive.(8)ECC arranges the media coverage for the whole emergency response, and, finally, ECC, fire brigade, and hospital do the media coverage together.

3.2. Cross-Organization Emergency Resource Allocation Mechanism

To support the effective emergency resource allocation of cross-organization emergency response processes, a two-layered framework is presented as shown in Figure 1.

3.2.1. Layer 1

Each emergency organization establishes its respective emergency response process based on the emergency requirements. Then, each emergency organization submits its emergency response process to the ECC for further integration and evaluation. Next, the ECC integrates the response process received from its subordinate emergency organizations.

3.2.2. Layer 2

The ECC first conducts the emergency resource requirement analysis in terms of minimum consumable resource requirement, minimum reusable resource requirement, and reliable reusable resource requirement. According the resource requirement analysis results, two strategies, that is, minimum execution time strategy and minimum resource consumption strategy, are obtained to guide the resource allocation. In this way, stakeholders can determine which strategy is more suitable according to the amount of available resources and expected finishing time.

The scope of this paper is to provide decision-making information to support emergency resource allocation in a cross-organization scenario. In this case, emergency resources are like the public transportation vehicles, public communication devices, emergency personnels, and so forth.

4. CE-Net-Based Modeling of Cross-Organization Emergency Response Processes

In this section, we propose the formal definition of a Petri net-based model for the cross-organization emergency response processes, named CE-net, which is an extension of our previous E-net [1]. The CE-net is different from our previous models, such as RM_WF_Net in [29] and OTRM_Net in [4], as it emphasizes (1) the uncertainty execution time of emergency activities and (2) effective resource allocation strategy of cross-organization emergency response processes.

4.1. CE-Net

Our work is based on Petri nets (or WF-net). Some of the essential terminologies and notations are reviewed following [13–15, 23, 24, 30–37].

Let Z = {0, 1, 2, …} and Z_n = {1, 2, …, n}, where n is a positive integer, and let R be the set of nonnegative real numbers.

Definition 1. (see [13]). A Petri net is a 4-tuple Σ = (P, T, F, M₀), where (1) P = {p₁, p₂, …, p_m} is a finite set of places; (2) T = {t₁, t₂, …, t_n} is a finite set of transitions; (3) F ⊆ (P × T) ∪ (T × P) is a finite set of arcs (flow relation); (4) M₀: P ⟶ Z is the initial marking; and (5) P ∩ T = ∅ and P ∪ T ≠ ∅.
For all x ∈ P ∪ T, the set ^•x = {y| y ∈ P ∪ T ∧ (y, x) ∈ F} is the preset of x, and x^• = {y| y ∈ P ∪ T ∧ (x, y) ∈ F} is the postset of x. p is marked by M if M(p) > 0. A transition t ∈ T is enabled under M, if and only if, ∀p ∈ ^•t: M(p) > 0, denoted as M[t > . If M[t > holds, t may fire, resulting in a new marking M’, denoted as M[t > M’, such that M′(p) = M(p) − 1 if, ∀p ∈ ^•t \ t^•, M′(p) = M(p) + 1 if ∀p ∈ t^• \ ^•t, and otherwise M′(p) = M(p). An initial marking is denoted by M₀ and R(M₀) is defined as the set of all reachable marking sets of Σ, where ∀M_i ∈ R(M₀) such that M₀[δ > M.

Definition 2. (see [13]). A weighted Petri net is a 5-tuple Σ_W = (P, T, F, M₀, W), where (1) Σ = (P, T, F, M₀) is a Petri net and (2) W: F ⟶ Z_n is a weight function that maps an arc to a positive integer.

Definition 3. (see [23]). A Petri net Σ = (P, T, F, M₀) is a WF-net if (1) there is one source place p_s ∈ P such that •p_s = ∅; (2) there is one sink place p_e ∈ P such that p_e• = ∅; (3) each node x ∈ P ∪ T is on a path from p_s to p_e; and (4) ∀p ∈ P, M₀(p) = 1 if p = p_s, and otherwise M₀(p) = 0.
In a WF-net, the transition set T is used to represent the normal activities, the place set P is used to represent logic connection relation of activities, and source place and sink place especially represent the start and end of the process. Based on the classical WF-net, we propose CE-net by extending it with uncertain execution time, resource, and message information to suit the cross-organization emergency response process modeling demand. It differs from our previous RM_WF_Net in [29] as it involves the emergency activity execution interval.

Definition 4. A 5-tuple Σ_CE = (P, T, F, α, β, W, M₀) is a CE-net if(1)P = P_L ∪ P_M ∪ P_R, where P_L ∩ P_R = ∅, P_R ∩ P_M = ∅, P_L ∩ P_M = ∅, P_L represents the logic place set, P_M represents the message place set, and P_R represents the resource place set in a Σ_CE, and P_R = P_RR ∪ P_CR, where P_RR is the reusable resource place set and is the consumable resource place set;(2)T is the transition set of a CE-net, and it represents an emergency activity set;(3)F = F_L ∪ F_M ∪ F_R, where(3.1)F_L = (P_L × T) ∪ (T × P_L) represents the logical structure of a Σ_CE;(3.2)F_M = (P_M × T) ∪ (T × P_M) represents the required and sent messages of a Σ_CE;(3.3)F_R = (P_R × T) ∪ (T × P_R) represents the required and released resources of a Σ_CE;(4)α: T ∪ P_R ⟶ R. ∀t ∈ T ∪ P_R, α(t) ≥ 0 is the minimum time to execute (or prepare) an emergency activity (or resource) t;(5)β: T ∪ P_R ⟶ R. ∀t ∈ T ∪ P_R, β(t) ≥ 0 is the maximum time to execute (or prepare) an emergency activity (or resource) t, such that α(t) ≤ β(t);(6)W: F ⟶ Z_n is the weighted function, such that, ∀f ∈ F, W(f) = 1 if f ∈ F_L ∪ F_M, W(f) = #req(r, t) if (f ∈ (P_RR ∪ P_CR) × T) ∧ (f = (r, t)), and W(f) = #sent(t, r) if (f ∈ T × P_RR) ∧ (f = (t, r)). #req(t, r) represents the required amount of resource r to execute activity t, and #sent(t, r) represents the sent amount of resource r when activity t finishes (only reusable resources have this flow); (7) ∀p ∈ P, M₀(p) = 1 if p ∈ P_L ∧ •p = ∅, M₀(p) = #num(p) if p ∈ P_R, and otherwise M₀(p) = 0. #num(p) represents the initial available amount of resource p.The firing rule of a CE-net is the same as that of a traditional Petri net. Given a marking M, ∀t ∈ T, t is enabled under M if, ∀p ∈ ^•t, M(p) ≥ 1, where p ∈ P_L ∪ P_M ∪ P_R. Firing an enabled t removes a token from each place in ^•t and deposits one to each place in t^•. All properties, such as reachability and boundedness, can be defined similarly. The main differences between an CE-net and a Petri net are the following: (1) the CE-net is a special type of Petri net extended with message place set (P_M) and resource place set (P_R); (2) a transition in CE-net is associated with two time functions to represent its minimum and maximum execution time; and (3) a weighted function is introduced to represent the amount of required or sent resources when an emergency activity starts or ends.

4.2. Modeling of Cross-Organization Emergency Response Processes Using CE-Net

Modeling of cross-organization emergency response processes involves the following steps: (1) modeling emergency activities with CE-net; (2) modeling control structure with CE-net; and (3) integration of control structure model with those activity models.

In a CE-net, an emergency activity model is shown in Figure 2, where p_ready is the ready place, p_end is the end place, P_resourceReq and P_resourceSent are resource places which mean the required and sent resources, p_messageReq and p_messageSent are required and sent message places, and α(t) and β(t) are the minimum execution time and maximum execution time, respectively. To distinguish the logic, resource, and message places properly, a logic place is drawn with a normal circle, a message place is drawn as a circle with dashed line, and a resource place is drawn as a two concentric circles with full line.

It is worth noting that the control structure of a CE-net, denoted as (P_L, T, F_L, M₀|_L), is a standard WF-net, where M₀|_L is the projection of M₀ on P_L. Therefore, its basic control structures, including sequence structure, concurrent structure, choice structure, and loop structure, can be modeled in the same way as that demonstrated in [29]. According to the emergency response descriptions in Section 3, emergency activity information, including activity ID, activity name, required resources/messages, sent resources/messages, of the Police state, ECC, EOD team, fire brigade, and hospital, is shown in Tables 1–3, respectively.

It is worth mentioning that we use multisets to represent the required resource set and the sent resource set of an emergency activity. M(R) is the set of all multisets over a set R. For some multiset m ∈ M(R), m(r) denotes the number of times element r ∈ R appears in m. For example, m = {a², b³} is a multiset over {a, b}. It represents that element a appears two times and element b appears three times in m. The ordering of elements is irrelevant for multiset.

Using the detailed modeling approaches in [29], a CE-net is obtained as shown in Figure 3, which represents the overall execution process of the cross-organization fire emergency response processes in Section 3.

It is worth noting that there are five resource places that correspond to five kind resources. For graphic simplicity, some resources may have more than one resource place.

5. Reduction Rules of CE-Net

Based on the modeling approaches in last subsection, a CE-net can be constructed. Unfortunately, the CE-net may contain an excessive number of places and transitions, which will lead to an inefficient analysis and troublesome understanding. Hence, two reduction rules are introduced to reduce the model scale while maintaining the structure, time, resource, and message invariant.

5.1. Rule 4.1

Given a CE-net Σ_EC = (P, T, F, α, β, W, M₀), if t_i, t_j ∈ T are two sequential activities such that t_i^• = ^•t_j, ^•t_i ∩ P_R = ∅, t_i^• ∩ (P_R ∪ P_M) = ∅, ^•t_j ∩ (P_R ∪ P_M) = ∅, and t_j^• ∩ P_R = ∅, and their timing constraints are [α(t_i), β(t_i)] and [α(t_j), β(t_j)], respectively. Then, transitions t_i and t_j can be merged to a new one, denoted as t_ij, such that ^•t_ij = ^•t_i, t_ij^• = t_j^•, α(t_ij) = α(t_i) + α(t_j), and β(t_ij) = β(t_i) + β(t_j).

Rule 1 shows the reduction rule for sequential activities that do not require any messages and resources, and an example of Rule 4.1 is shown in Figure 4, where t_i and t_j are merged to t_ij.

5.2. Rule 4.2

Given a CE-net Σ_EC = (P, T, F, α, β, W, M₀), if t_i, t_j ∈ T are two concurrent activities such that ^•t_i ∩ (P_R ∪ P_M) = ∅, t_i^• ∩ (P_R ∪ P_M) = ∅, ^•t_j ∩ (P_R ∪ P_M) = ∅, and t_j^• ∩ (P_R ∪ P_M) = ∅, and their timing constraints are [α(t_i), β(t_i)] and [α(t_j), β(t_j)], respectively. Then, transitions t_i and t_j can be merged to a new transition, denoted as t_ij, such that α(t_ij) = max{α(t_i), α(t_j)} and β(t_ij) = max{β(t_i), β(t_j)}.

Rule 2 shows the reduction for two concurrent activities that do not require any messages and resources, and an example of Rule 4.2 is illustrated in Figure 5, where t_i and t_j are replaced by t_ij.

We have the following explanations for reduction rules: (1) we only introduce the atomic reduction rules, and some advanced composite rules can be realized on top of these basic ones; (2) we only introduce rules that suit the sequence and concurrent structures, while choice and loop structures are not considered because their reduction results are usually not deterministic and can cause property changes compared with the original model; and (3) the firing rule of a transition obtained by reduction is the same as that of a traditional one; that is, the firing rule of a reduced CE-net is the same as that of a Petri net.

In the following, we show how to use our reduction rules to reduce the CE-net in Figure 3. t_11−12−13 is obtained by merging transitions t₁₁, t₁₂, and t₁₃ using reduction Rule 4.1 such that α(t_11−12−13) = α(t₁₁) + α(t₁₂) + α(t₁₃) = 5 + 8 + 2 = 15 and β(t_11−12−13) = β(t₁₁) + β(t₁₂) + β(t₁₃) = 8 + 15 + 4 = 27. t_19−20−21 is obtained by (1) merging transitions t₂₀ and t₂₁ using reduction Rule 4.2 to obtain t₂₀₋₂₁ such that α(t₂₀₋₂₁) = max{α(t₂₀), α(t₂₁)} = max{6, 6} = 6, and β(t₂₀₋₂₁) = max{β(t₂₀), β(t₂₁)} = max{8, 8} = 8 and (2) merging transitions t₁₉ and t₂₀₋₂₁ with reduction Rule 4.1 such that α(t_19−20−21) = α(t₁₉) + α(t₂₀₋₂₁) = 8 + 6 = 14 and β(t_19−20−21) = β(t₁₉) + β(t₂₀₋₂₁) = 12 + 8 = 20. t_{24−25−26−27−28} is obtained by (1) merging transitions t₂₅ and t₂₆ using reduction Rule 4.2 to obtain t₂₅₋₂₆ such that α(t₂₅₋₂₆) = max{α(t₂₅), α(t₂₆)} = max{8, 6} = 8, and β(t₂₅₋₂₆) = max{β(t₂₅), β(t₂₆)} = max{12, 8} = 12 and (2) merging transitions t₂₄, t₂₅₋₂₆, t₂₇, and t₂₈ to obtain t_{24−25−26−27−28} with reduction Rule 4.1 such that α(t_{24−25−26−27}) = α(t₂₄) + α(t₂₅₋₂₆) + α(t₂₇) + α(t₂₈) = 4 + 8 + 4 + 2 = 18 and β(t_{24−25−26−27}) = β(t₂₄) + β(t₂₅₋₂₆) + β(t₂₇) + β(t₂₈) = 6 + 12 + 6 + 3 = 27.

The CE-net of the cross-organization fire emergency response processes after reduction is shown in Figure 6. To give a comparison, Table 4 gives the number of transitions, message places, and resource places of the CE-net before and after reduction. Based on the comparison, we can clearly see that (1) its scale (in terms of the number of transitions and logic places) is much smaller and (2) the collaboration elements (resources and messages) stay invariant.

6. CE-Net-Based Minimum Resource Requirement Analysis

In this section, we discuss the minimum resource requirements of cross-organization emergency response processes based on the CE-net. During this procedure, we analyze reusable and consumable resources separately. For simplicity, we first redefine two vector operators, “<” and “≥.” Let X = <x₁, x₂, …, x_n> and Y = <y₁, y₂, …, x_n> be two n-dimension vectors. If, ∀X.x_i ≥ Y.y_i, for 1 ≤ i ≤ n, we have X ≥ Y. If ∃X.x_i < Y.y_i, for 1 ≤ i ≤ n, we have X < Y. Assume that the available consumable resource vector and available reusable resource vector of cross-organization emergency response processes are denoted as R_AC and R_AR, respectively.

6.1. Minimum Consumable Resource Requirement

The minimum consumable resource vector is denoted as R_MC = <q(r₁), q(r₂), …, q(r_n) >, where (1) r_i (i = 1, 2, …, n) refers to a kind of consumable resource and it is modeled as a resource place p_ri in P_CR and (2) q(r_i) represents the number of r_i. V_MC can be computed by taking as input a CE-net based on the following algorithm.

The complexity of Algorithm 1 is Ο(|P_CR| × |T|), where |P_CR| is the number of consumable resource types and |T| is the number of emergency activities. For real-life emergency resource management, the cross-organization emergency response processes will break down because of shortage of consumable resources if R_AC < R_MC.

	Input: Σ_CE = (P, T, F, α, β, W, M₀).
	Output: R_MC.
(1)	/Step 1: initialization/
(2)	Step 1: sum ⟵ 0, R_MC ⟵ 0.
(3)	/Step 2: to obtain the minimum consumable resource vector/
(4)	Step 2: FOR ∀p_ri ∈ P_CRDO
(5)	FOR ∀t_i ∈ T DO
(6)	sum ⟵ sum + W(p_ri, t_i);
(7)	END DO
(8)	q(R_MC.r_i) ⟵ sum;
(9)	sum ⟵ 0;
(10)	END DO
(11)	Step 3: Output R_MC.

6.2. Minimum Reusable Resource Requirement

The minimum reusable resource vector is denoted as R_MR = <q(r₁), q(r₂), …, q(r_m) >, where (1) r_i (i = 1, 2, …, n) refers to a kind of reusable resource and it is modeled as a resource place p_ri in P_RR and (2) q(r_i) represents the number of r_i. Algorithm 2 shows how to compute V_MR by taking as input a CE-net.

	Input: Σ_CE = (P, T, F, α, β, W, M₀).
	Output: R_MR.
(1)	/Step 1: initialization/
(2)	Step 1: R_MR ⟵ 0;
(3)	/Step 2: to obtain the minimum reusable resource vector/
(4)	Step 2: FOR ∀p_ri ∈ P_RRDO
(5)	FOR ∀t_i ∈ T DO
(6)	IF W(p_ri, t_i) > q(R_MR.r_i) THEN
(7)	q(R_MR.r_i) ⟵ W(p_ri, t_i);
(8)	END IF
(9)	END DO
(10)	END DO
(11)	Step 3: Output R_MR.

The complexity of Algorithm 2 is Ο(|P_RR| × |T|), where |P_RR| is the number of reusable resource types and |T| is the number of activities. For real-life emergency resource management, the cross-organization emergency response processes will break down because of shortage of reusable resources if R_AR < R_MR.

6.3. Reliable Reusable Resource Requirement

Even though we have R_AR ≥ R_MR, resource conflicts may still exist during the execution of cross-organization emergency response processes because of resource dependency and limited available resources. This kind of conflicts may delay the execution time of the emergency process. Therefore, the reliable reusable resource vector of a CE-net, denoted as R_RR = <q(r₁), q(r₂),…, q(r_m)>, is introduced, where r_i (i = 1, 2, …, n) refers to a kind of reusable resource and is represented as a resource place p_ri in P_RR. Algorithm 3 shows how to compute R_RR by taking as input a CE-net.

	Input: Σ_CE = (P, T, F, α, β, W, M₀), DependencySet and R_MR.
	Output: R_RR.
(1)	/Step 1: initialization/
(2)	Step 1: sum ⟵ 0, V_RR ⟵ V_MR;
(3)	/Step 2: to obtain the reliable reusable resource vector/
(4)	Step 2: FOR ∀p_ri ∈ P_RRDO
(5)	FOR ∀(t_i, t_j) ∈ DependencySet DO
(6)	sum ⟵ W(p_ri, t_i) + W(p_ri, t_j);
(7)	IF sum > q(R_RR.r_i) THEN
(8)	q(R_RR.r_i) ⟵ sum;
(9)	END IF
(10)	sum ⟵ 0;
(11)	END DO
(12)	END DO
(13)	Step 3: Output R_RR.

The complexity of Algorithm 3 is Ο(|P_RR| × |T|), where |P_RR| is the number of reusable resource types and |T| is the number of emergency activities. If R_AR ≥ R_RR, there is no resource conflict during process execution; that is, potential resource conflicts are avoided as sufficient resources are provided to support parallel execution of activities in resource dependency.

Theorem 1. The proposed approaches to analyze resource requirements of cross-organization emergency response processes on the basis of CE-net have Ο(m × n) time complexity, where m is the number of resource types and n is the number of emergency activities.

Proof. To analyze the resource requirement, three kinds of resource metrics, that is, the minimum consumable resource vector, the minimum reusable resource vector, and there liable reusable resource vector, are needed. Their calculation algorithms are implemented in Algorithms 1–3, the complexity of which is no bigger than Ο(m × n), where m is the number of resource types and n is the number of emergency activities. Therefore, the proposed method to analyze the resource requirement has its Ο(m × n) time complexity.
Taking the cross-organization fire emergency response processes as an example, we have R_MC = <6>, R_MR = <1, 1, 2, 1>, and R_RR = <3, 2, 6, 1> by executing Algorithms 1–3.

7. Two Effective Resource Allocation Strategies

In this section, we propose two optimized resource allocation strategies, that is, the minimum execution time strategy and the minimum resource consumption strategy. The former pursues time efficiency of cross-organization emergency response processes, and the latter focuses on high resource utilization rate. For each strategy, we estimate its corresponding time performance, based on which the stakeholder can determine which strategy is suitable according to the timing constraints. Before rendering the detailed strategies, we first introduce the time performance estimation and resource conflict detection approaches.

7.1. Time Performance Estimation and Potential Resource Conflict Detection

In a cross-organization emergency response processes scenario, an emergency activity starts to be executed only (1) after the termination of all its preactivities, (2) after receiving the required messages sent by other organizations, and (3) under the condition that all of its required resources are available and sufficient. In this subsection, the minimum execution time of a cross-organization emergency response process can be obtained.

Without considering resource factor, if each emergency activity is completed in its minimum execution time, the earliest time to start activity t, denoted by T_e1(t), is as follows:

Without considering resource factor, if each activity is completed in its maximum execution time, the earliest time to start activity t, denoted byT_e2(t), is as follows:

The minimum execution time of a cross-organization emergency response process can be found if no resource conflict occurs. However, resource conflicts are inevitable during the execution of a cross-organization emergency response process. Therefore, resource conflict checking approach is investigated here.

In the following discussion, we use T_start(t) and T_end(t) to represent the real start and end time of an emergency activity t. We have two types of resources, reusable and consumable ones. The former one becomes available and can be reused after being released, while the latter is consumed during execution and cannot be reused. For this reason, resource conflict mentioned in our work is essentially caused by the reusable resources. If a conflict is caused by consumable resources, the only way to solve it is to add more such type resources.

Definition 5. ∀t_i, t_j ∈ T(t_i ≠ t_j), t_i and t_j have resource dependency, denoted as t_i Θ t_j, if ^•(t_i) ∩ ^•(t_j) ⊆ P_R.
According to Definition 5, an algorithm to obtain the resource dependency in a cross-organization emergency response process is presented as follows.
In Algorithm 4, the complexity of Step 2 is Ο(|T|²). Therefore, the complexity of Algorithm 3 is Ο(|T|²). By executing Algorithm 4, the resource dependency set of the emergency response process scenario is obtained: DependencySet = {(t₂, t₁₀), (t₄, t₅), (t₄, t₆), (t₅, t₆), (t₁₈, t₂₃), (t₁₇, t₂₂)}. Here, if two activities have resource dependency; that is, they share same emergency resources. However, this does not necessarily mean that resource conflicts will occur between them. Only when these two activities need to be executed simultaneously will resource conflicts take place. In the following, the resource conflict between two emergency activities is formulized.

	Input: Σ_CE = (P, T; F, α, β, W, M₀)
	Output: DependencySet = {(t_i, t_j)\|t_i Θ t_j}.
(1)	/Step 1: initialization/
(2)	Step 1: DependencySet ⟵ ∅;
(3)	/Step 2: to detect resource dependency among emergency tasks/
(4)	Step 2: FOR ∀t_i, t_j ∈ T (t_i ≠ t_j) DO
(5)	IF •(t_i) ∩ •(t_j) ⊆ P_RTHEN
(6)	DependencySet ⟵ DependencySet ∪ {(t_i, t_j)};
(7)	END IF
(8)	END DO
(9)	Step 3: Output DependencySet.

Definition 6. ∀t_i, t_j ∈ T(t_i ≠ t_j), t_i and t_j are in potential resource conflict, denoted as t_i ⊗ t_j, if (1) t_i Θ t_j and (2) [T_start(t_i), T_end(t_i)] and [T_start(t_j), T_end(t_j)] are overlapping.
Definition 6 defines the potential resource conflicts, based on which we present an algorithm to check resource conflicts.
In Algorithm 5, because Ο(|ConflictSet|) ≤ Ο(|T|), the complexity of Step 2 is Ο(|T|). Hence, Algorithm 5 has its computational complexity Ο(|T|). By executing Algorithm 5, we can obtain that ConflictSet = {(t₄, t₅), (t₄, t₆), (t₅, t₆), (t₁₈, t₂₃), (t₁₇, t₂₂)}. However, even if t₄ and t₅ are in potential conflicts, t₄ requires 2 public communication devices, and t₅ also requires 2 public communication devices and if the total number of available investigators in this case is less than 4, conflict occurs because of the competition for public communication devices. If the total number of available investigators is more than 4, t₄ and t₅ will no longer be in conflict. Based on the aforementioned analysis, we can see that whether a cross-organization emergency response process can be accomplished in its ideal execution time depends on the total quantity of available resources. In this way, effective resource allocation strategies are needed to support its successful execution.

	Input: Σ_CE = (P, T; F, α, β, W, M₀) and DependencySet.
	Output: ConflictSet = {(t_i, t_j)\|t_i ⊗ t_j}.
(1)	/Step 1: initialization/
(2)	Step 1: ConflictSet ⟵ DependencySet, T_e1(t) ⟵ 0, T_e2(t) ⟵ 0, T_l1(t) ⟵ 0, T_l2(t) ⟵ 0;
(3)	/Step 2: to detect if time interval of tasks with resource dependency overlaps/
(4)	Step 2: IF ConflictSet ≠ ∅ THEN
(5)	For ∀(t_i, t_j) ∈ ConflictSet DO
(6)	Calculate T_e1(t_i), T_e2(t_i), T_e1(t_j), T_e2(t_j);
(7)	IF [T_e1(t_i), T_e2(t_i) + β(T_i)] ∩ [T_e1(t_j), T_e2(t_j) + β(t_j)] ≠ ∅ THEN
(8)	GOTO Step3;
(9)	ConflictSet ⟵ ConflictSet − {(t_i, t_j)};
(10)	END DO
(11)	END IF
(12)	Step 3: Output ConflictSet.

7.2. Minimum Execution Time Strategy

A cross-organization emergency response process is a real-time service, where timeliness is critical to its mission success. Thus, to maintain a cross-organization emergency response process finish in a high time performance, parallel executions of independent emergency activities are needed to reduce the whole execution time. In the last subsection, ideal execution duration is analyzed for this scenario. To achieve this goal, the consumable and reusable resource vectors, V_AC and V_AR, should be allocated as V_AC ≥ V_MC and V_AR ≥ V_RR. In this resource allocation condition, consumable resources can meet the minimum requirement and reusable resources are sufficient enough to support parallel executions and avoid potential resource conflicts. Therefore, the whole process can be finished in its minimum execution interval.

Definition 7. For a time interval Interval = [T_l, T_U], it is defined as the minimum execution duration of a Σ_EC = (P, T, F, α, β, W, M₀) if T_l = max{T_e1(t_i) + α(t_i)|t_i ∈ T} and T_u = max{T_e2(t_i) + β(t_i)|t_i ∈ T}.
According to the above-mentioned formulas (1) and (2), T_e1(p) and T_e2(p) of each activity in Figure 6 can be obtained and are shown in Table 5. From Table 5, we can obtain the ideal execution time for the cross-organization fire emergency response process, that is, if no resource conflict occurs, the minimum execution interval is [64, 107], where T_l = T_e1(t₁₄) + α(t₁₄) = 61 + 3 = 64 time units and T_u = T_e2(t₁₄) + β(t₁₄) = 102 + 5 = 107 time units.

7.3. Minimum Resource Consumption Strategy

To finish an emergency response process with the smallest resource consumption, the optimized consumable and reusable resource vectors, V_AC and V_AR, should be allocated as V_AC ≥ V_MC and V_AR ≥ V_MR. In this resource allocation condition, both consumable and reusable resources can meet their minimum requirements. Therefore, the whole process can be finished with the smallest resource consumption. However, resource conflicts may exist during the process execution. Thus, some activities in conflict may be postponed because of waiting for reusable emergency resources which are exclusively occupied by others. As a result, time performance of the emergency response process is affected. Next, Algorithm 6 is proposed to estimate the execution duration for this case.

	Input: Σ_CE = (P, T; F, α, β, W, M₀), ConflictSet, Interval.
	Output: M_Interval = [M_l, M_U]
(1)	/Step 1: initialization/
(2)	Step 1: M_l ⟵ T_l, M_U ⟵ T_U;
(3)	/Step 2: to obtain the maximum execution time/
(4)	Step 2: FOR ∀(t_i, t_j) ∈ ConflictSet DO
(5)	M_l ⟵ M_l + min{α(t_i), α(t_j)};
(6)	M_U ⟵ M_U + min{β(t_i), β(t_j)};
(7)	END DO
(8)	Step 3: Output M_Interval.

The complexity of Algorithm 6 is Ο(|T|), where |T| is the number of emergency activities. By executing Algorithm 6 by taking the timing information of the cross-organization emergency response process as an example, we can obtain that its execution duration is [64, 107] using minimum resource consumption strategy.

8. Conclusion

Efficient emergency resource allocation decision support is of vital importance for cross-organization emergency management. To some extent, this will influence emergency resource utility rate and the whole emergency mission success. In the work, we first propose CE-net to model a cross-organization emergency response process, based on which emergency resource allocation decision-making strategies, including minimum execution time strategy and minimum resource consumption strategy, are presented. According to the available emergency resources and emergency time constraint, certain strategy is selected by the emergency manager according to their specific requirements. It is proved that the minimum execution time strategy can ensure the global emergency response process execution without resource conflict or block, and therefore the performance is optimal.

The minimum resource consumption strategy can guarantee the whole emergency to be finished with the least emergency consumption, and, in this way, the resource related cost is reduced. However, there may exist some resource conflicts during real-life emergency process execution when we choose the latter. To resolve these conflicts and maintain a success execution, efficient resource conflict resolution strategies are needed. Therefore, resource conflict resolution strategies with corresponding controller design approaches will be our future work. In addition, it would be interesting to discover such emergency response process models from historic emergency response logs by using process discovery techniques and advanced learning algorithms to realize data-driven emergency decision-making [38].

Data Availability

The data used in this manuscript come from an emergency management branch, and the authors cannot release all information at the current stage for privacy protection.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 61902222 and U1931207, the Taishan Scholars Program of Shandong Province under Grants ts20190936 and tsqn201909109, Science & Technology Development Fund of Shandong Province of China under Grants 2019KJN024, ZR2019LZH001, and ZR2017MF027, the Humanities and Social Science Research Project of the Ministry of Education under Grant 18YJAZH017, and Shandong University of Science and Technology Research Fund under Grant 2015TDJH102.

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Copyright © 2021 Ying Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Two Effective Strategies to Support Cross-Organization Emergency Resource Allocation Optimization

Abstract

1. Introduction

2. Related Work

2.1. Workflow Resource Allocation and Emergency Resource Scheduling

2.2. Modeling of Cross-Organizational Workflow and Emergency Response Processes

2.3. Summary

3. A Two-Layered Framework to Support Emergency Resource Allocation

3.1. A Cross-Organization Fire Emergency Scenario

3.2. Cross-Organization Emergency Resource Allocation Mechanism

3.2.1. Layer 1

3.2.2. Layer 2

4. CE-Net-Based Modeling of Cross-Organization Emergency Response Processes

4.1. CE-Net

4.2. Modeling of Cross-Organization Emergency Response Processes Using CE-Net

5. Reduction Rules of CE-Net

5.1. Rule 4.1

5.2. Rule 4.2

6. CE-Net-Based Minimum Resource Requirement Analysis

6.1. Minimum Consumable Resource Requirement

6.2. Minimum Reusable Resource Requirement

6.3. Reliable Reusable Resource Requirement

7. Two Effective Resource Allocation Strategies

7.1. Time Performance Estimation and Potential Resource Conflict Detection

7.2. Minimum Execution Time Strategy

7.3. Minimum Resource Consumption Strategy

8. Conclusion

Data Availability

Conflicts of Interest

Acknowledgments

References

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