Multitasked maintenance crews to serve emergency scenarios in electric distribution utilities

Vinícius Jacques Garcia, Daniel Pinheiro Bernardon,

Guilherme Dhein, Olinto de Araújo Bassi, Alzenira Abaide, Alberto Francisco Kummer Neto

Federal University of Santa Maria - UFSM, Brazil. viniciusjg@ufsm.br, dpbernardon@ufsm.br,

gdhein@redes.ufsm.br, olinto@smail.ufsm.br, alzenira@ufsm.br, alberto@inf.ufsm.br

Julio Fonini, Eric Fernando Boeck DazaAES Sul - Power Utility, Brazil.

Julio.Fonini@aes.com, Eric.Daza@aes.com

Abstract – This paper proposes a mathematical model to

handle emergency service requests in electric power distribution utilities. Given available maintenance crews and their already assigned service orders, a mathematical model based on mixed integer linear programming is developed to solve the dynamic vehicle routing problem related to the task of deciding which maintenance crew will complete each pending emergency service request. One key aspect refers to the real-time constraint, what means that computational system must be able to handle a solution to the emergency work order dispatch problem with response times in the order of milliseconds or even microseconds. First, the problem definition is presented, followed by preliminary results that have shown how suitable can be the proposed definition when addressing the referred problem and also by using Google Earth plataform. Finally, conclusions point out the main contributions of this work.

Index Terms -- work orders, combinatorial optimization, power systems automation, vehicle routing, integer linear programming.

I. INTRODUCTION

Energy supply and the restoration procedures in contingency scenarios is a relevant and permanent concern when operating electric distribution systems. Electric distribution utilities look for improving business process related to managing human and materials resources in order to have an effective operation related to reliability indexes without increasing operational costs.

This challenge is particularly important in emergent markets by economical aspects and also by new policies from the regulators taking place in Brazil nowadays. Exactly by facing a great era of opportunities that reflect on inherently increasing of power demand, the most common scenario that engineers are in charge of involves how to meet the power demand, maintaining certain reliability indexes related to frequency and duration of power not supplied without increasing costs, especially those ones related to human beings in maintenance procedures. The reasons that support this decision are multifaceted: the most obvious one refers to economical aspects; the other but even not less important is related to security, the smaller the number of people involved in electric maintenance, the lower will be the risk of accidents and the lower will be the costs involved in training for safety procedures.

This work proposes decision support system architecture to handle emergency service requests in electric power distribution utilities, involving geographic information about service location and also GPS data from vehicles used to visit each one of those requests. The main concept is related to vehicle routing optimization problem and information system technology associated with in order to furnish useful information to the decision maker, called system operator in this context. Architecture proposed is closely related to that one proposed by Mendoza et al [8], where a decision support system is proposed to a water public utility, involving a variant of vehicle routing problem was developed and solved by a hybrid evolutionary algorithm.

The main criterion assumed to be improved refers to the waiting time: how much time takes to the vehicle arrives at the emergency order position assigned to. The consideration of several emergency scenarios makes the optimization problem derived from this context hard to solve and require immediate responses from the distribution operation center, mainly by assuming the real time aspect inherently associated to and also by regulation policies that establish strict penalties by not observing predefined reliability indexes. The proposed approach is based on mathematical programming techniques to optimize the developed the problem called “dispatch of emergency orders”, considering the real time requirement and the key aspect involved with the available vehicles: all of them are always charged of pre-established routes that include orders known a priori when a set or emergency orders come up. The proposed methodology is tested on actual scenarios from a Brazilian electric power distribution utility, including practical and atypical operations concerns (different numbers of demanded emergency orders comparing to the number of available vehicles). The obtained results have shown the relevance of the proposed methodology to be used as part of a decision support system in distribution operation centers.

This paper is organized as follows: section 2 defines the vehicle routing problem assumed as the root of the proposed decision support system, including not only the system architecture but also the mathematical model developed. Section 3 presents preliminary results obtained and Section 4 shows final remarks and conclusions.

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II. PROBLEM DEFINITION

When developing a system able to assign a service order to a given maintenance crew, the following goals must be assumed:

• Reducing the dispatch time; • Improving network security on operation and

maintenance procedures; • Standardization of dispatch criteria in such a way

they could be closely related to business process. Arising from this context, the emergency work order

dispatch problem (EWODP) is carried out within 24 hours a day, 7 days a week, corresponding to a main task of the electric network operation center. Assuming this non-stop period and critical issues involved, a real time system may be suitable to assign a maintenance crew (vehicle) to each emergency service request, in the context of this work just called emergency work order (EWO).

The main issue involved is the aim of reducing the average service time, which is defined as the sum of the waiting time, the travel time and of the order execution time. In this work we consider the decision problem of assigning a EWO to a given maintenance crew available, mainly focusing on the waiting time. The challenge comes from the business process usually adopted by utilities: they have multitasked maintenance crews generally in charge of commercial services (customer demand orders) when EWO comes up. From this assumption follows specific characteristics that make the whole optimization problem some orders of magnitude greater in the sense of the complexity involved.

In this work is described a problem that emerge from the specific characteristics of route construction to meet customer demand in the context of an electric power distribution utility in Brazil, specifically with concern to the occurrence of EWO. The main inspiration for the analysis carried out to represent and solve the EWODP track its origin from the well-known traveling salesman problem [7] and its famous generalization: the vehicle routing problem [12].

In the considered utility, a set of service orders must be executed by maintenance crews, what remounts the construction of multiple routes. These crews have their start point in a depot that can be distinguished to each one and they do not need to return to their start point when the last service is completed.

The fundamental aspect that must be considered refers to the definition of several kinds of service orders, with high importance to the ones that are not known a priori. Two different set can be defined: those orders known a priori and related to commercial services requested by customers and those orders that have their inherently aspect of emergency that may occur at any moment. Every maintenance crew is able to execute these two kinds of orders.

When a maintenance crew begins its journey, its corresponding route to execute only those commercial orders known a priori is available. The occurrence of emergency scenarios imposes the most appropriate treatment in order to

consider these EWOs that are coming up and have precedence over the commercial orders. Following the number and their corresponding geographical location of EWOs, one or more maintenance crews will be considered to complete these services and, as consequence, they will have their routes modified.

The problem that arises from this context is related to the need of restructuring the existing routes only populated by commercial orders, now including the pending EWOs in the beginning of each existing route. From this perspective, two scenarios may be assumed: (1) reprogramming the set of remaining commercial services of all maintenance crews; and (2) only inserting the pending EWOs in the beginning of each route while maintaining unchanged the route related to commercial services. The first option have strict technological constraints since each maintenance crew receives a batch of orders to be executed when its journey starts and the communication to reprogram the route during the day may be a bottleneck by the existing status quo of telecommunication services in Brazil.

One important definition is related to the main goal of the problem. There are several objectives that can be assumed, including those conflicting ones. One of these is reducing the waiting time to execute emergencies, exactly by the risks associated with security of the electric power network.

Another objective, this one related to economical aspect, is reducing the total cost of routes, corresponding to the total time to complete all routes designed. In this case, both commercial and emergency are considered when calculating the cost. Even in this case is already possible to note a conflict between cost and precedence of emergency services: the most pressing are emergency services, the greater will be the cost.

The third and last aspect that can be considered is the relative balance on the workload between maintenance crews, what suggests possible approaches already considered in literature. Okonjo and Adigwe [9] propose a method to generate balanced routes to the vehicle routing problem that includes upper and lower bounds on the route time of each vehicle, obtained by a heuristic algorithm. After that and incorporating these limits, one mathematical model is derived and the problem is optimally solved. Chandran et al [3] have developed an approach to have balanced workload by modeling the vehicle routing problem first as a clustering problem, in a classical cluster-first, route-second approach. Weintraub et al [13] consider the emergency vehicle dispatching problem and the workload balanced is obtained by a post-optimization procedure that includes order interchange between routes, clustering and routing.

Anbuudayasankar et al [1] have pointed out that the workload balanced should not be assumed in the sense of total route cost but in the sense of equity when considering dangerous and strenuous activities.

One can note that the goal of balancing routes has strict relation with human relations in the company, since it is the most apparent aspect that is evaluated when comparing the

work effort between two given crews. considerations of Anbuudayasankar et al [the form of priority and execution time of allows minimizing and balancing the total r

The methodology to solve the EWODPpaper comprises a mixed linear programmmodel to be included in a computationexecute a real-time automatic dispatch of Edefinitions and the architecture of Decision[11]. These systems provide concepts anhelp decision makers in the decision procanalyzing and furnishing alternatives of main a reasonable time.

Considering the example of Figure 1. represents a EWO coming up in a certaspecific geographic position, with all infoFrom this point, one must decide whichdispatched to execute that service. It can be1 (v1) is 20 minutes far from the EWO, vminutes far from the EWO and finally veminutes far from the EWO. Considering thmust be minimized, vehicle 1 would be athe EWO.

Figure 1. Example of an emergency work

The following subsections will present thsystem architecture proposed and also model developed to the EWODP.

A. Decision support system architecture propoThe methodology proposed in this pa

emergency work order dispatch problemcomputational system able to execute a rdispatch of EWOs, including definitions aof Decision Support Systems [11].

Following this principles, the sysdeveloped is showed in Figure 2.

In order to provide real-time capabilitiecomputational system, the load schedulingdefining one thread for each geographical be mentioned that this geographical area iportion of the electric network consideregisters of all maintenance crews and eq

In this work, the [1] are included in each service, what

route time. P proposed in this ming mathematical al system able to

EWOs, considering n Support Systems nd techniques that cess, especially by athematical models

, the blue square ain time and in a rmation related to.

h vehicle must be e noted that vehicle vehicle 3 (v3) is 30 ehicle 2 (v2) is 70 hat the waiting time assigned to execute

order assignment.

he decision support the mathematical

osed aper to solve the

m corresponds to a eal-time automatic nd the architecture

stem architecture

es in the proposed g is carried out by area. Here it must

includes not only a ered but also the quipment bounded.

Thus, the architecture of Figure the geographical areas assumed

Figure 2. System arc

When observing Figure 2. it system is event-driven, mainly event queue”. This queue includwith the dispatch problem, eiththat requires action: dispatch ofserve a EWO.

Switching the best executioother task provided, included scenario”, what makes posappropriate mathematical moproblem. Scenario definition between supply and demand, into the available maintenance workday journey and demandcharacteristics of pending EWapproach is the efficient definterms caused by extreme climahuge number of EWOs and crews. In low demand conditionthe equilibrium between suppdemand less than supply.

The component “Apply the scomprises a set of proceduresfrom the scenario diagnostic carThis approach considers that assigned to any of the maintegeographic area.

The final scheduling of eaconsidering the pending EWOs“Define crew routes”. From tcorresponding mathematical mbe assigned to the best maintena

Finally the component “Warnactions and procedures adoptesame time that show technicalthe occurrence of non assignecrew area.

Next is described the mathem

Checking event queue

Define

Wara

Execute action

Data

2. is replicated to each one of .

hitecture proposed.

can be noted that the proposed by the component “Checking

des all the operations regarded her registers or even someone f a given maintenance crew to

n scenario at each instant is in the component “Define a

ssible to switch the most odel to solve the dispatch is based on the relationship

n such a way that supply refers crew hours remaining in its

d refers to the number and WOs. The main goal of this nition of critical conditions in ate events, usually involving a

requiring more maintenance ns, what might be observed is ly and demand, occasionally

scenario mathematical model” s when solving the problem, rried out in the previous phase. each pending EWO must be

enance crews available in the

ach maintenance crew when s is carried out by component the scenario defined and the

model chosen, each EWO will ance crew to serve it. ning and alerts” refers to signal d by the system core, in the l inconsistencies, for instance ed EWOs on a non available

matical model proposed.

e a scenarioApply the scenario

mathematical model

Define crew routes

ning and alerts

Core

abase

B. The mathematical model developed In order to solve the vehicle routing associated with the

EWODP, one mathematical model was developed by considering that there are a given set of crews with a previous known route, which includes services called commercial orders. Given an instant of time in that a certain number of emergency orders come up, it is assumed that they will be assigned to the given crews in such a way that previous routes will not be changed. This fact will cause an insertion of emergency services in the previous known route, called as offline route, of a certain crew chosen, involving a decision of which subset will be assigned to each crew and in which position on the route.

On the following mathematical model, two criteria are used to integrate the objective function: the former, weighted by W1, aims to reduce the latency cost of all orders; the latter, weighted by W2, includes the cost of unassigned emergency orders.

The following parameters are considered: 0 : dummy order to define the final destination

point of every crew; Ve : set of emergency orders; Vc : set of commercial orders; Vs : set of start points, which represent the initial

position of each crew; V : }0{∪∪∪= sce VVVV R : set of routes / crews; t0 : initial time for every crew; T : end time for every crew workday; suc(i) : the successor point of i in the a priori route,

cVi ∈ ; pre(i) : the antecessor point of i in the a priori route,

cVi ∈ ; rC(i) : the route index in which point i is inserted

cVi ∈ ;

ite : time when the emergency request i came up, eVi ∈ ;

its : execution time of order i, }0{\Vi ∈ ;

C : cost related to each non-assigned emergency order;

E :

},,;,0,{},,,

;,,{)}(,,,;,,{)}(

,,,;,,{

RrVjVirijiRrVjVi

rjiirCrRrVjVirjijrCr

RrVjVirjiE

e

ee

e

e

∈∈∈><∪≠∈∈∈

><∪==∈∈∈><∪==

∈∈∈><=

jic , : travel time between points i and j;

M : a huge value, typically 2T; W1,W2 : weighted factors of each objective function

component, with W1+W2 =1.

The following decision variables are defined:

xijr 1 if point j is successor of point i in the route r; 0 otherwise;

yi 0 if the emergency order i is assigned to some route;

1 otherwise; ti : time when order i is completed;

Min ∑∑∈∈

+ee Vi

iVi

i yCWtW 21 (1)

Subject to:

1,,

=+∑>∈<

iErjiijr yx eVi ∈∀ (2)

1,,

=+∑>∈<

jErjiijr yx eVj ∈∀ (3)

1,,

≤∑>∈< Erji

ijrx RrVVi sc ∈∀∪∈∀ , (4)

1,,

≤∑>∈< Erji

ijrx RrVj c ∈∀∈∀ , (5)

0,,,,

=− ∑∑>∈<>∈< Erlj

jlrErjiijr xx RrVj e ∈∀∈∀ , (6)

0),(,,,

=− ∑∑∈>∈< eVh

risuchErjiijr xx RrVVi sc ∈∀∪∈∀ , (7)

0tti = sVi ∈∀ (8)

∑>∈<

−+

+++≥

Erjiijr

jijij

Mx

tsctt

,,)1(

)(

ViVj ∈∀∈∀ , (9)

iiipreiprei tsctt ++≥ ),()( cVi ∈∀ (10)

Ttst ii ≤− eVi ∈∀ (11)

0≥it Vi ∈∀ (12)

}1,0{∈iy eVi ∈∀ (13)

}1,0{∈ijrx Erji >∈<∀ ,, (14)

The objective function is presented in (1), corresponding to a weighted sum of two factors, as mentioned before. Constraints are shown in (2)-(18).

In (2) and (3) it is imposed that one emergency point must have successor and predecessor or remain unassigned, leading, in this case, the corresponding y variable to 1. In (4) is defined that each commercial order may have at most one emergency order as its successor and in (5) it is imposed that each commercial order may have one or zero emergency

order as predecessor. When one or more emergency orders are included in a route, one linking arc between two successive points is replaced by one point (or even a sub route) and its two linking arcs. Constraints (6) and (7) ensure this reconstruction by imposing linking arcs before and after the new route point. In (8) it is defined the initial time for all starting points and (9) establish the end time for all emergency orders or even for all commercial orders that succeed emergency ones. Constrains (10) define the end time for the remaining commercial orders. In (11) it is imposed that all emergency orders must have its execution time before the end time for every crew workday. And finally constraints (12) to (14) define domain set for all decision variables considered.

III. PRELIMINARY RESULTS

Preliminary results were obtained when the system faces the following actual case:

• 40 commercial orders; • 3 repair crews; • 9 emergency work orders (EWO).

Figure 3 shows 3 repair crews and their corresponding routes, namely 3056, 4019, and 4025. All of them begin their work at 8 am and finish their journey on 5 pm, assuming that there will be one hour for lunch at 12pm. The scenario of Figure 5 shows that every repair crew is already charged of commercial orders when it will serve EWOs. The overlappings in the routes are consequence of the latency cost minimization assumed as the objective criterion.

Figure 3. Maintenance crew routes for commercial orders.

From scenario of Figure 3, Table I shows the schedule for each maintenance crew considering only the commercial orders previously assigned to. There will be also three kinds of priority levels for all commercial orders: lower will be the most critical service and all routes have their first part formed by orders of level 0 (p0), followed by orders of level 1 (p1) and finally orders of level 2 (p2).

TABLE I SCHEDULE FOR COMMERCIAL ORDERS.

#Crew Start time

Finish time

#orders p0

#orders p1

#orders p2

3056 8:00am 4:53pm 4 1 10 4019 8:00am 4:46pm 5 4 4 4025 8:00am 4:35pm 3 7 2

At 8:00 am, 9 EWOs come up and they must be attended

before every other order. This aspect conducts a new routing for all crews in order to minimize the latency cost, whose result is shown in Figure 4.

Figure 4. Maintenance crew routes after considering 9 EWOs.

Table II shows the summary of the schedule for each crew. It can be noted that finish time were postponed for all crews. Two main course actions may be assumed: (1) maintaining end time at 5 pm and collecting the last orders (of priority p2) to be scheduled next day; or (2) paying each crew for his corresponding overtime and completing the schedule.

TABLE II SCHEDULE FOR BOTH COMMERCIAL AND EMERGENCY ORDERS.

#Crew Start

time

Finish

time

#emergency

orders

#order

p0

#orders

p1

#orders

p2

3056 8:00am 7:56pm 5 3 5 3 4019 8:00am 6:30pm 2 4 1 10 4025 8:00am 7:55pm 2 5 6 3

IV. FINAL REMARKS

This paper has presented a mathematical model to address the emergency work order dispatch problem. The consideration of several levels of priority has proven to be suitable to give alternative scenarios to the decision maker in order to define which is the most appropriated routes when emergency order occur.

By considering the minimization of latency cost in the whole routing problem, the waiting time for exactly emergency services is also reduced. When adopting this approach, decision maker will be able to developed several analysis and calculations in order to choose the most suitable routing.

Future works might involve investigations about the consideration of other criteria in the objective function and certain mechanisms to postpone emergency attendance.

ACKNOWLEDGEMENTS

The authors would like to thank the AES SUL Distribuidora Gaúcha de Energia SA for financial support provided to the project PD-0396-0031/2011, namely “Sistema de Apoio à Decisão para Despacho automático e integrado de ordens de serviços emergenciais”.

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