2.1. Organization and Management of the Emergency Service

In current health care systems, emergency structure is a pivot link in the chain of patients’ care process. Considered as the main entrance and the central mission of health care facilities, emergency structures are influenced by the changes that have affected hospital systems. To these mutations are added the regularly increasing flows of patients in emergency structures leading to congestion and disruption in the functioning of these structures. The major challenges of these changes are the reduction of waiting times deemed excessive by patients, preventing the saturation of the structures and ensuring the safety and quality of care for patients. The multiplicity of nature and form of demands of emergency care explains the complexity of such an organization. Inflows and outflows to the emergency structure make the system management of emergency a complex interacting system. In addition, activity in emergency structures is characterized by the irregularity of the quantity and the nature of the work involved [1]. Patients’ satisfaction is far from being guaranteed due to waiting time which is sometimes excessive.

In France, the recognition of PED is today acquired and is part of the health policy emergency regional pattern and the regional health organization scheme. Indeed, the origin of the establishment of a dedicated structure exclusively to pediatric emergency is the need to treat children in a specific environment suited to the child. The need for adaptation is essential in the case of the care of children. This need is required in the case of the care of children and their families is all the more true that the child is young. This need is also explained by the large number of children attending hospital emergency departments. Given the growth in the number of pediatric emergency consultations, several studies have been conducted since the mid-90s to understand the causes and consequences in order to contribute to the improvement of pediatric emergency organizations.

For several years in France [2], as in Europe or elsewhere [3] [4], urgent pediatric care demand increases to clog all care systems (hospital pediatric centers, liberal pediatric care systems). Some studies talk about inflation, while others highlight the problems of false emergencies or the “perceived emergency.” In most of these studies, the emphasis is always put on children emergency consultations and believes they represent between 25 and 30% of hospital emergencies at national level. Although the majority of these consultations is in private practice, a significant number of patients turn to hospital emergency services leading to saturation.

The hospital system is qualified as a real care production system whose main mission is to provide the best care for patients. Field observations have shown the complexity of the hospital: multiple missions, prioritization, silos, heterogeneity of equipment and facilities, etc. [5]. There is also a wide range of professions. In addition to typical hospital professions there are some activities not directly related to the care activity (administrative, technical, computer, etc.). Finally, the care activity is intrinsically a complex activity, specific to each patient, which differentiates it from a conventional industrial production activity. The specificity of hospital activity is itself complex and can only increase the complexity of the organizations that are responsible. So the human characteristic seems to have an impact on the complexity of production operations as well as their duration and their quality. This complexity is enhanced by the diversity of demand and the interdependence of the care process (time dependence, spatial or related to possible sharing of resources).

2.2. Overcrowding Phenomenon in the Pediatric Emergency Department

One of the most discussed issues in PED is around overcrowding. This phenomenon is manifested by a lack of human and material resources (mainly admission beds) in front of an urgent demand for care [6]. This leads to the dissatisfaction of patients [7] [8] not finding the required care quality [9] [10] and a tired and overwhelmed staff [11], without neglecting the substantial financial losses [12] and the risk of mortality which is the most serious issue [13] [14] [15].

The overcrowding phenomenon occurs when the demand exceeds supply. This limits the scope for organization and planning. The situation is worse in the case where several patients arrive at the same time (case of food poisoning in a canteen for example). In [16] the overcrowding is defined as “a situation in which the identified need for emergency services exceeds the resources available to support patients in the emergency department, in the hospital or in both at once”. This definition has been widely adopted thereafter. However it does not focus on time horizon or the consequences whereas the overcrowding phenomenon is not a peak of activity. The overcrowding phenomenon can be extended over the term and the magnitude of its adverse effects is proportional to its duration in the time. That is why we propose the following definition: A state of overcrowding in PED is an imbalance between the flow of care and support capacity for a sufficient time which can lead to disturbances in the functioning.

Many researched have studied the problems in PED and various methods have been proposed but actually, there is no decision support system able to manage the PED and the problems corresponding to an overcrowding situation.

2.3. Decisional Models for the Pediatric Emergency Department management

The simulation is highly advantageous when it is used to model certain complex patient flow through the hospital and to test different scenarios by changing the control rules. This happens typically in the emergency department, where patients arrive stochastically and require a wide range of treatments (from light care to the management of severe injury), covering multi services and specialties. Wrong direction can cause a significant increase in waiting times and costs.

Centeno et al. consider four specific areas of maternity service to optimize (i) patients flow process and (ii) the use of resources. A flow diagram has been established, modeling the pathways of emergency patients (childbirth) and patients who have appointments for examinations or interventions. The studied system mixes stochastic arrival and deterministic process, which strengthens the interest of this study. Miller et al. have focused on improving the functioning of emergency services in order to minimize the length of stay of patients. This work has attempted to identify and analyze the various discrete patient-centered processes. It has proved a better understanding of the organization of the PED for medical staff. Samaha et al. show that an organizational problem is not necessarily related to the resources involved; the operation was to reduce the residence time of patients in the PED by identifying resources bottleneck and visualizing the different processes of this service. An experimental plan is used by Baesler et al. to estimate the additional demand that can be accepted by an emergency care service, while maintaining a reasonable waiting time for patients and considering the current material and human resources. It is therefore to estimate the maximum capacity of the service. Glaa et al. propose a model of the patient journey in an emergency service through GRAI methodology, with the aim of optimizing this route and improve the quality of patient care [17]. The models are characterized by great diversity in activities and by a large number of stakeholders. The simulation helped identify organizational problems of the system and evaluate several alternative organizations on the physical layout, staffing, etc.

2.4. Human Resources Scheduling

Resource management and planning known under the name of scheduling is to plan and give a chronological order to tasks (elementary activity) in a process to perform an activity in several steps, while using the available resources (labor, machinery, energy, transport, etc.). Generally there is obvious shortfall in resources. Moreover, this process evolves under various constraints (cost, deadlines, stock, priority tasks, etc.), which makes scheduling subject to combinatorial problems of NP complexity sometimes difficult to resolve [18] in a way optimal in practice [19]. Indeed, scheduling has invaded almost all areas as it has proven its benefits by optimizing the processes and increasing productivity. It is mainly applied in industry (scheduling workshops), but also in computing (scheduling of processes in operating systems) or construction (project monitoring) .etc. Several scheduling methods exist, each method has its specificities. Generally we classify them according to the nature of the solution (exact or approximate). Scheduling is commonly used in industrial looking to minimize manufacturing costs and increase productivity. Each process requires one or more human resources (doctors, nurses, anesthetists, stretcher …) and material (operating rooms, hospital rooms, medical equipment, imaging, radiology…) that can be shared in a common environment. The evolution of the process is done under the constraints (time, cost, regulatory).

Several works in the Operating Room made analogies with workshops and used heuristics [20] and genetic algorithms [21]. Other studies have used constraint programming [22]. For home hospitalization, Ben Bachouch et al. have studied how to assign tasks and balance the nursing workload [23]. The proposed mathematical model takes into account the availability of practitioners, skills and qualifications required by the tasks. In the emergency department the objective of Daknou et al. was to minimize the waiting time for patients and minimize costs while maintaining a good quality of care [23]. The author proposes scheduling based on List algorithm that takes into account the priorities assigned to tasks. The assignment of medical staff is a crucial problem for the proper functioning of the PED and more difficult because of the irregularity of the quantity and the nature of the activities characterizing the functioning of emergency organizations [24]. It is therefore essential to optimize the assignment of medical staff members respecting on one hand, skills and availability, and on the other hand, patient flow.

Hence, scheduling is no longer restricted to the industry and now health care field also needs to optimize its operation to better achieve its objectives based on the world of engineering.

In this paper, we are particularly focused on human resources planning in pediatric emergency organizations, which is not yet processed depending on the analysis of the state of art.

4.1. Parameters

4.2. Variables

4.3. Institutional Parameters

4.4. The objective Function

Minimize:

The objective function is a sum of penalty terms. Each of the terms refers to a specific soft constraint.

4.5. Hard Constraints

The following hard constraints condition the feasibility of the solution.

• SSOrp : The Sum of Splittable Operations (or portions) allocated to treatment room r at period p should not exceed the capacity of the treatment room:

  (2)∀r∈R, ∀p∈R,∑Ajpr≤SrR

  Linking the variables X_jpr and A_jpr relative to splittable exams:

  (3)∀Pj€Pjs, ∀r∈R,∀p,{Ajpr≤Card(Pjs)*XjprAjpr≥Xjpr

  The two parts of equations above are required to check X_jpr = 1 if A_jpr ≠ 0.

• SPSrp : The Sum of Patients who have Splittable health care operations should be equal to :

  (4)Card(Pjs), ∀Pj€Pjs↓

  Linking the variables X_jpr and X_jp relative to splittable operations:

  (5)∀Pj€Pjs, ∀p∈R,{∑r∈RXjpr≤npRXjp∑r∈RXjpr≥Xjp

  At most npR treatment rooms can be used to schedule health care operations in period p.

  Equation (5) confirms that, when X_jp = 1, there is at least one variable X_jpr set to one and at most npR .

• NSOrp : A Non Splittable health care Operation should be assigned to exactly one treatment room:

  (6)∀Pj∈Pjns,∑p∈□∑r∈RXjpr=1

• ROPrpq : A room cannot be used by two patients in two overlapping periods p and q:

  (7)Xj1pr+Xj2qr≤1,∀Pj1,Pj2∈NP,∀r∈R

• MSPrpq : Two Medical Staff members who have Patients in common cannot be allocated in the same period or in two overlapping periods p and q:

  (8)Xj1p+Xj2q≤1,∀Pj1,Pj2∈NP

4.6. Soft Constraints

The solution quality is determined through the following soft constraints.

• CPPlkSP : Whenever two health care providers having patients in common are placed in two Consecutive Periods in two different sites, a Patient travel penalty is applied:

  (9)CSP=wT∑ml,mk∈MSClkSP

• MPC_p: Whenever a Medical staff member is allocated to treat one or more Patients in the Corridor at period p, a corridor penalty is applied:

  (10)Uc=wc∑Pj∈NP,p∈□Ujpc

• Cappr : Whenever at least two patients are treated at the same period p in the same room, a capacity penalty is applied:

  (11)BCr=BCpr∑Pj∈NP,r∈R,p∈□Ujpr

4.7. Criteria

5.1. Fuzzy homogenization criteria

According to the criteria we defined, we are interested in this part in the evaluation of solutions. These criteria have different weights and therefore are not of the same importance and the relation between them is complex and non-linear. Hence, to take into account these difficulties and to evaluate the obtained solutions, we will start with the definition of lower-bounds. For each objective function f_q (.) related to a criterion we define a lower-bound fq* , such that: ∀ x ∈ Ω, fq(x)≥fq* . The objective functions can have different values belonging to intervals with different lengths. This makes some objectives dominating others. So, in order to homogenize the objective functions, we apply fuzzy logic: to each feasible solution x, we associate a vector characterized by its components which are the objectives to be optimized: f (x) = (f₁ (x), f₂ (x), …., f_L (x))^T,

Let fqbest the best value of the q^th objective function given by a chosen evaluation method. For each f(x) we make fuzzification as follows:

Fig.1.

Fuzzy Logic Application for Solving Scale Problem

ε_q is a little positive value designed to avoid the problem of dividing by zero (when fq*=fqH ) with:

We consider two fuzzy subsets: good solutions and bad solutions for the q^th objective. The result is a vector characterizing a solution where the components are homogeneous and belong all to the interval [0,1]. At the end we formulate the fuzzy fitness function.

5.2. Lower-Bounds Calculation

Criterion 4: Workload Balancing: Cr4

Because the workload of a medical staff members must be an integer, we will take the integer value of ∑j∑iγi,jM

• Lemma 3

The integer value of ∑j∑iγi,jM is the lower-bound of Cr₄.

⌊∑j∑iγi,jM⌋≤∑j∑iγi,jM≤⌊∑j∑iγi,jM⌋+1

So if ∑j∑iγi,jM is an integer then ∀ S, Cr4(S)≥∑j∑iγi,jM Else ∀ S,Cr4(S)≥⌊∑j∑iγi,jM⌋+1

Recently, Evolutionary Algorithms (EAs) have been proposed in different fields (engineering framework, computer science and operation research) to solve Multi-objective Optimization Problems [25] [26] [27].

The principal advantage of this optimization technique is the fact that it operates on data without using preliminary knowledge on the processed problem. It also evolves from an initial population of possible solutions iteratively bringing a global improvement according to one predefined criterion [28] [29]. Therefore, the EAs can represent a suitable technique for implementation of the multi-objective optimization based on the aggregative approaches. The most common fitness function used to evaluate the quality of solutions is: Ffitness(x)=∑q=1q=Lwq·fq(x) with w_q the weight of the q^th objective function and w_q ∈ [0,1] ∀ 1 ≤ q ≤ L. The sum of weights is equal to l.

• Dynamic aggregative approach evaluation

In the EA we use the fitness function fg(x)=∑q=1q=Lwq·μqG(fq(x)) the weights w_q (1 ≤ q ≤ L) are dynamically computed using a specific fuzzy rule. The idea is to measure the mean quality of solutions according to each objective function at each iteration and compute the different weights according to this quality.

Let f¯qk the mean of the q^th objective function values of the solutions at the k^th iteration of the EA:

(28)f¯qk=∑x∈Pkfqk(x)cardinal (Popk)

where Pop_k is the population of the solutions at the k^th iteration of the EA.

At the k^th iteration of the EA, we evaluate the quality of solutions according to the q^th objective function. The evaluation is done using the membership functions shown in figure 2.

Fig. 2.

Membership functions for objective function values

So, two fuzzy subsets could be distinguished:

• •

  Near_q: the subset of solutions near the lower-bound value fq* according to the q^th objective,

• •

  Far_q: the subset of solutions far from the lower-bound value fq* according to the q^th objective.

As shown in figure 2, the membership functions could be formulated as follows:

(29)μq,kFar(f¯qk)=f¯qk−fq*f¯q0−fq*+ε′q  if  f¯qk∈[fq*,f¯q0+ε′q];else μq,kFar(f¯qk)=0

where ε′ _q is a little positive value to solve the problem of dividing by zero (when f¯q0=fq* ). It is formulated as follows:

(30)ε′q=0.01·fq* if f¯q0=fq*;  else  ε′q=0

The calculation of the weights wqk+1 will be made using the fuzzy rule:

IF  (f¯qk  near  fq*)  THEN (wqk+1↓),IF  (f¯qk  far  fq*)  THEN (wqk+1↑).

The application of the previous rule can be expressed as follows

wq1=1L  ∀1≤q≤L;wqk+1=μq,kFar(f¯qk)∑q=1q=Lμq,kFar(f¯qk)∀  1  ≤  q  ≤  L  and ∀  1  ≤ k ≤Q-1

where Q is the number of iterations.

The different weight vectors (W¹, W²,.., W^k,.., W^Q) will be calculated dynamically, by evolving from the k^th generation P_k to the next generation P_k+1) according to the distance between the lower-bounds and the mean of the individuals of the generation P_k (showed by a black circles in figure 3). The objective is to explore the possible improvements of the solutions. The priority is given to the optimization of the objective functions whose values mean is far from the optimal value (or the lower-bound value). Thereafter, while using such a fuzzy technique, it would be possible to control the direction of search to construct a final set of solutions close to the optimal one. This final set will be used for selecting Pareto-optimal solutions and the others will be rejected.

Fig. 3.

Fuzzy dynamic control of search directions

6.1. Overview of the adopted method

The considered problem presents two sub-problems. The first is the assignment of each operation O_i,j to the medical staff member m_k. The second is the calculation of starting time t_i,j of each health care operation O_i,j.

To solve such a problem, we apply initially an assignment approach. It is used to assign operations to health care tasks taking into account the skills of medical staff members and the workloads of medical staff members to whom we have already assigned operations. Then, it solves the problem of tasks sequencing through a scheduling algorithm which calculates the execution start dates t_i,j taking into account the availability of medical staff members and constraints precedence. Conflicts are resolved by applying conventional priority rules (FIRO, FIFO, LIFO and we get a set of scheduling according to the priority rules applied. In emergency department priority is given at first to the most urgent cases, then to the patient who has arrived first. The scheduling procedure is as follows: according to the availability date of a medical staff members and the availability of the corresponding health care operation, the starting time of the operation is the minimum date among the two availabilities’ dates. On the set of scheduling, we apply an evolutionary algorithm that will serve to the construction of new individuals and the acceleration of convergence. The objective is to make EAs more efficient and faster. Indeed, the construction of solutions is promoting reproduction of individuals respecting the schedule generated before and not from the entire set of chromosomes. More details will be given in the following section.

Starting Time Calculation

BEGIN

initialize the vector of medical staff availabilities Dispo_Staff[k]=0 for mK (k ≤ M);

initialize the vector of operations ready to be executed Dispo_Op[i, j]=0 for each patient Pj (j ≤ N) and for each operation Oi,j, i ≤ nj;

FOR (j=1 ;1 ≤ j ≤ N)

FOR (i=1,i ≤ Maxj (nj))

  construct the set Ei of operations to schedule from S:

  Ei ={Oi, j / Si, j, k =1, 1 ≤ j ≤ N};

  classify the operations of Ei according to the chosen priority rule;

    calculate starting times by following the same order given by the classification of Ei according to the formula:

    Dispo_Staff[k]= Fuzzy Availability Processing (Ci,j,k, Evi,j,k);

    ti, j = Max(Dispo_Staff[k], Dispo_Op [j]) such that Si,j,k =1;

    updating of the vector of medical staff members availabilities:

    Dispo_Staff[k]= ti, j + Fuzzy Availability Processing (Ci,j,k, Evi,j,k);

    updating of the vector of treatment tasks availabilities: Dispo_Op [j]= Fuzzy Availability Processing (Ci,j,k, Evi,j,k);

  End FOR

End FOR

End

6.2. Application of the Evolutionary Algorithm

In this step we apply an evolutionary algorithm based on the scheme theory application [25].

In this stage, we generate from the set of assignment constructed above, an assignment scheme to control the genetic algorithm. This scheme is going therefore to represent a constraint that must be respected by the new created individuals. This method consists in considering the assignments S^Z given by the earlier scheduling method and to determine (for each operation) the set of possible medical staff members using a genetic algorithm.

The objective is to rapidly find out efficient solutions by starting only from individuals who respect the generated model. So, since the set E, we gather the set of assignments A^z (1 ≤ z ≤ cardinal(E)) given by the application of the first steps. Besides, we define the set of medical staff members who may lead to a good scheduling solution. Thus, to limit the blind aspect of genetic operators, in order to obtain a viable chromosome without correction operators, we make genetic manipulations to accelerate convergence. After that, we make tests to check whether the individual respects what the assignment scheme has imposed. Finally, we apply multi-criteria evaluation based on Fuzzy Logic to decide about the solutions.

The crossover operator of our evolutionary approach is a Crossover Mask. The efficient applied coding was inspired from [1] respecting the constraints of our problem.

For mutation, we propose artificial mutation operators able to ensure this optimization referring to the criteria previously defined. For example, for the minimization of the response time to health care treatment for patient j, the proposed algorithm is as follows:

Mutation 1: Operator of mutation reducing the response time for treatment for patient j

- Select randomly an individual S ;

- Choose the treatment task j whose response time the most long : (Maxj{RTLj such that RTLj =∑i∑k Si,j,k.di,j,k}) ;

- i=1; r = 0 ;

- WHILE (i≤nj And r = 0)

    Find K0 such that Si,j,K0 =1;

    FOR (k=1, k≤M)

      IF (di,j,k < di,j,k0) Then {Si,j,K0 =0; Si,j,K =1; r=1 ;}

      End IF

    End FOR

    i=i+1 ;

 End WHILE

- Call to “Starting Time Calculation Algorithm” to calculate the starting and completion times;

• Simulation Scenario

The access to the PED Jeanne de Flandre database has followed a privacy protocol. We have recovered for each patient a certain number of information: Age, sex, mode of arrival, diagnosis, the exact entry and exit dates that enabled us to deduce the length of stay, the date of the first consultation and finally the orientation or hospitalization.

To solve the MHCTS in the PED, we propose the following illustrative example. We will detail the different aspects and logic adopted by our decision support system. Our initial situation is a waiting room with patients already signed up with the registration nurse. In treatment rooms there are medical staff members executing health care operations corresponding to several patients. The table below represents the patient database. We choose a sample from the database given above. It contains 10 patients who arrived at the PED in 27^th of November 2013. To each patient correspond a pathology, an emergency degree and an arrival date. Patients’ information is requested by a nurse and processed into our system. Data received by the reception nurse passes through a pathology test in order to collect several data including emergency degree and needed resources. These data will be used to generate a priority degree giving patients positions in the waiting queue. The position is generated using the proposed scheduling algorithm.

For pathologies, we chose 3 items: concussion, gastroenteritis and compound fracture. To each pathology corresponds a list of health care operations is defined. We attribute 1 to the cells corresponding to operation which must be done at first, 2 for the next operations and 3 for the last ones. We do not sort operations in the same group of attributes. (Table 6)

The table below gives details about health care operations to be executed in order to treat patients. The third column represents the execution time (in seconds) related to each operation. The four last columns correspond to the score of medical staff member able to execute the health care operation. The highest score means that the medical staff member is the most suitable for the operation performance.

If score=3 then the medical staff member has the needed level of experience, he is the most suitable for this operation execution. However, if this medical staff member is not available, we can choose another medical staff member with a lower score (2 or 1). If the score=0, the health care operation cannot be executed by a medical staff member without the minimum level of experience. For the medical staff details, they are given in the table below:

The medical team of the Pediatric Emergency is as follows: 2 care pediatricians (specialists), 1 internal general medicine, 2 Internal Pediatrics, 1 surgical intern, 2-3 nurses and 2 childcare assistants. To each medical staff member corresponds an availability parameter; it is equal to 1 when the health care provider is available at the time of simulation, 0 when he is executing a health care operation. This parameter is updated through the whole process when the situation of the medical staff changes.

In the table below are represented the set of patients, the corresponding health care operations and the needed skills for their execution. For each patient, we have a maximum of five health care operations are executed by the medical staff members, and for its execution a level skill is needed. In the studied case we have six different skills.

We tested the proposed approach on the four available instances. Overall, the algorithm is able to give satisfying solutions which were better than all the solutions produced by the health care practitioner. However, because the approach encloses different parameters, our goal is to analyze the impact of each parameter of the algorithm to define the best configuration to adopt. The parameters set are varied in series of values to extract the best value corresponding to each parameter. For each instance, the best solution in the population is chosen as the representative for each test.

The maximum number of generations in our genetic algorithm is a key parameter of the method. Decreasing or increasing it would impact the number of generations and the challenges of producing new solutions.

Figure 4 presents the results when varying the number of generations between n and 2n. The y-axis represents the aggregative objective function, a sum of the four defined weighted criteria. The columns in grey represent the results when the number of generations set to n and in black when the number of generations is set to 2n. The figure shows that running the algorithm with 2n does not help find better solutions. Out of four instances, 2n is worse than n three times. This can be explained by the problem complexity for the considered instances and the existence of splittable and non-splittable health care operations.

Fig. 4.

Impact of The Number of Generations on the Four Instances.

On the other hand, increasing the number of maximum iterations has an influence. The run time can increase with at least 10% if the maximum number of iterations is doubled. This is in fact a draw back for some emergency departments as they seek to have a tasks scheduling in the less time possible.

The probability of applying the local search (assignment process) can be a key factor in our approach. Table VI shows the effects on the four instances with the different values of p_m. These values are considered to test whether a high probability would enhance the algorithm. Columns 0.1, 0.4, 0.5 and 0.6 present the tested values of p_m. Each column contains two columns: the rum time (CPU) in seconds and the quality of the solution (Cost). The default value for p_m being 0.1, fallouts show increasing the probability of calling the local search is not always beneficial. This can be explained by the fact that calling the local search more frequently does not necessary improve the best solution in the population.

This shows that the impact of the probability on the best solution is usually not considerable as the most important part is the local search itself. It is also worth noting that increasing the probability does not impact the run time. p_m is the probability using local search operators.

The proposed multi-skill scheduling applied has given the Gantt of figure 5. This practical problem consists of a mix of classical constraints that can be found in the benchmarks of the literature and a set of new constraints.

Fig. 5.

Gantt

In particular, the new constraints (hard and soft) consider health care operations that take place on multiple sites of the PED. The hard constraints forbids medical staff from treating patients in two overlapping periods and rooms from being used more than once in two overlapping periods. Splittable health care operations are also managed using hard constraints. The new soft constraint imposes a penalty when for example a patient has to be treated in the corridor in an overcrowding situation.

The approach was tested on four available instances. A parameter tuning was performed to determine the best parameter settings for the approach. The tuning results showed that the probability of applying the local search and the size of the population does not have a big impact on the instances. The results also showed that the proposed approach outperforms the approach currently used by the health care practitioner.

When we start the simulation the different databases are loaded. Our software includes managing interfaces covering essentially a Main Interface which allows administrator to visualize the different transactions and interactions in our system, a Theater (PED) Interface describing our PED architecture with different compartments and showing an animation representing medical staff paths while executing health care tasks and patients pathways and an Indicators Interface used to monitor the status of the different actors in the PED (figure 6).

Fig. 6.

Indicators Interface

In fact, the first panel shows the evolution of patients’ treatment process; at the beginning, while the patient is still in the waiting room, the corresponding led is red. When the treatment of the patient starts, the indicator becomes orange and it increases with each completed operation. When the last operation is completed, the indicator becomes green, the patient is thus ready to leave the PED. In the second panel we monitor medical staff availabilities. Indeed, the red color indicates that the corresponding medical staff member is already executing a health care operation and the green color indicates his availability. We have as well the Evaluation Interface representing the evolution of patients’ pathways and the health care activities being completed for each patient. The parallel line to x-axis represents the time spent in the PED. For example we have in the figure 7, 6 patients; the first one has arrived first, then patient 2, then patient 3, then 4 and then 5 and 6. At t=t₁, the length of stay of the first patient is the highest one, so he needs attention. However, the last patient has already arrived, so if his emergency degree is not high, we consider that he undergoes the normal treatment process and there is no need to worry about him at the moment.

Fig. 7.

Evaluation Interface

This tracking helps to know at each moment how many patients we have as well as the evolution of their treatment process. It also improves the service quality and information delivery through indicating the length of stay of each patient in the PED. Figure 7 represents a comparison between patients’ treatment time with/without using our approach. It corresponds to the time spent in the PED by each patient (treatment time = exit date-entrance date). The graph shows a decrease of the time that patients spent in the PED. The last green shape represents the average treatment time of patients. The comparison shows a reduction of the average time spent in the PED.

Fig. 8.

Treatment Time Analysis

In figure 9 we compare results with/without using our approach. We made some tests using our approach, the results reveals a waiting time minimization.

Fig. 9.

Waiting Time Analysis

The graph of figure 9 represents a comparison between patients’ waiting time using our approach and the normal waiting time according to the data base with real statistics. It shows that waiting time takes an average wait less than 10 minutes using our approach. So, the main goal which is patients waiting time reduction is accomplished.