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Integrated planning and scheduling of the surgical ward with considering the relevant sections of operating room under patients’ uncertainty processing time
Abstract
Today, the health sector and hospitals serving to the people is very important. Operating room as a critical components of a hospital has a fundamental role in the performance of this collection. In this paper, by considering the sections relating to the operating room for surgery, we provide a plan and integral scheduling. Based on this, two mathematical models has been developed to study the issue. The first model is mixed integer programming with the minimizing objective function of the total patient waiting time. This model was designed for three-step of preoperative care, operating room and the recovery of patients after surgery, which includes scheduling, allocation and sequence groups of patients in each section that is determined based on the priorities of considered for each patient, so that the time of served to patients at every stage according to the level of expertise and the existence groups’ skill in every step has been taken. In the second model due to the uncertainty of the time of surgery of patients in this issue, we have used the MOLVEY optimization approach. In this approach three scenarios to consider the entire patients serving time, has been used. The solution and resolution analysis of this model provided robust results, so that fluctuations in the solutions of this model is less than deterministic model in the acceptable level.
Keywords: health systems, planning and operating room scheduling, uncertainty, robust optimization
Introduction
The purpose of health systems are issues related to hospitals, clinics and labs. The problems which can be mentioned in this area are long time waiting, canceled time and a lot of resources. Although, traditional approaches to solve the mentioned problems applied some solutions such as hire more people and buy equipment, but because of problems like lack of specialized staff and hospitals financial constraints, did not have the efficiency. Also, there are reasons such as lack of efficiency in scheduling staff, allocation of resources and lack of communication between staff and hospital administrators, has led to new approaches to improve service management and reform in their organizations. Health center managers are looking at new approaches to providing good services for patients, reduce costs and optimize the financial assets with regard to patient satisfaction. Operating room is the most expensive and highest-paid department of hospital that has the greatest impact on hospital performance, so that 40% of the costs of hospital’s total costs usually include surgical cost and provides about 67 percent of hospital’s total revenues. According to studies, 60% of patients during their participation in the hospital are under surgical process [1]. So managing conflicting priorities, reaction of stakeholders on this issue and predicting demand for surgeries are very difficult, so based on these factors, the need to develop a method to create an effective plan and schedule is clear.
2- Literature Review
The aim of timing is determining of sequence and allocate time to each activity, where the start and completion time of each activity is shown by a detailed timetable. Scheduling in health scope in the hospital is done in different sectors of hospital, but what were studied mostly is scheduling operating room as a separate part from other parts of the hospital. This is while operating room has noticeable effect on the function of the hospital, so the timing of this sector and its related sectors is essential as critical components of any hospital.
Surgical ward is includes the public sector (PHU), operating room (OR) and recovery room (PACU). Several factors have an effect on planning and scheduling of the surgery ward, including human resources (surgery, anesthesia, nurses, etc.), equipment, prior surgery capacity such as preoperative care unit, operating room installations and capacity of action noted.
The figure below presents the structure of the department of surgery and surgical services procedure to patients:
Figure 1. The flow shop scheduling problem of operating room and related sectors
According to Hans and Naybrg [2] approximately 70% of hospital admissions are related to the surgery. So majority proportion of hospital’s income and expenses related to the operating room in the hospital. In addition, the hospital operating room is in dealing with broad sectors such as ICU, CCU and emergency. Therefore, improving the performance of the department of surgery with effective use of available resources for providing high quality surgical services to patients, can lead to increased patient satisfaction and hospital’s income.
Magrlyn and Martin [3], Blake and Carter [4], Przasnysky [5] and Daniel Smith and colleagues [6] who studied the problem of planning and scheduling the operating room for the first time. Whereas, the best categorize of the planning and operating room scheduling problem in recent years has been done by Kardvyn and colleagues [7]. The details of the plan and schedule operating rooms have been divided into six general categories:
2-1 Patients characteristics:
Two main patients is considered: patient selection and non-selection. Selected patients split to hospitalized patients [8], [9], [10] and Outpatient [11], [12], [13]. Non-selection split to urgent patients [14], [15] and emergency [16], [17]. It should be noted that non-selective patients are randomly entered the hospital.
2-2 performance measurement:
Many of these performance metrics are considered as the cause of the problem. Make span and waiting time [18] practical [19], value, and preferred [20], operation power [21] and [22] A number of these objectives are being taken on this issue.
2-3 decision design:
The decision is usually based on history] [9.19, time [7,8,10,18], Room [21] and capacity [11], [23]. However, there are different levels for this decision which depends on the particular system can be based hospital surgeons [25] or patients [8.22] that is used.
2-4 Methods:
Refers to the method of selection and analysis, for example, optimization, scenario or method used to resolve such mathematical programming, simulation and meta-heuristic algorithms.
2-5 Uncertainty:
Uncertainty on this issue is relate to two main sources: 1) the entrance of patients [7], [13], [15], [24], [25] and 2) duration of surgery [15], [18], [ 26], which surgical duration is one of the most unpredictable processes.
2-6 application of research:
Effectiveness of the model and solving in real world is very important. Many authors use their studies theoretically [8], [15] or assess with the actual data, [7], [10], [11], [12], [22], [27].
3. Describe the problem
This research is examining a three-stage scheduling problem of the operating room, where each patient according to priority assigned to the beds in the PHU to receive essential services before surgery and be prepared for surgery, then the patients assigned to the first available operating room in order to surgery, and eventually the surgical patient allocated to the PACU beds for recovery. It should be noted that when the operating room or bed is not available for the patient, the patient must wait until the vacant of one of the operating rooms.
3.1 Problem’s assumptions
One of the most important factors affecting the appropriate timing is efficient access to the surgeons. Surgeons first assigned to the operations cases in the second part for starting surgery and after that the timing and sequence of operating room will be performed. Our limited resources in this sector are PHU and PACU beds, surgeons, and operating room. In this problem priorities according to the experts is intended for patients. Therefore, patients who have common points from the perspective of surgery are assumed in the same surgery group, since demand of all surgical sectors is high, so it seems reasonable to consider the individual timing for each section. After each surgery, the room must be disinfected and ready for the next operation, decontamination and room’s preparation time is dependent to sequence.
4. Computational model
In this section, we present the mathematical model of the problem, in this case, first introduce the model’s symbols and variables and then we will explain the objective function and constraints related to it.
4-1 introduction of symbols and variables
i, j: patients
k: Step
L: Group on stage as k l = 1,2, ..., lk
n: surgeons
tikal: ii patient serving time in stage k by l
saj: Preparing the operating room for surgical patient after the patient i j
wi: weight on patient preferences i
M: a positive large number
Xikl: binary decision variable to allocate patients in stage k i l group
Yijkl: binary decided Variable to allocate patient after the patient i j l in the group stage k
Vni: binary decided Variable to allocate the patient's surgeon to operate n i
Znij: binary decided Variable to allocate n surgeon surgery patient after the patient i j
Sikl: the start time of operations on patients in stage k l i by group
4-2 objective function and constraints
(1)
S.t
Equation (1) is calculated the waiting time for all patients surgery duration.
(2)
Equation (2) ensures that only one allocation for each patient at each step is possible, so that at each step only one group is assigned to each patient.
(3)
Equation (3) states that the start time in each stage must be greater than the start time and the serving time of before stage, in this manner serving to the patient would not be taken in the next stage unless the previous operation done.
(4)
Equation (4) states that two patients enters to the operating room sequences or bed, if earlier, both of them were allocated to a bed or a special operating room.
(5)
(6)
Equations (5) and (6) limits patients’ sequence start time in every stage. So that the constraint (5) identify start time of the sequence of patients in stage one and three, in constrain (6) as well identify start of the sequence of patients in the operating room in stage two. It should be noted that in the constrain (6) the preparation room’s operating time is intended that this time is dependent on surgical sequence in operation room.
(7)
Constraint (7) is as the equation (4), with the difference that here the allocation of patients to the surgeons involved.
(8)
Constraint (8) limits the start time of the patients’ sequence allocated to surgery.
(9)
Constraint (9) limits the allowed duration for PHU, PACU and state duration available for each day at that these sectors.
(10)
Limitation (10) states that the total duration of surgery and the operating room preparation should not exceed the allowed time, which is intended to model.
(11)
Constraint (11) also defines the allowed duration for each surgeon. In this way, the allocated time to each surgeon should not be greater than available permitted duration.
(12)
Constraint (12) shows that each patient is assigned to only one surgeon and the surgeon performs the surgery for the patient.
(13) (14)
Equations (13) and (14) are non-negative binary variables.
5. Solution approach
In this study, in order to reduce waiting time for patients, surgical ward integrated scheduling problem by taking the associated fields has been studied. Scheduling considered in three stages, where at the first stage patients admitted according to the number of beds available in the public sector (PHU), It should be noted that for each patient weight is allocated, which represents a priority for surgery, In the next step, by considering the number of available operating rooms and surgeons, patients are assigned to operating rooms and surgeons. At this point the expertise of the surgeons for patients’ surgical should be in consider and also should be noted that in real-world operating rooms allocate time to themselves after each surgery for sterilization and preparation for the next surgical. Because different devices may be used for both practice and since some patients suffer from infectious diseases, therefore taking the time to prepare and sterilize operating rooms after each surgery helps us to provide an efficient schedule. In the third stage based on operation sequence patients go out of the operating room and assigned to the intensive care beds or recovery section. But because of the uncertainty of patients’ serving time in each of the represented sectors, especially surgery duration to each patient, we use a robust approach to deal with this uncertainty. It may be due to delay in patients’ serving the in the operating room, surgical procedure changed and some patients’ surgery is not performed on that day and be canceled. Mulvey robust approach is used to solve this problem.
5.1 Molvey robust model
Molvey introduced two categories of variables in his model including control variables and the design variables so that in the design variables there is no possibility of an adjustment after determining the parameters, but about control variables it is possible. In his model constraints were divided into two categories: structural and control, where the control constraints are subject to change by the changeable data, while the structural constraints are same as the linear programming constraints. (Molvey et al., 1995)
The general model is as follows:
(15)
S.t
(16)
The first constrain is structural and is innocent of data variability and second constraint is control constrain. Suppose that are total scenarios and parameters under each scenario are uncertain. Note that in this model the probability of each scenario is equal to ps.
It should be noted that the answer is robust, when it is close to optimal value under each scenario. Also, the answer is robust in case of feasibility, when it is feasible under any scenario. You cannot find an answer in general terms that under any scenario is feasible and optimal, so between solution’s robustness and model’s robustness creating balance through multi-criteria decision-making.
Is error variable in control constraints that control answer’s feasibility. If we have in that case is a random variable with probability ps occurs under scenario s.
(17)
S.t
For all
For all
In this model is penalty function which is defined to reduce the fluctuation of control variables under all scenarios, and is a function which is suggested to robust answer. This function is defined by Molvey as follows:
This approach was developed and "Li Yu" defined function as follows:
In this equation also defined parameter to linearize model, where general models have been as follows:
(20)
S.t
According to the scenario-based of patients’ scheduling problem, Molvey model is used to robust model of this paper. Also, here, our uncertain parameter is patients’ serving time in each stage that for Molvey model three scenarios including optimistic, pessimistic, and likely is used. Robust model under Molvey approach will express as fallows.
6. Mathematical model under uncertainty space
In this section, we will introduce to the non-deterministic mathematical model, where first, the model symbols and variables will introduce and then we will explain the purpose and constraints related to it.
6.1 Symbols and new parameter model uncertain
S: scenarios for uncertain parameter processing time
tiklS: patients serving time in stage i k l under the scenario by S
SiklS: start time of operations on patients in stage k l i by scenario S
6-2 uncertainties of processing time parameter
Given that patients’ time serving in each of these sectors is uncertain, therefore it is essential that in view of the uncertainty of this parameter by using Molvey model try to scheduling model in order to satisfy this uncertainty. For this uncertain parameter three scenarios: optimistic, pessimistic and likely is used. To estimate this scenarios, data of serving time in the operating room and related sections used by each group.
6-3 non-deterministic models and restrictions
Equation (21) which is made up of two parts, Part I expect the average duration surgery under any scenario suggests The second part calculates the variance same amount under any of the scenarios, the objective of ensuring a solid answer.
Equation (22) is one of the constraints that the Molvey model that prevent from getting negative of second part of the objective function (variance objective function value under each scenario),
(23)
Equation (23) ensures that only one allocation for each patient at each step is possible that this limit is unchanged compared to the deterministic model.
(24)
Equation (24) states that the start time in each step under each scenario should be greater than the start time.
(25)
Equation (25) states that the patient enters the operating room sequence or sequences are in bed, If both of them allocated to bed earlier or certain operating rooms that this equation is innocent of any changes.
(26)
Equations (26) and (27) start time of the sequence of patients in every stage limits under any scenario.
(28)
Limitation (28) as the equation (25), with the difference that here the allocation of patients to the surgeons involved.
Equation (29) start time of the sequence limits the patients allocated to surgery.
(30)
(31)
(32)
Equations (30), (31) and (32) states a limit capacity for the operating room, surgeons and parts PHU, PACU, this means that the limited time in a day can be considered for them.
Limitation (33) show that each patient is assigned only to a surgeon that the equation is as deterministic model.
(34)
Equations (34) and (35) are non-negative binary variables.
Our solution to the problem of planning and scheduling the surgery ward in this paper is the first such definitive model for a given problem we have to solve. Then, due to the uncertainty in parameter based approach to solve the problem of the model and analyzed.
6-4 Numerical example
We have solved problem for 18 groups which each group has 5 patients and are in a surgery group.
The materials in this example are 3 Beds in PHU, an operating room and 3 beds in PACU. Time availability of each of the relevant sections is from 8 am to 6 pm. There are also two surgeons for allocation to the operating room. The problem was solved by using two models for this group of patients, Results are shown in Table solution.
Table 6-1 solution results for robust models and deterministic model for a scenario with probability 2.0, 6/0 2/0
Figure 6.1 The total waiting time for the robust model and deterministic model for the scenario with probability 2.0, 6/0 2/0
We solve the problem once again with the possibility of different scenarios for previous example. By assuming that the change in scenarios’ probability how much can effect on fluctuations of deterministic model and robust model how to be successful in controlling these fluctuations.
Table 6-2 solution results for robust models and deterministic model for a scenario with probability of 2.0, 3/0 5/0
Figure 6-2 The total waiting time for the robust model and deterministic model for the scenario with probability 2.0, 3/0, 5 /
As shown in the table and figure, since the pessimistic scenario in this example was increased to 0.5, sequentially fluctuations related to deterministic models answer has increased in comparison with the previous example; however, the robust model also able to greatly reduce the fluctuations. In following to compare the two models in the two examples which mentioned above, results’ Variance of the robust models and deterministic model were earned and is shown in the table. As can be seen variance of robust model is less deterministic models on both.
Table 6-3 results’ Variance from both models
The issue in question in this research was for a section of the hospital that scheduled the number of daily surgery for all surgery department. Due to scheduling problems is NP Hard needs a long time to solved, but for problems with the size of our problem which schedule maximum 10 patients per a day it does not need to provide meta-heuristic methods to reduce solution time, but if we extend the model for the entire hospital it require to provide meta-heuristics. In Figure 4 problem’s solution time with different sizes for two models is provided.
Figure 4 compare two models’ solution time with different sizes
As can be seen solution time of two methods in problem with small size is not long, but solution time for both models increases exponentially increasing size of problem.
7. Conclusion
In this study, the integrated planning and scheduling of hospital’s surgery section was solved by considering limitations such as operating room’s capacity and related sections such as public sector, the recovery, patients’ priority, limits of the operating room and surgeons, operating room preparation time after any surgery which is depending on the sequence of operations, and expertise of the surgeons. To validate the model, a numerical experiment for the average size for two groups of patients with different priorities were done. The results indicate that considering other related departments with surgery section and mentioned constraints is effective in decreasing patient waiting time. Molvey robust method was applied into considering the uncertainties in the problem related to patients’ serving in all three phases PHU, PACU, OR. With regard to the comparison of the results of resolving both model came to the conclusion that robust model has reduced the answer’s fluctuations significantly in an acceptable level, by considering uncertainties in problem.
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...-deterministic models and restrictions Equation 21 which is made up of two part...
^^^
Line 119, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
... objective of ensuring a solid answer. Equation 22 is one of the constraints th...
^^^
Line 121, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...ve function value under each scenario, 23 Equation 23 ensures that only one al...
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Line 123, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...d compared to the deterministic model. 24 Equation 24 states that the start ti...
^^^^^^^^^^^
Line 125, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...should be greater than the start time. 25 Equation 25 states that the patient ...
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Line 127, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...s equation is innocent of any changes. ...
^^^^^^^^^^^^^^^^^^^^^
Line 128, column 65, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
... 26 Equations 26 and 27 start time of the se...
^^^^^
Line 130, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...every stage limits under any scenario. 28 Limitation 28 as the equation 25, wi...
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Line 132, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
... of patients to the surgeons involved. Equation 29 start time of the sequence l...
^^^^^^^^^^^^^^^
Line 134, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...its the patients allocated to surgery. 30 ...
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Line 135, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
... 30 31 ...
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Line 136, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
... 31 32 Equations 30, 31 and 32 states a lim...
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Line 138, column 3, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...in a day can be considered for them. Limitation 33 show that each patient is ...
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Line 140, column 7, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...ation is as deterministic model. 34 Equations 34 and 35 are non-negat...
^^^^^^^^^^^^^^^^^^^
Line 141, column 1, Rule ID: WHITESPACE_RULE
Message: Possible typo: you repeated a whitespace
Suggestion:
...ic model. 34 Equations 34 and 35 are non-negative bin...
^^^
Line 154, column 433, Rule ID: IT_VBZ[1]
Message: Did you mean 'requires'?
Suggestion: requires
...nd the model for the entire hospital it require to provide meta-heuristics. In Figure 4...
^^^^^^^
Line 154, column 441, Rule ID: ALLOW_TO[1]
Message: Did you mean 'providing'? Or maybe you should add a pronoun? In active voice, 'require' + 'to' takes an object, usually a pronoun.
Suggestion: providing
...odel for the entire hospital it require to provide meta-heuristics. In Figure 4 problem&ap...
^^^^^^^^^^
Line 158, column 349, Rule ID: PROGRESSIVE_VERBS[1]
Message: This verb is normally not used in the progressive form. Try a simple form instead.
...reparation time after any surgery which is depending on the sequence of operations, and expe...
^^^^^^^^^^^^
Transition Words or Phrases used:
also, but, first, however, if, look, may, second, so, then, therefore, third, well, whereas, while, as for, for example, in addition, in general, such as, with regard to
Attributes: Values AverageValues Percentages(Values/AverageValues)% => Comments
Performance on Part of Speech:
To be verbs : 146.0 15.1003584229 967% => Less to be verbs wanted.
Auxiliary verbs: 32.0 9.8082437276 326% => Less auxiliary verb wanted.
Conjunction : 135.0 13.8261648746 976% => Less conjunction wanted
Relative clauses : 72.0 11.0286738351 653% => Less relative clauses wanted (maybe 'which' is over used).
Pronoun: 155.0 43.0788530466 360% => Less pronouns wanted
Preposition: 465.0 52.1666666667 891% => Less preposition wanted.
Nominalization: 137.0 8.0752688172 1697% => Less nominalization wanted.
Performance on vocabulary words:
No of characters: 18568.0 1977.66487455 939% => Less number of characters wanted.
No of words: 3487.0 407.700716846 855% => Less content wanted.
Chars per words: 5.32492113565 4.8611393121 110% => OK
Fourth root words length: 7.68445349819 4.48103885553 171% => OK
Word Length SD: 3.01064106367 2.67179642975 113% => OK
Unique words: 958.0 212.727598566 450% => Less unique words wanted.
Unique words percentage: 0.274734728993 0.524837075471 52% => More unique words wanted or less content wanted.
syllable_count: 5627.7 618.680645161 910% => syllable counts are too long.
avg_syllables_per_word: 1.6 1.51630824373 106% => OK
A sentence (or a clause, phrase) starts by:
Pronoun: 24.0 9.59856630824 250% => Less pronouns wanted as sentence beginning.
Interrogative: 8.0 0.994623655914 804% => OK
Article: 30.0 3.08781362007 972% => Less articles wanted as sentence beginning.
Subordination: 18.0 3.51792114695 512% => Less adverbial clause wanted.
Conjunction: 13.0 1.86738351254 696% => Less conjunction wanted as sentence beginning.
Preposition: 37.0 4.94265232975 749% => Less preposition wanted as sentence beginnings.
Performance on sentences:
How many sentences: 122.0 20.6003584229 592% => Too many sentences.
Sentence length: 28.0 20.1344086022 139% => OK
Sentence length SD: 117.98698451 48.9658058833 241% => The lengths of sentences changed so frequently.
Chars per sentence: 152.196721311 100.406767564 152% => OK
Words per sentence: 28.5819672131 20.6045352989 139% => OK
Discourse Markers: 1.38524590164 5.45110844103 25% => More transition words/phrases wanted.
Paragraphs: 121.0 4.53405017921 2669% => Less paragraphs wanted.
Language errors: 70.0 5.5376344086 1264% => Less language errors wanted.
Sentences with positive sentiment : 45.0 11.8709677419 379% => Less positive sentences wanted.
Sentences with negative sentiment : 39.0 3.85842293907 1011% => Less negative sentences wanted.
Sentences with neutral sentiment: 38.0 4.88709677419 778% => Less facts, knowledge or examples wanted.
What are sentences with positive/Negative/neutral sentiment?
Coherence and Cohesion:
Essay topic to essay body coherence: 0.0 0.236089414692 0% => The similarity between the topic and the content is low.
Sentence topic coherence: 0.0 0.076458572812 0% => Sentence topic similarity is low.
Sentence topic coherence SD: 0.0 0.0737576698707 0% => Sentences are similar to each other.
Paragraph topic coherence: 0.0 0.150856017488 0% => Maybe some paragraphs are off the topic.
Paragraph topic coherence SD: 0.0 0.0645574589148 0% => Paragraphs are similar to each other. Some content may get duplicated or it is not exactly right on the topic.
Essay readability:
automated_readability_index: 17.9 11.7677419355 152% => OK
flesch_reading_ease: 43.06 58.1214874552 74% => It means the essay is relatively harder to read.
smog_index: 11.2 6.10430107527 183% => OK
flesch_kincaid_grade: 14.2 10.1575268817 140% => OK
coleman_liau_index: 14.17 10.9000537634 130% => OK
dale_chall_readability_score: 7.57 8.01818996416 94% => OK
difficult_words: 562.0 86.8835125448 647% => Less difficult words wanted.
linsear_write_formula: 12.5 10.002688172 125% => OK
gunning_fog: 13.2 10.0537634409 131% => OK
text_standard: 14.0 10.247311828 137% => OK
What are above readability scores?
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Try to use less pronouns (like 'It, I, They, We, You...') as the subject of a sentence.
Write the essay in 30 minutes. We are expecting: No. of Words: 350 while No. of Different Words: 200
Maximum five paragraphs wanted.
It is not exactly right on the topic in the view of e-grader. Maybe there is a wrong essay topic.
Rates: 3.33333333333 out of 100
Scores by essay e-grader: 1.0 Out of 30
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Note: the e-grader does NOT examine the meaning of words and ideas. VIP users will receive further evaluations by advanced module of e-grader and human graders.