ENGG953 Assignment 2: Simulation and Decision-Making in Healthcare

This document presents a detailed solution to a simulation-based decision-making assignment, focusing on the operations of an emergency room. The assignment explores limitations and assumptions in the simulation model, including factors like patient arrival times, service times for doctors and nurses, and the absence of a defined queuing system. The solution includes a Microsoft Excel-based simulation, analyzing customer arrival, attention needed, and finish times. It calculates average waiting times and probabilities, and assesses the impact of simulation errors using line graphs. The analysis further extends to a second problem involving room bookings and cost optimization, and a third problem simulating a single-teller system and comparing it to a two-teller system to determine average waiting times. The results show the simulation's effectiveness in estimating waiting times and probabilities, and provide insights into optimizing resource allocation in the emergency room and other service systems.

Simulation Based Decision-Making
Question 1
Limitations and Assumptions
a) The presences of idleness when either the doctor or nurse is not with a patient. The doctor
will choice to take his time if most of the patients wait to see the nurse instead of
attending to the patients that want to see him
b) The lack of a defined queuing system that will allow the patients to efficiency optimize
on the immediate availability of a doctor or nurse to ensure that there is no time wastage.
c) In the computations the patients who arrived later on after the doctor or nurse was free
were given negative waiting time values which were corrected to negative values.
Part 1
The simulation is in Microsoft Excel document worksheet 1 (simulation work 1.xlx). It can be
represented with the image below
Customer Rand Number 1Interval Arrival TimeRand Number 2 Attention Needed Rand Number 3Doctor AloneRand Number 4Nurse AloneRand Number 5Both Finish Time Time in SystemWait Time Corrected Time Wait
1 0.44087 15 15 0.694677488 Nurse Alone 0.097233 0 0.107712 15 0.642628 0 30 15 0 0
2 0.230984 10 25 0.929922464 Both 0.206246 0 0.571922 0 0.884428 35 60 35 5 5
3 0.097423 5 30 0.969370267 Both 0.91886 0 0.192084 0 0.139362 20 50 20 30 30
4 0.529403 20 50 0.386345424 Doctor Alone 0.597812 20 0.007069 0 0.171933 0 70 20 0 0
5 0.36631 15 65 0.753767337 Both 0.426594 0 0.772586 0 0.959538 40 105 40 5 5
6 0.357304 15 80 0.877063414 Both 0.666564 0 0.375092 0 0.630805 30 110 30 25 25
7 0.073742 5 85 0.71570429 Nurse Alone 0.139228 0 0.163264 15 0.084947 0 100 15 25 25
8 0.325105 15 100 0.126098468 Doctor Alone 0.429451 15 0.282234 0 0.164914 0 115 15 0 0
9 0.898469 25 125 0.402582944 Nurse Alone 0.321872 0 0.889334 25 0.060909 0 150 25 -10 0
10 0.559151 20 145 0.006453041 Doctor Alone 0.777579 25 0.821338 0 0.252788 0 170 25 5 5
11 0.218113 10 155 0.440252773 Nurse Alone 0.126611 0 0.127099 15 0.671377 0 170 15 15 15
12 0.482109 20 175 0.808793215 Both 0.920978 0 0.106238 0 0.104713 20 195 20 -5 0
13 0.05723 5 180 0.044400201 Doctor Alone 0.828882 25 0.811109 0 0.888883 0 205 25 15 15
14 0.493122 20 200 0.99092875 Both 0.330882 0 0.589671 0 0.507184 30 230 30 5 5
15 0.386081 15 215 0.118736311 Doctor Alone 0.77418 25 0.404653 0 0.749301 0 240 25 15 15
16 0.815061 25 240 0.682019046 Nurse Alone 0.155139 0 0.580259 20 0.821624 0 260 20 0 0
17 0.642938 20 260 0.349564488 Doctor Alone 0.104647 10 0.776685 0 0.14783 0 270 10 0 0
18 0.100323 10 270 0.07290249 Doctor Alone 0.788847 25 0.469654 0 0.473794 0 295 25 0 0
19 0.142609 10 280 0.945896252 Both 0.866867 0 0.767478 0 0.860919 35 315 35 15 15
20 0.534276 20 300 0.241246841 Doctor Alone 0.935454 30 0.674239 0 0.042317 0 330 30 15 15
21 0.739647 25 325 0.630496824 Nurse Alone 0.699229 0 0.311921 15 0.836785 0 340 15 5 5
22 0.561989 20 345 0.912982061 Both 0.674433 0 0.472861 0 0.837923 35 380 35 -5 0
23 0.426237 15 360 0.56241471 Nurse Alone 0.895198 0 0.467916 20 0.507331 0 380 20 20 20
24 0.211013 10 370 0.891865187 Both 0.955219 0 0.356228 0 0.348122 25 395 25 10 10
25 0.23966 10 380 0.205010005 Doctor Alone 0.552872 20 0.11124 0 0.334909 0 400 20 15 15
26 0.255333 15 395 0.888880452 Both 0.693233 0 0.242688 0 0.127131 20 415 20 5 5
27 0.275208 15 410 0.540694888 Nurse Alone 0.233778 0 0.595368 20 0.734773 0 430 20 5 5
28 0.566085 20 430 0.506812477 Nurse Alone 0.784286 0 0.191861 15 0.888965 0 445 15 0 0
29 0.26544 15 445 0.73970667 Nurse Alone 0.842607 0 0.894591 25 0.279048 0 470 25 0 0
30 0.792525 25 470 0.518586105 Nurse Alone 0.961114 0 0.028376 10 0.348839 0 480 10 0 0
31 0.828251 25 495 0.524040166 Nurse Alone 0.713926 0 0.661852 20 0.571825 0 515 20 -15 0
32 0.688788 20 515 0.385676903 Doctor Alone 0.56876 20 0.492327 0 0.458826 0 535 20 0 0
33 0.075108 5 520 0.251313392 Doctor Alone 0.464925 15 0.730966 0 0.516804 0 535 15 15 15
34 0.373228 15 535 0.089160745 Doctor Alone 0.541841 20 0.116339 0 0.180094 0 555 20 0 0
35 0.795096 25 560 0.238594477 Doctor Alone 0.67882 20 0.371495 0 0.677709 0 580 20 -5 0
36 0.020433 5 565 0.964197156 Both 0.09964 0 0.249479 0 0.807316 35 600 35 15 15
37 0.359388 15 580 0.949508249 Both 0.399016 0 0.77148 0 0.863345 35 615 35 20 20
38 0.265024 15 595 0.564265254 Nurse Alone 0.599452 0 0.542398 20 0.440959 0 615 20 20 20
39 0.298908 15 610 0.748114031 Nurse Alone 0.650693 0 0.708653 20 0.431708 0 630 20 5 5
40 0.257182 15 625 0.603941239 Nurse Alone 0.623537 0 0.346217 15 0.636216 0 640 15 5 5
41 0.747398 25 650 0.650161178 Nurse Alone 0.213743 0 0.838335 20 0.77056 0 670 20 -10 0
42 0.001315 5 655 0.186659146 Doctor Alone 0.288115 15 0.066816 0 0.117337 0 670 15 15 15
43 0.892223 25 680 0.790497798 Both 0.401791 0 0.105141 0 0.510911 30 710 30 -10 0
44 0.943129 30 710 0.351255187 Doctor Alone 0.154388 10 0.766104 0 0.35664 0 720 10 0 0
45 0.611222 20 730 0.595755351 Nurse Alone 0.763177 0 0.956957 25 0.308955 0 755 25 -10 0
46 0.365035 15 745 0.011151619 Doctor Alone 0.027652 10 0.146557 0 0.774581 0 755 10 10 10
47 0.407561 15 760 0.589330025 Nurse Alone 0.545781 0 0.604298 20 0.772409 0 780 20 -5 0
48 0.552294 20 780 0.456161139 Nurse Alone 0.683113 0 0.156849 15 0.631072 0 795 15 0 0
49 0.11524 10 790 0.365630616 Doctor Alone 0.529141 20 0.837752 0 0.330035 0 810 20 5 5
50 0.708327 20 810 0.178941904 Doctor Alone 0.455669 15 0.822863 0 0.003626 0 825 15 0 0

Part 2
But adding an extra 1950 simulations we are able to better estimate the average 2waiting time as
welll as average probability of waiting. The extra 1950 simulations are faded out to pay keen
emphasises on the 50 main simulation. However, the average of waiting time and probability will
be taken from all 2000 simulations. Therefore, the average waiting time is roughly 6 minutes,
and the probability that a patient will have to wait is roughly 0.5 or 50% .
The calculations are also in worksheet 1 of (simulation work 1.xlx). They are given by the
following image
10 1
0 0
0 0
10 1
15 1
15 1
0 0
6.0125 0.522
Average Wait Time Average Probability
Part 3.
By plotting the simulation errors on a line graph we are able to recognize where the simulation
fails as the line becomes more flat. Hence, there are three graphs for 2000, 300, and 150 patients
respectively. it is therefore clear that the optimum minimum number of patients is roughly 150
patients . The calculations are also in worksheet 1 of (simulation work 1.xlx).

2 226 450 674 898 1122134615701794
-5
-4
-3
-2
-1
0
1
2
3
Simulation Error (2000)
Simulation Error
Number of Clients
Error
1 22 43 64 85 106127148169190211232253274295
-5
-4
-3
-2
-1
0
1
2
3
Simulation Error (300)
Series1
Number of Clients
Error

1 14 27 40 53 66 79 92 105 118 131 144
-5
-4
-3
-2
-1
0
1
2
3
Simulation Error (150)
Simulation Error
Number of Clients
Error
Part 4.
No, the system does not provide adequate health care because the emergency room is supposes to
be always available for high priority causes. But in this situation, patients are being forced to
wait approximately 6 minutes with a probability of 50% to see the nurse, doctor, or both.
Question 2
Part 1
All charts are given below
No. of Rooms booked Certainty of having a
cost of less than
100,000$
500 50.11%
600 63.76%
700 74.25%
800 84.28%
900 49.21%

If we lower the cost to $85,00 we have the following probabilities
No. of Rooms booked Certainty of having a cost of

less than 85,000$
600 39.45%
700 51.66%
800 7.17%

Hence the best choose would be 700 rooms
Part 2
By adding Room Increments by amounts of 50 between 500 and 900 we will be able to better the
accuracy of rooms to be booked with regard to the minimum cost of $85,000
The probabilities are as follows for 650, 700, and 750 rooms
No. of Rooms booked Certainty of having a cost of
less than 85,000$
650 44.74%
700 51.66%
750 25.67%
Hence the best choose is still 700 rooms

Question 3
Part 1
We will run the entire simulation in excel for 50 customers with an addition 450 simulation
(faded out used for the purpose of simulation error assessment)
One teller
Average waiting time is 1 minute