Questions and Answers of Simulation With Arena

For the hand simulation of the simple processing system, def ne another timepersistent statistic as the total number of parts in the system, including any parts in queue and in service. Augment Table
to track this as a new global variable, add new statistical accumulators to get its time average and maximum, and compute these values at the end.
In the preceding exercise, did you really need to add state variables and keep track of new accumulators to get the time-average number of parts in the system? If not, why not? How about the maximum
In the hand simulation of the simple processing system, suppose that the queue discipline were changed so that when the drill press becomes idle and f nds parts waiting in queue, instead of taking
In the hand simulation of the simple processing system, suppose that a constant setup time of 3 minutes was required once a part entered the drill press but before its service could actually begin.
In the hand simulation of the simple processing system, suppose the drill press can work on two parts simultaneously (and they enter, are processed, and leave the drill press independently).
In Section 2.2.2, we used the M/M/1 queueing formula with the mean interarrival time !A and the mean service time !S estimated from the data in Table
as 4.08 and 3.46, respectively. This produced a “predicted” value of 19.31 minutes for the average waiting time in queue. However, the hand-simulation results in Section 2.4.4 produced a value of
, and got a value of 3.60 for the average waiting time in queue (as you can imagine, it really took us a long time to do this by hand, but we enjoyed it). Why is this yet different from the values
Here are the actual numbers used to plot the triangles for the double-time-arrival model in Figure
: Replication Performance Measure 1 2 3 4 5 Total production 6 4 6 4 5 Average waiting time in queue 7.38 2.10 3.52 2.81 2.93 Average total time in system 10.19 5.61 5.90 6.93 5.57 Time-average no.
. Comparing these conf dence intervals to those in Table
, can you clarify any differences beyond the discussion in Section 2.6.3 (which was based on looking at Figure 2-4)?
In the hand simulation of the simple processing system, suppose the drill press is taken down for burn-in maintenance at time 4 minutes, and it takes 4 minutes to do this work and bring it back up;
, carry out this simulation by hand and note any differences in the output performance measures from the original model. (See Exercise
for the question of whether this model change induces statistically signif cant changes in the output performance measures.)
In Exercise 2-8, ref ne the output performance measure on the status of the drill press from just the two states (busy vs. idle, where in Exercise
the drill press was to be regarded as “busy” during its down time) to three states: 1. busy working on a part and not down, 2. idle and not down, and 3. down, with or without a part being stuck
Modify the news vendor problem in Section 2.7.1 to use independent demands for each trial value of q , and note the difference in the behavior of the output, particularly in the mean plot on the left.
Increase the sample size on the news vendor problem in Section 2.7.1 from 30 days to 150. As in the original problem, use the same realized demands in column E for all values of q . Don’t forget to
Based on your results from Exercise 2-11, try a different set of trial values of q to try to hone in more precisely on the optimal q . Keep the sample size at 150 days. Depending on what you choose
Modify the M/U/1 queue spreadsheet simulation from Section 2.7.2 to have exponential service times with mean 1.28 minutes, rather than the original uniform service times, resulting in the M/M/1
Modify the M/U/1 queue spreadsheet simulation from Section 2.7.2 to make ten replications rather than f ve, and to run for 100 customers rather than 50. To avoid clutter, plot only the
Supermarket customers load their carts with goods totaling between $5 and $200, uniformly (and continuously) distributed; call this the raw order amount . Assume that customers purchase independently
In Exercise 2-4, what would happen in the long run (that is, a simulation of run length 20 billion or so minutes rather than 20 minutes) if the interarrival and service times kept these same
Make f ve replications of Model
by just asking for them in Run . Setup . Replication Parameters . Look at the output and note how the performance measures vary across replications, conf rming Table 2-4. To see the results for each
Implement the double-time arrival modif cation to Model
discussed in Section 2.6.3 by opening the Create module and changing the Value 5 to 2.5 for the mean of the exponential distribution for Time Between Arrivals (don’t forget to click OK , rather
Lengthen the run in Model
to 8 hours for a more interesting show. If you want the plots to be complete, you’ll have to open them and extend the Maximum in the Scale for the Time (X) Axes (mind the units!), as well as
described in Exercise
from Chapter 2. Open the Process module, change the Delay Type to Expression , and enter the appropriate Expression (use the Expression Builder if you like). Run the model for 20 minutes and check
Implement the additional statistic-collection function described in Exercise 2-1, and add a plot that tracks the total number of parts in the system (also called work in process , abbreviated as WIP)
Modify Model
with all of the following changes in the same single model (not three separate models). Put a text box in your model with your results on the number of parts that both pass and fail inspection
In Exercise 3-6, suppose that parts that fail inspection after being washed are sent back and re-washed, instead of leaving; such re-washed parts must then undergo the same inspection, and have the
In Exercise 3-7, suppose the inspection can result in one of three outcomes: pass (probability 0.75, as before), fail (probability 0.11), and re-wash (probability 0.14). Failures leave immediately,
In Model 3-1, suppose that instead of having a single source of parts, there are three sources of arrival, one for each of three different kinds of parts that arrive: Blue (as before), Green, and
and are the same regardless of the color of the part. Make just a single replication. Put a text box in your Arena f le with the values for the output performance measures mentioned (average time in
In science museums, you’ll often f nd what’s called a probability board (also known as a quincunx ): This is like a big, shallow, tilted baking pan with a slot at the midpoint of the top edge
chance of rolling left vs. right). The next parallel row of pegs has three pegs in it, again offset so that each marble will hit exactly one of them and roll left or right, again with equal
In Exercise 3-9, as part of the processing of parts, an inspection is included (there’s no extra processing time required for the inspection, and during the inspection, the part entity continues
In Exercise 3-11, after (f nally) passing inspection, paint on the parts needs to be touched up, so they are sent to one of three separate touch-up-paint booths, one for each color, with each part
In Model 3-3, time studies showed that moving to this integrated work entailed an average increase of 18% in the time it takes to complete each of the four tasks to process an application since
Five identical machines operate independently in a small shop. Each machine is up (that is, works) for between 7 and 10 hours (uniformly distributed) and then breaks down. There are two repair
A compromise between complete specialization (Model 3-2) and complete generalization (Model 3-3) of work might be for Alf e and Betty to form a two-unit resource, each unit of which would check
and compare (in a Text box in your model) the pertinent results with those from Models 3-2 and 3-3.
In Exercise 3-15, increase each service time by 9%, similar to the 18% increase in Exercise
but not as big an increase since there’s still some specialization here. Compare (in a Text box in your model) your results to those of Models
and 3-3, as well as to Exercise 3-15.
In Model 3-2, the long-run (a.k.a. steady-state ) expected total time in system of a loan application is 20 hours, which can be derived from queueing theory, namely, exponential queues in series.
produced an average total time in system of 16.0831 hours, well under the steady-state mean of 20. Why is our result so much lower than the 20? (a) Maybe it’s just because of random f uctuation, as
starts out empty and idle , that is, it’s empty of entities and all resources are idle . So for a while at the beginning, the model could be uncharacteristically uncongested (in comparison to
(one replication of length 160 hours, of which only the last 160 2 40 5 120 hours will be counted in the output), as well as each of parts (a ) – (c) above, to see what difference this warm-up
Embellish your model for Exercise
as follows: (a) After drilling, each part goes immediately to a polishing station, where a single person hand-polishes the part. Polishing times are (continuously) uniformly distributed between 5 and
A two-workstation system processes two different kinds of parts. Parts of type 1 arrive according to an exponential interarrival-time distribution with mean 5.5 (all times are given in minutes) and
A painting system contains two operations. Parts arrive according to an exponential interarrival-time distribution with mean 5 (all times are in minutes), with the f rst part’s arriving at time 0.
In Exercise 3-20, the parts undergoing drying were not animated, which is a kind of animation error; more importantly, we were not able to get the time-average number of parts undergoing drying; and,
for a better, more general, and easier way of doing this, using the concept of Storages, which will be introduced in Chapter 5.) kel01315_ch03_053-120.indd 118 17/12/13 10:11 AM A Guided Tour Through
A small manufacturing department contains three serial workstations (that is, parts go through each of the three workstations in order, one workstation after the other). Parts arrive according to an
Travelers arrive at the main entrance door of an airline terminal according to an exponential interarrival-time distribution with mean 1.6 minutes, with the f rst arrival at time 0. The travel time
Develop a model of a simple serial two-process system. Items arrive at the system with a mean time between arrivals of 10 minutes, with the f rst arrival at time 0. They are immediately sent to
Modify the Exercise
check-in problem by adding agent breaks. The 16 hours are divided into two 8-hour shifts. Agent breaks are staggered (that is, one agent goes on break, and immediately upon return, the next agent
in this text box for ready comparison; write a few words in your text box to address the question about comparison with Exercise 4-1.
Two different part types arrive at a facility for processing. Parts of Type 1 arrive with interarrival times following a lognormal distribution with a log mean of 11.5 hours and log standard
During the verif cation process of the airline check-in system from Exercise 4-3, it was discovered that there were really two types of passengers. The f rst passenger type arrives according to an
to include this new information. Compare the results. Put a text box in your model with the numerical results requested, and repeat those same results from Exercise
in this text box for ready comparison; write a few words in your text box to address the question about comparison with Exercise 4-3.
Parts arrive at a single workstation system according to an exponential interarrival distribution with mean 21.5 seconds; the f rst arrival is at time 0. Upon arrival, the parts are initially
A proposed production system consists of f ve serial automatic workstations. The processing times at each workstation are constant: 11, 10, 11, 11, and 12 (all times given in this exercise are in
A production system consists of four serial automatic workstations. The f rst part arrives at time zero, and then (exactly) every 9.8 minutes thereafter. All transfer times are assumed to be zero and
An off ce that dispenses automotive license plates has divided its customers into categories to level the off ce workload. Customers arrive and enter one of three lines based on their residence
Customers arrive at an order counter with exponential interarrivals with a mean of 10 minutes; the f rst customer arrives at time 0. A single clerk accepts and checks their orders and processes
Using the model from Exercise 4-2, set the interarrival-time distribution to exponential and the process-time distribution for each Process to uniform on the interval [9 − h , 9 1 h ]. Setting the
Using the model from Exercise 4-11, assume the process time has a mean of 9 and a variance of 4. Calculate the parameters for the gamma distribution that will give these values. Make a 100,000-minute
Parts arrive at a single machine system according to an exponential interarrival distribution with mean 20 minutes; the f rst part arrives at time 0. Upon arrival, the parts are processed at a
Using the model from Exercise 4-13, make two additional runs with run times of 60,000 minutes and 100,000 minutes and compare the results with those of Exercise 4-13.
Items arrive from an inventory-picking system according to an exponential interarrival distribution with mean 1.1 (all times are in minutes), with the f rst arrival at time 0. Upon arrival, the
Using the model from Exercise 4-15, change the packer and domestic shipper schedules to stagger the breaks so there are always at least three packers and one domestic shipper working. Start the f
in a text box in your model.
Using the Input Analyzer, open a new window and generate a new data f le (use File . Data File . Generate New ) containing 50 points for an Erlang distribution with parameters: ExpMean equal to 12, k
Hungry’s Fine Fast Foods is interested in looking at their staff ng for the lunch rush, running from 10 am to 2 pm . People arrive as walk-ins, by car, or on a (roughly) scheduled bus, as follows:
In the discussion in Section 4.2.5 of Arena’s Instantaneous Utilization vs. Scheduled Utilization output values, we stated that if the Resource has a f xed Capacity (say, M ( t ) 5 c . 0 for all
In the discussion in Section 4.2.5 of Arena’s Instantaneous Utilization vs. Scheduled Utilization output values, we stated that neither of the two measures is always larger. Prove this; recall
Modify your solution for Exercise
to include transfer times between part arrival and the f rst workstation, between workstations (both going forward and for reprocessing), and between the last workstation and the system exit.
Management wants to study Terminal 3 at a hub airport with an eventual eye toward improvement. The f rst step is to model it as it is during the 8 hours through the busiest part of a typical weekday.
Modify Model
to include a packing operation for “shipped” parts (those that pass the initial inspection and don’t need rework) before they exit the system; don’t count parts as having left the system
and this exercise (just one replication of each).
In the results from Exercise 4-23, you might have noticed that AJ doesn’t have much to do. So say goodbye to him, and send salvaged parts to Brett for packing, along with the shipped parts. Both
Compare the results for Model 4-1, Exercise 4-23, and Exercise 4-24, looking at the average total times in system of the three different exit possibilities (shipped, salvaged, and scrapped). In an
Modify Model
so that, in both inspections, only half of what had failed before now really fail, and the others have returned for a re-do and the preceding operation (that is, to the Sealer and Rework for the f
An acute-care facility treats non-emergency patients (cuts, colds, etc.). Patients arrive according to an exponential interarrival-time distribution with a mean of 11 (all times are in minutes). Upon
Modify your solution from Exercise
to include lunch breaks for the doctors who staff the examination rooms. There are three doctors on duty for the f rst 3.5 hours of each 8-hour shift. For the next 90 minutes, the doctors take

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