Simulation With Arena 6th Edition W. David Kelton, Randall Sadowski, Nancy Zupick - Solutions

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Design a conceptual model for the simple queue model case described in Appendix 1 (Section A1.2.1). Identify the modelling objectives, model inputs and outputs, model content and any assumptions and simplifications.
For each of the following situations identify a method of simplification that could be employed in a simulation model of the system:a) A factory that produces a range of products: 80 per cent of orders are for two product types, 18 per cent for five product types and the remaining 2 per cent for 17
Obtain and read some simulation case studies (see Exercise E1.3 in Chapter 1 for potential sources). Identify the objectives of the simulation study, the model outputs and inputs, and any assumptions and simplifications that were made. As far as possible try to identify the scope and level of
Take a typical operations system, preferably one that can be observed(e.g. a supermarket or airport), and identify in broad terms at least three conceptual models that could be developed of the system. For each model identify the objectives and model content.
A bank is planning its requirements for ATMs (automated teller machines)in a new branch. There are spaces for up to six ATMs, not all of which have to be used. Three types of ATM can be purchased: general ATMs(giving cash, balances, mini statements and PIN change facilities), ATMs for paying money
Section 5.6.2 introduces various methods for representing a conceptual model. Investigate these methods in more depth, identifying the strengths and weaknesses of the various approaches. Use the references provided in Section 5.6.2 as a starting point.
Section 2.3.5 describes how samples can be taken from a normal distribution.Various algorithms are available for sampling from a range of statistical distributions. For each of the distributions described in appendix 5 identify a sampling algorithm. (Hint: use the references in section 2.3.5 as a
Section 2.3.6 describes an algorithm for generating random numbers.Research and identify alternative mechanisms for generating random numbers. What are the benefits and problems with alternative generators?How can the efficacy of a random number generator be tested?(Hint: use the references in
Section 2.2.3 introduces three alternative discrete-event simulation approaches: event scheduling, activity scanning and process-based. Use each of these simulation approaches to simulate the airport problem in exercise E2.2. Evaluate the advantages and disadvantages of the three methods and
Following a discussion with the airport’s operations manager, more accurate data on the take-off and landing of aeroplanes have come to light. Aeroplanes are classified into two sizes: small and large. Small aeroplanes only require a 1.5 minute slot on the runway, while large aeroplanes require
For the airport problem described in exercise E2.1 develop a three-phase discrete-event simulation of the problem.a) Define the B-events and C-events for the problem.b) Simulate 20 minutes of operation at the airport.
An airport is planning its requirements for runway facilities and wishes to know whether the current plan to have a single full-length runway is sufficient.It is expected that during peak periods aeroplanes will land every four minutes (exactly) and that aeroplanes will take-off with the same
The paper by Tako and Robinson (2010, p. 787) describes a case study of modelling the UK prison population as follows:[T]wo types of offenders are considered, petty and serious. There are in total 76,000 prisoners in the system, of which 50,000 are petty and 26,000 serious offenders. Offenders
There are many case studies describing the application of simulation to real problems. Obtain and read some simulation case studies. Why was simulation used? What benefits were obtained? Some journals that often publish simulation case studies are: IIE Solutions, Interfaces, OR Insight and the
Take a typical operations system, preferably one that can be observed(e.g. a bank or supermarket), and identify the elements of variability, interconnectedness and complexity.
Think of situations where simulation could be used, for instance, from day-to-day life, a place of study or work. What aspects of each situation make simulation appropriate?
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 number of parts in the system?
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 the f rst one, it instead takes the one that will require the shortest processing time (this is
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. When a setup is going on, regard the drill press as being busy. Plot the total number of parts in
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). There’s no difference in processing speed if there are two parts in the drill press instead of one. Redef
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 2.53 minutes for this measure. (a) If these two (very different) numbers are supposed to estimate
, 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 19.31 and 2.53 being compared in part (a)? (c) We consulted an oracle, who sold us the information
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. parts in queue 2.88 0.52 1.71 0.77 2.25 Drill-press utilization 1.00 0.92 1.00 0.95 1.00 For each of
. 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; it then stays up for the rest of the 20-minute simulation length. If there’s a part in service when
, 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 in the machine for the down time. Give the output performance measures from this simulation under
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 change the statistical-summary and histogram cells appropriately at the bottom of the columns, as
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 to try, you may need to rescale the axes on the mean plot on the left.
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 queue. Change the steady-state expected wait in queue appropriately; see the exponential-distribution
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 cross-replication average queue-wait curve. Compare with the original in Section 2.7.2.
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 of each other. At checkout, 63% of customers have a loyalty card that gives them 4% off their raw
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 averages? Why?
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 of the f ve replications individually, you’ll need to open the Category by Replication report; the
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 than Cancel , if you want this change to happen). Make f ve replications and compare the results to
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 possibly adjust the Major Increment there. Make just one replication. 3-4 Implement the change to Model
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 against your hand-simulation results. If they’re different, what might be the explanation (assuming
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) over time. Note that at any given point in simulated time, WIP is the number in queue plus the
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 (which you can just read off of your f nal “frozen” animation), and at the inspection center, the
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 same probability of failing (as improbable as that might seem). There’s no limit on how many times
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, and re-washes loop back to the washer. These probabilities hold for each part undergoing inspection,
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 Red. For each color of arriving part, interarrival times are exponentially distributed with a mean of
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 queue for all part types together, average queue length for all part types together, server
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 through which marbles roll, one at a time, from a reservoir outside the board; let’s say the
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 probabilities. This continues through the last row; let’s say that the number of rows is n so that the last
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 to occupy the resource). Each part passes this inspection with probability 0.85, regardless of its
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 being directed to the booth for its color (of course); each touch-up booth has its own FIFO queue and
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 employees are no longer specialized in just one task, as they were in Model 3-2. Model this as increasing
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 technicians available, and it takes one technician between 1 and 4 hours (uniformly distributed) to f x a
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 credit and prepare the covenant for a loan application. The application would then move on to a second
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. This means that in a mythical simulation of inf nite length (rather than the 160 hours we ran), loan
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 we’ve discussed, and we made only one replication that might have just bounced low. Instead, make
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 long-run steady-state conditions) until it starts f lling up with application entities. As you’ve no
(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 period makes in these different cases.Other than changing entries in Run . Setup . Replication
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 15 minutes. Animate both the queue and the resource for polishing. For the resource animation, open
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 are f rst processed at workstation 1, and then workstation 2; each workstation has only a single
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. Parts f rst enter a painting station (there is only one painting resource) that has a triangular
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, you should have noticed a discrepancy between the time-average number of parts in the system 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 Arena 119
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 exponential interarrival-time distribution with mean 8 (all times are given in minutes), with the f
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 from the entrance to the check-in is distributed uniformly between 2 and 3 minutes. At the check-in
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 Process 1, which has a single resource with a mean service time of 9.1 minutes. Upon completion, they are
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 goes on break, until all agents have had their breaks), starting at 90 minutes into each shift. Each
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 deviation of 2.0 hours (note that these values are the mean and standard deviation of this lognormal random
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 exponential interarrival distribution with mean 2.41 minutes and has a service time (in minutes)
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 processed. The processing-time distribution is TRIA(16, 19, 22) seconds. There are several easily identif
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 minutes). The part interarrival times are UNIF(13.0, 15.1). There is an unlimited buffer in front of
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 all processing times are constant. There are two types of failures: major and jams. The data for
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 location. Model this arrival activity as three independent arrival streams using an exponential
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 payments, taking UNIF(7.9, 10) minutes. Upon completion of this kel01315_ch04_121-206.indd 197 05/12/13
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 value of h to 1.732, 3.464, and 5.196, compute the (exact) variance of this distribution and make
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 run and compare the results with those from the h 5 3.464 case of Exercise 4-11. Note that here
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 machine. The processing-time distribution is TRIA(11, 16, 18) minutes. The parts are inspected and for
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 items are packed by one of four identical packers, with a single queue kel01315_ch04_121-206.indd 198
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 rst 15-minute packer break 1 hour into the shift, the 30-minute lunch break 3 hours into the shift,
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 equal to 3, and Offset equal to 5. Once you have the data f le, perform a Fit All to f nd the

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Simulation With Arena 6th Edition W. David Kelton, Randall Sadowski, Nancy Zupick - Solutions

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