Questions and Answers of Simulation With Arena

in a text box in your Arena f le.
Further study of the facility in Exercise
reveals that after registration, 5% of arriving patients are told to go immediately to a nearby emergency room (the emergency room is outside the boundaries of this model), that is, for each patient
to include this new feature and compare your results to those from Exercise
in a text box in your Arena model f le. Do not include patients who are sent to the emergency room in your system-time statistics.
Patients arrive to a 24-hour, 7-days-a-week outpatient clinic with interarrival times being distributed as exponential with mean 5.95 (all times are in minutes); the f rst patient arrives at time 0.
for better ways to address this question.) This is a modif cation of a model developed by Bretthauer and Côté (1998) and Bretthauer (2000). The latter does an analytical evaluation and optimization
A grocery store has three checkout lanes (checkout 1, checkout 2, and checkout 3), each with a single checker. Shoppers arrive at the checkout area with interarrival times having an exponential
Modify your solution to Exercise
so that shoppers choose the checkout lane has the smallest total service time, including the shoppers already in the queue and the total service time of the shopper currently being served (don’t
in a text box in your model, and comment brief y. HINT: Generate the service time when the shopper enters the system. See Exercise
for a better way to do this comparison, which pays proper attention to statistical-analysis issues.
Modify your solution to Exercise
and add a new checkout, Fast Checkout, that shoppers with a service time of less than 5 minutes will always use; those with service times that are 5 minutes or more will choose from the original
and 4-32; comment brief y. See Exercise
for a better way to do this comparison, which pays proper attention to statistical-analysis issues.
A small town hidden somewhere in the Midwest holds a mini-marathon each year with the proceeds going to charity. The f le Exercise
Input Data.xls in the Book Examples folder has the f nishing times (in minutes) of 447 runners from several recent years. Fit a probability distribution to these data.
The race in Exercise
will have 125 runners this year. Develop a simulation model of the race and note the f rst-place and the last-place times, using the f tted distribution you found in Exercise
for the times for runners to complete the race. Also develop an animation of your model. Make just one replication, and put a text box in your model with the f rst- and last-place f nishing times.
Two part types arrive to a three-workstation system. Part type 1 arrives according to an exponential distribution with interarrival-time mean 5 (all times are in minutes); the f rst arrival is at
Packages arrive with interarrival times distributed as EXPO(0.47) minutes to an unloading facility. There are f ve different types of packages, each equally likely to arrive, and each with its own
A merging conveyor system has a main conveyor consisting of three segments, and two spur conveyors, as depicted in the following f gure. Separate streams of packages arrive at the input end of each
A small automated power-and-free assembly system consists of six workstations. (A power-and-free system could represent things like tow chains and hook lines.) Parts are placed on pallets that move
A small production system has parts arriving with interarrival times distributed as TRIA(6, 13, 19) minutes. All parts enter at the dock area, are transported to workstation 1, then to workstation 2,
A special-order shop receives orders arriving with interarrival times distributed as EXPO(30)—all times are in minutes. The number of parts in each order is a UNIF(3, 9) random variable (truncated
A food-processing system starts by processing a 25-pound batch of raw of product, which requires 1.05 + WEIB(0.982, 5.03) minutes. Assume an inf nite supply of raw product. As soon as a batch has
A small automated system in a bakery produces loaves of bread. The doughmaking machine ejects a portion of dough every UNIF(0.5, 1.0) minute. This portion of dough enters a hopper to wait for space
Customers arrive, with interarrival times distributed as EXPO(5)—all times are in minutes—at a small service center that has two servers, each with a separate queue. The service times are
A small cross-docking system has three incoming docks and four outgoing docks. Trucks arrive at each of the three incoming docks with interarrival times distributed as UNIF(35, 55)—all times are
Develop a model and animation of a Ferris-wheel ride at a small, tacky county fair. Agitated customers (mostly small, over-sugared kids who don’t know any better) arrive at the ride with
Develop a model of the problem we described in Chapter 2 and modeled as Model 3-1, but this time only using modules from the Advanced Process panel to replace the Process module. Use the Plot and
Parts arrive at a two-machine system according to an exponential interarrival distribution with mean 20 minutes; the f rst arrival is at time 0. Upon arrival, the parts are sent to Machine 1 and
Stacks of paper arrive at a trimming process with interarrival times of EXPO(10); all times are in minutes and the f rst stack arrives at time 0. There are two trimmers, a primary and a secondary.
Trucks arrive with EXPO(9.1) interarrival times (all times are in minutes) to an unload area that has three docks; the f rst truck arrives at time 0. The unload times are TRIA(25, 28, 30), TRIA(23,
Kits of ceiling fans arrive at an assembly system with TRIA(2, 5, 10) interarrival times (all times are in minutes). There are four assembly operators, and the kits are automatically sent to the f
The quality-control staff for the fan-assembly area of Exercise 5-5, has decided that if a fan is rejected a second time it should be rejected from the system and sent to a different area (outside
Develop a model of a three-workstation serial production line with high reject rates: 7% after each workstation. Parts rejected after the f rst workstation are sent to scrap. Parts rejected after the
To decrease the part cycle time in Exercise 5-7, a new priority scheme is being considered. The queue priority is based on the total number of times a part has been rejected, regardless of where it
Parts arrive at a machine shop with EXPO(25) interarrival times (all times are in minutes); the f rst part arrives at time zero. The shop has two machines, and arriving parts are assigned to one of
A small warehouse provides work-in-process storage for a manufacturing facility that produces four different part types. The part-type percentages and inventory costs per part are: Inventory Cost
A medium-sized airport has a limited number of international f ights that arrive and require immigration and customs. The airport would like to examine the customs staff ng and establish a policy on
A state driver’s license exam center would like to examine its operation for potential improvement. Arriving customers enter the building and take a number to determine their place in line for
An off ce of a state license bureau has two types of arrivals. Individuals interested in purchasing new plates are characterized to have interarrival times distributed as EXPO(6.8) and service times
The off ce described in Exercise
is considering cross-training Kathy so she can serve both customer types. Modify the model to represent this, and see what effect this has on system time by customer. For the output statistics
Modify the model from Exercise
to include 30-minute lunch breaks for each clerk. Start the f rst lunch break 180 minutes into the day. Lunch breaks should follow one after the other covering a 150-minute time span during the
Modify the probability-board model from Exercise
so that the bounce-right probabilities for all the pegs can be changed at once by changing the value of just a single variable. Run it with the bounce-right probabilities set to 0.25 and compare
Re-create Model
(the inventory model) without using anything from the Blocks or Elements panels, and using only modules from the Basic Process and Advanced Process panels.
In Model 5-4, the relative timings of the inventory-evaluation interval and the delivery lag were such that at no time could there be more than one order outstanding. What if the numbers were
still work? (Note that in Model
we represented the order quantity, if any, by an attribute of the inventory-evaluator entity; what if that order quantity had been represented instead by a variable?)
In Model 5-4, remove the “fudge factor” of ending at time 119.9999 rather than the correct 120. Run the simulation to exactly time 120, but add logic to prevent a useless inventory evaluation at
Generalize Model
to have two additional types of items (doodads and kontraptions), as well as widgets; initially, there are 60 widgets, 50 doodads, and 70 kontraptions. The customers arrive in the same pattern as
(that is, it’s okay to fudge the ending point to avoid useless inventory evaluations at time 120), and get the total daily cost, as well as separate holding and shortage costs for each type of
In Exercise 5-20, suppose that the suppliers for the three items merge and offer a deal to eliminate multiple setup costs on a given day’s orders—that is, if Bucky orders any items of any type at
to do this. What kind of incentives do you think this alternate cost structure might place on Bucky in terms of picking better values of s and S for each item (see Exercises
and 6-14)?
In the machine-repair model of Exercise 3-14, suppose it costs $80 in lost productivity for each hour that each machine is broken down and $19/hour to employ each repair technician (the technicians
for a statistically valid way to experiment).
Modify Model
so that the Resource animations are really accurate, that is, so that each of Alfe, Betty, Chuck, and Doris is individually animated. If a loan application arrives to f nd more than one of them idle,
Modify Model
so that the Resource animations are really accurate, that is, so that each of Alfe, Betty, Chuck, and Doris is individually animated. If a loan application arrives to f nd more than one of them idle,
In Exercise 5-20, base the reorder decision (for widgets, doodads, and kontraptions) not on just the inventory level on hand, but rather on the inventory level on hand PLUS the total inventory on
Modify Model
to use a nonstationary Poisson process (as used in Models
and 5-3) to implement the stopping rule for this model differently. Get rid of the second two Variables and the non-default entries in the Entities per Arrival f eld and the Max Arrivals f eld in the
and your solution to this exercise; repeat this comparison, except make 100 replications of each model and report the means and half-widths of 95% conf dence intervals from the Category Overview
Redo Exercise 3-21, except now use a Storage to represent the parts that are undergoing the drying process. Collect and report the same statistics as before, and again reconcile the total number of
In Exercise 5-1, statistically compare your results to what we got earlier; do this comparison informally by making 95% conf dence intervals based on 50 replications from both models and see if they
Using the model from Exercise 5-2, change the processing time for the second pass on Machine 1 to TRIA(6.7, 9.1, 13.6). Run the simulation for 20,000 minutes and compare the results with respect to
In Exercise 5-3, about how many replications would be required to bring the half width of a 95% conf dence interval for the expected average cycle time for both Figure 6-14. Category Overview Report
For the facility of Exercise
you’ve been asked to decide how much space should be planned for the trucks in queue to unload; address this question (being mindful of statistical issues, and of the fact that the space should be
In Exercise 5-5, suppose you could hire one more person and that person could be a second (identical) operator at any of the four locations. Which one should it be? Use PAN with 50 replications per
In Exercise 4-1, suppose that 7% of arriving customers are classif ed just after their arrival as being frequent f iers. Run your simulation for f ve replications (5 days). Assume all times are the
In Exercise 5-13, make 30 replications and compute a 95% conf dence interval on the expected system or cycle time for both customer types. For the output statistics requested, put a text box inside
In Exercise 5-14, make 30 replications, and estimate the expected difference between this and the model of Exercise
(based on system time by customer). Be sure to use an appropriate formal statistical technique. For the output statistics requested, put a text box inside your .doe f le, or paste in a partial
In Exercise 5-15, make 30 replications and estimate the expected difference between this model and the one in Exercise
(based on system time by customer), using an appropriate formal statistical technique. For the output statistics requested, put a text box inside your .doe f le, or paste in a partial screenshot that
For the inventory system of Model 5-4, set up a PAN comparison to investigate the average total cost resulting from each of the following ( s , S ) pairs: (20, 40) (20, 60) (20, 80) (20, 100) (40,
For the inventory system of Model 5-4, use OptQuest to look for the best (total-cost-minimizing) setting for ( s , S ). Let s run between 1 and 99 (by ones) and let S run between 2 and 100 (by ones);
In Exercise 6-11, investigate whether taking inventory at the beginning of each day is necessarily the best policy by adding the inventory-evaluation interval (currently set at one day) to the
Apply OptQuest on all six values of ( s , S ) in Exercise 5-20. Let each s range between 1 and 99 (by ones), and let each S range between 2 and 100 (by ones); of course, s and S must be integers and
Apply OptQuest on all six values of ( s , S ) in Exercise 5-21, with the same ranges as in Exercise 6-13. Compare your results with those from Exercise
and explain this in terms of the incentives offered by the supplier in this different cost structure.
In Exercise 4-22, suppose you could hire one more person, and that person could be assigned either to manual check-in, automated check-in, or security. Where would this additional person be best
In Exercise 6-15, suppose you could hire a total of f ve more people (rather than just one more) to be allocated in any way to the existing staff at manual check-in, automated check-in, or security.
In Exercise
(with staff ng f xed at the original levels), the airline noticed that a lot of the people who opt for the manual check-in really don’t need the extra services there and could have used the
Exercise
described a change in Model 3-1. Carry out a statistically valid study to measure the effect of this change on the average waiting time in queue and on the server utilization. Make your own decisions
Recall Models 3-2, 3-3, 3-4, and

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