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simulation with arena
Simulation With Arena 6th Edition W. David Kelton, Randall Sadowski, Nancy Zupick - Solutions
(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 screenshot that provides the requested results. In a text box, brief y discuss whether (and why) you’re
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 provides the requested results. In a text box, brief y discuss whether (and why) you’re f nding a
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, 60) (40, 80) (40, 100) (60, 80) (60, 100) (80, 100) Run 100 replications of each case, and pick the
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); remember that s and S must be integers and that we must have s < S . Make your own judgments about
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 optimum-seeking variable mix, and allow OptQuest to vary it (continuously) between a half day and 5 days,
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 for each of the three items in inventory we must have s < S .
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 used? As an overall criterion of “goodness” of a system, use the average total time in system of all
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. You can’t reduce staff ng anywhere from the levels in Exercise 4-22. Using average total time in
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 automated check-in. Instead of the original 35% and 50% that go to manual and automated, respectively,
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 about numbers of replications to arrive at meaningful and reasonably precise conclusions.
Recall Models 3-2, 3-3, 3-4, and
from Chapter 3, comparing specialized serial vs. generalized parallel operations in environments of both high-variance and low-variance (no-variance, actually) service times. It appeared in Table
that the generalized parallel arrangement provided better service, though the improvement was much stronger in the high-variance service-time environment. For output performance measures, use both time-average work in process (number of applications present anywhere in the whole system), and
(from just a single run) statistically justif ed?
Recall Exercise 3-13, which modif ed Model
to add 18% onto the individual-task times in the generalized integrated-work parallel conf guration of Model 3-3. Make a valid statistical comparison to see if the model of Exercise
differs signif cantly from the original specialized serial conf guration of Model 3-2. In other words, if you had to endure this 18% increase in task-processing times, should you still move from the specialized-work serial setup to the generalized-work parallel setup? For output
For the enhanced machine-repair model of Exercise 5-22, do a valid statistical analysis to defend your choice of the number of repair technicians to hire to minimize total average cost per hour. Make 20 replications, and modify it if necessary.
Use Arena to simulate the news vendor problem of Section 2.7.1. Consider just the case q5 160, and run for 30 days to get an average daily prof t and 95% conf dence interval, as well as the proportion of days in which a loss is incurred. The 30 days are independent of each other (that is, nothing
Generalize your Arena model from Exercise
to consider all f ve values of q in Section 2.7.1, in a single Arena run, using the same daily demand realization for each value of q .
In the outpatient clinic of Exercise 4-30, suppose you could add one unit of resource to any one of the f ve stations (receptionist, nurse, exam room, checkout administrator, or lab technician). Where would be the most useful addition? Look at both average patient total time in system, as well as
The outpatient clinic of Exercise
has received an economic-stimulus capital grant of $400,000 to expand service and reduce patients’ average total time in system. They can allocate these funds in any way they like to add any number of resources to any of the f ve stations, though they cannot reduce any resources below current
Armed now with the statistical-analysis tools of this chapter, do a better job with Exercise 4-25. Stick with 100 replications for each of the two scenarios (with AJ as in Exercise 4-23, and without AJ as in Exercise 4-24; forget about the original Model
that was included in Exercise 4-25), but expand the output performance measures to the mean total time in system of parts sorted according to each of: (a) Part As, regardless of how/where they exit (Shipped, Salvaged, or Scrapped) (b) Part Bs, regardless of how/where they exit (c) All parts
In Section 6.6, we chose both the starting point (“Suggested Value” in OptQuest) and the number of scenarios (“Simulations” in OptQuest) allowed pretty much arbitrarily. Experiment with different starting points and number of scenarios to see how sensitive the “optimal”
the Suggested starting values we used for the six Controls in the order listed there were (3, 3, 3, 3, 3, 29); consider this as well as (0, 0, 0, 0, 0, 26) and (5, 5, 5, 5, 5, 50). And for the number of scenarios consider both the 500 we used, as well as 2,000, so carry out f ve more OptQuest runs.
Exercises 4-31, 4-32, and
considered three different versions of a grocery-store checkout area. Do a better of job of comparing them, on the basis of average total time in system of customers, using the Process Analyzer. Make 50 replications of each of the three scenarios, and create a box-and-whisker plot in PAN to
Make 25 replications of the race model from Exercise 4-35, and report 95% conf dence intervals on the expected f rst- and last-place f nish times. Put a text box in your model with these conf dence intervals, and comment brief y on the differences in their half-widths in light of the nature of the
In Exercise 4-7 (with a reprocess probability of 8%), is the run long enough to generate a batch-means-based conf dence interval for the steady-state expected average cycle time? Why or why not? If not, about how long would the run need to be to produce such a conf dence interval?
Modify your solution for Exercise 5-2 to include transfer times between part arrival and the f rst machine, between machines, and between the last Machine 1 and the system exit. Assume all part transfer times are UNIF(1.5,3.2). Animate your model to show part transfers with the part entity picture
Using the model from Exercise 7-2, change the processing time for the second pass on Machine 1 to TRIA(6.7, 9.1, 13.6) using Sequences to control the f ow of parts through the system and the assignment of process times at each machine. Run the simulation for 20,000 minutes. To the extent possible,
A part arrives every 10 minutes to a system having three workstations (A, B, and C), where each workstation has a single machine; the f rst part arrives at time 0. There are four part types, each with equal probability of arriving. The process plans for the four part types are given here. The
Modify your solution for Exercise 7-4 to use the Expressions feature for determining the processing times (rather than assigning them in the Sequence data module). Run for a single replication of length 10,000 minutes and compare the results to those from Exercise 7-4 in a text box in your Arena
Modify your solution for Exercise 7-5 so that all parts follow the same path through the system: Workstation A – Workstation B – Workstation C. If a part does not require processing at a workstation, it must still wait in queue, but incurs a zero processing-time delay. Compare the results to
Three types of customers arrive at a small airport: check baggage (30%, that is, for each arriving customer there is a 0.30 probability that this is a “check-baggage” customer), purchase tickets (15%), and carry-on (55%). The interarrival-time distribution for all customers combined is
Parts arrive at a four-machine system according to an exponential interarrival distribution with mean 10 minutes. The four machines are all different, and there’s just one of each. There are f ve part types with the arrival percentages and process plans given here. The entries for the process
Modify your solution for Exercise 7-8 to include the travel times that are move-specifc. The travel times are given here as the parameters for a triangular distribution (in minutes). Compare your results. Is this a statistically reliable comparison? From/To Machine 1 Machine 2 Machine 3 Machine 4
Modify your solution to Exercise 4-21 to use sequences to control the f ow of parts through the system. (HINT: Reset the value of Entity.Jobstep or IS.) Compare your results with those from Exercise 4-21.
Modify Model 7-1 to account for acquiring a new customer, in addition to the one supplying the existing three part types. This new customer will supply two new types of parts—call them Type 4 and Type 5. The arrival process is in addition to and independent of that for the original three part
Modify your solution to Exercise 5-2 to use Sequences to control the f ow of parts through the system. Also add a transfer time between arrival and the f rst machine, between both machines, and between the last machine and the system exit that follows a triangular distribution with parameters 7,
Modify your solution to Exercise 7-12 to account for a 20% increase in processing time when the part returns to the f rst machine for its last operation. View this as a terminating simulation, and make 100 replications of this model as well as the one from Exercise 7-12, using PAN to compare the
In Exercise 7-7, suppose that you had the option of adding one agent to the system, and could add that agent to any one of the check-bag counter, the gate, the ticket-buying counter, or the X-ray station. What’s your recommendation? Set up and run a Process Analyzer (PAN) experiment (and also
Change your model for Exercise
to include fork trucks to transport the parts between stations. Assume that there are two fork trucks that each travel at 85 feet per minute. Loading or unloading a part by the fork truck requires 0.25 minute. The distance between stations is given (in feet) here; note that the distances are, in
Change your model for Exercise 7-4 to use nonaccumulating conveyors to transfer the parts between stations. Assume that there is a single conveyor that starts at the arrive area and continues to the exit area: Arrive – WS A – WS B – WS C – Exit. Assume that the distances between all
Change your model for Exercise 5-2 to use a fork truck (45 feet/minute) for transportation of parts in the system. Assume that the parts arrive at an incoming dock and exit at a second dock. Assume that the distance between the incoming dock and Machine 2 is 200 feet; all other distances are 100
Using the model from Exercise 8-3, set the number of transporters to four and make three runs using transporter selection rules of Smallest Distance, Largest Distance, and Cyclical. Run your simulation for 20,000 minutes and compare the results using average cycle time.
Modify Model 4-3 to include the use of a single truck to transfer parts from the two prep areas to the sealer. Assume that the distance between any pair of the three stations is 100 feet and that the truck travels at a rate of 70 feet per minute. Animate your solution.
Modify Model 4-3 to include the use of two conveyors to transfer parts from the two prep areas to the sealer. Both conveyors are 100 feet long and are made up of 20 cells of 5 feet each. The conveyor velocity is 35 feet per minute. Animate your solution.
A prototype of a new airport bag-screening system is currently being designed, as in the following f gure. Bags arrive to the system with interarrival times of EXPO(0.25) (all times are in minutes), and are loaded on a load conveyor (75 feet long) and conveyed to an initial scan area. At the
Develop a model of a cross-dock system that groups and transfers material for further shipment. This facility has f ve incoming docks and three outgoing docks. Trucks arrive at each of the incoming docks with loads of material on pallets. The interarrival time is UNIF(30, 60) between truck
A military ground force maintains a forward position and a rear depot 22 miles away to supply it. There is a single commodity that is consumed at the forward position and resupplied to it from the rear supply depot; the commodity could be anything (ammunition, fuel, food, etc.). Initially, there
Starting with Model 10-1, modify the logic to store the time between arrivals and the processing time (excluding any waiting time) in attributes. Then use the ReadWrite module from the Advanced Process panel to write this pair of attributes to an Excel or Access f le (or a text f le if you don’t
Start with Model 10-2 and use the data f le you generated in Exercise 10-1 to specify both call-arrival logic and call-handling time. Note that since the data are time between arrivals rather than absolute arrival time, slightly different logic will be required. How do your results compare to
Build a simple, single-server queueing model with entity interarrival times of EXPO(0.25) minutes. Using the ReadWrite module, prompt and query at the beginning of the simulation run for the server’s process time mean (give a default value of 0.2 minutes). Use this value to establish a uniform
Create the model described in Exercise 10-3, replacing the ReadWrite modules with a VBA form that’s displayed at the beginning of the simulation run.
Using the single-server model from Exercise 10-4, add logic to play a sound or display a message whenever the number of entities in the service queue exceeds some threshold value. Allow the modeler to establish this threshold in the form that’s displayed at the beginning of the run.
Present a VBA form at the end of the simulation run, reporting the average and maximum queue lengths for the product queues in Model 10-1. If you have a charting kel01315_ch10_423-478.indd 477 05/12/13 3:20 PM 478 Chapter 10 program (for example, Excel) installed on your computer, also draw a bar
Create a model that writes 1,000 records to a f le. Each record will include the record number and ten random samples, each between 0 and 100,000. In Run > Setup > Reports , disable the normal model output by selecting SIMAN Summary Report as the default output and select Disable generation of
Build a discrete-event model that changes the value of the volume in a tank as described for Model 11-2b using a maximum step size of 0.01 minutes. Record time-persistent statistics on the volume in the tank, and compare the average reported volume for an 800-hour run with the results from the
The owner of a franchise of gas stations is interested in determining how large the storage tank should be at a new station. Four gas pumps, all dispensing the same grade of fuel, will be installed to service customers. Cars arrive according to an exponential distribution with a mean of 0.8
to incorporate the availability of coal in the storage yard so that barges will wait at the dock until coal is available for loading. Compare the average and maximum number of barges waiting and the loading time of barges with the results from Model 11-3.
O’Hare Candy Company, maker of tasty sweets, is preparing to install a new licorice production facility and needs to determine the rates at which equipment should run. In particular, they are interested in the cutting/wrapping machines, as they are prone to frequent breakdowns. At this
Hope Bottling Company operates a bottling plant, handling many types of products. They are interested in analyzing the effective capacity of an orange juice bottling line as part of their plans for future business expansion. At this facility, trucks deliver bulk orange juice (2,000 gallons per
For the soaking-pit furnace problem (Model 11-5), use the model to evaluate the performance improvement resulting from preheating arriving ingots so that their temperature is uniformly distributed between 600 and 700°F. Assume that the ingots waiting in the cold bank (that is, ones that could
Simulate the population dynamics involving the growth and decay of an infectious, but easily curable disease. The disease occurs within a single population, and recovery from the disease results in immunity. The population consists of the following three groups: (1) those who are well, but
The Lanchester combat equations , developed by the British mathematician Frederick W. Lanchester during World War I to analyze the new phenomenon of aerial warfare, consider the levels x ( t ) and y ( t ) of two opposing forces at time t , and how these levels are depleted. The modern Lanchester
The ancient Lanchester combat equations have the same def nition of x ( t ) and y ( t ) as in Exercise 11-8, but instead model the rate of depletion of each side to be proportional to the product of the current level of both sides: dx / dt 5 2 a x ( t ) y ( t ) dy / dt 5 2 b x ( t ) y ( t ) where
In Exercise 11-8, suppose that both sides receive random-sized re-enforcements that increase their numbers, and that these re-enforcements arrive at random times. Re-enforcements to x ( t ) arrive with interarrival times that have an exponential distribution with mean 8 hours, and the f rst
Modify your ancient Lanchester model in Exercise 11-9 so that both sides receive re-enforcements as described in Exercise 11-10. The parameters of the re-enforcements, however, are different here: the mean times between x and y re-enforcements are respectively 5 and 4 hours, and the mean sizes of
Modify Model
for a different way to allocate random numbers to support synchronization for CRN, as follows. When a new part arrives, (pre-)generate and store in attributes of this entity its processing-time requirements for all of the cells in its sequence. When a part entity gets to a cell, take its
Modify Model 12-3 from Section 12.5.1 to demand, in addition to the 95% conf dence-interval half width on the expected average total WIP being no more than 0.4, that the half width of the 95% conf dence intervals on expected average total time in system (for all part types combined) be no more than
Modify Model 12-3 from Section 12.5.1 to demand instead that the ratio of the 95% conf dence-interval half width to the point estimate on the expected average total WIP be less than 0.04, as described at the end of Section 12.5.1; that is, form a 4% relative-precision conf dence interval. The Arena
Combine Exercises 12-3 and 12-4, as follows. Set up a sequential-sampling run so that you get 4% relative-precision conf dence intervals on both the expected average total WIP as well as on the expected total time in system. kel01315_ch12_519-548.indd 546 06/12/13 9:44 AM Further Statistical Issues
Modify Model 12-4 from Section 12.5.2 to terminate the replication when the ratio of the half width to the midpoint (point estimate) of the automatic batch-means run-time conf dence interval on steady-state expected total WIP falls below 0.04; that is, when the relative precision is 4%. The Arena
As noted in Section 12.4.1, Chance-type Decide modules use random-number stream 10 for their hypercoin f ips, and there’s no way to change that in the module. Describe (in words) how you could work around this to use whatever stream you want to accomplish the same thing. Also, build a useless
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