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

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: ■ Walk-ins—one at a time, interarrivals are exponential with mean 3 minutes; the f rst walk-in
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 times t ), then Instantaneous Utilization and Scheduled Utilization will be the same. Prove this.
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 that to prove that a general statement is not true you only have to come up with a single example
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. Assume all part transfer kel01315_ch04_121-206.indd 200 05/12/13 3:29 PM Modeling Basic Operations and
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. We’ll model the check-in and security operations only, that is, once passengers get through
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 until they’re packed. Packing takes between 2 and 4 minutes, distributed (continuously) uniformly, and
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 types of parts have the same priority for Brett, but they reside in separate queues. (HINT: It’s
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 attempt to make the comparison more statistically meaningful, make 100 replications of each. Make a
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 rst and second inspections, respectively). The redone parts still have to be reinspected with the same
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 arrival they check in at a registration desk staffed by a single nurse. Registration times follow a
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 rotating 30-minute lunch breaks, resulting in only two doctors being available at any point during these
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 there is a 0.05 probability of being sent to the emergency room. These patients immediately leave
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. The clinic has f ve different stations (like nodes in a network), where patients might be directed
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 under the assumption that this is a Jackson network of queues, where service times also have
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 distribution with mean 2.4 minutes. The shoppers enter the lane that has the fewest number of other
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 account for any partial service time of the shopper currently being served). Again, break ties in
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 three checkout lanes according to the same rules as in Exercise 4-32. On the basis of only average and
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. See Exercise 29 for a statistical analysis of the f rst- and last-place f nish times, and
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 time 0. This part type is f rst processed at workstation 1 and then workstation 2. Its processing time
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 unload station (see following f gure). The unloading stations are located around a loop conveyor that
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 of the three conveyors, with interarrival times distributed as EXPO(0.76) minutes. Incoming packages
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 through the system and stop at each workstation for an operation. There are 12 pallets in the
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, then to workstation 3, and f nally back to the dock, as indicated in the f gure that follows. All
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 to the next smallest integer). Upon receiving the order, the parts are immediately pulled from
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 completed processing, it is removed from the processor and placed in a separator where it is divided
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 in the oven. The portions will be ejected from the hopper in groups of four and placed on the
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 EXPO(9.8) and EXPO(9.4) for Servers 1 and 2, respectively. Arriving customers join the shortest queue.
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 in minutes. Each arriving truck contains UNIF(14, 30) pallets (truncated to the next smaller
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 interarrival times distributed as EXPO(3) minutes and enter the main queue. When the previous ride has f
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 Variable features from the Animate toolbar to complete your model. Run it for 20 minutes and compare
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 processed. The processing-time distribution is TRIA(4.5, 9.3, 11) minutes. The parts are then processed
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. All arrivals are sent to the primary trimmer. If the queue in front of the primary trimmer is shorter
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, 26, 28), and TRIA(22, 25, 27) for docks 1, 2, and 3, respectively. If there is an empty dock, the
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 rst available operator for assembly. The fan assembly time is operator-dependent as given. Operator
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 the boundaries of this model) for rework. Make the necessary changes to the model and run the
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 second workstation are returned to the f rst workstation where they are reworked, which requires a
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 was rejected, with the more rejections already convicted against a part, the further back it is in
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 the machines by f ipping a (fair) coin. Except for the processing times, both machines operate in
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 Part Type Percentage Per Part 1 20 $5.50 2 30 $6.50 3 30 $8.00 4 20 $10.50 The interpretation of
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 the number of passengers who should have bags searched and the staff ng of the customs facility. The
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 the written exam, which is self-administered by one of f ve electronic testers. The testing times are
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 as TRIA(8.8, 13.7, 15.2); all times are in minutes. Individuals who want to renew or apply for a
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 requested, put a text box inside your Arena f le.
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 middle of the day. The breaks should be given in the following order: Mary, Sue, Neil, Kathy, and Jean.
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 with the results of the wind-blown version of the model from Exercise 3-10.
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 different so that there could be multiple orders on the way at a given time? Would Model
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 time 120. What is the effect on the output?
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 before, but now each customer will have a demand for doodads and kontraptions, as well as for
(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 item. Make separate Level (“thermometer”) and regular Plots for each of the three types of items in
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 the beginning of a day, he only has to pay the $32 setup cost once for that day, not a separate $32
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 are paid this hourly wage regardless of whether they are busy or idle). Modify the model to collect
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, assume that a random choice is made. Produce output statistics on the utilization of each
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, assume that a random choice is made. Produce output statistics on the utilization of each
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 order (that is, en route from the supplier based on prior orders). Use the same values of s and S for
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 “Create Call Arrivals” create module. Also get rid of the three modules in the “Arrival
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 report. Is the stopping rule for this exercise “equivalent” to the original stopping rule in Model
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 parts in the system with the sum of the time- average number or parts in all the different places in
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 overlap. As performance measures, use the average waiting time in queue, average queue length, and
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 the same three output performance measures. Do an “informal” statistical comparison by making 20
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 kel01315_ch06_279-310.indd 303 05/12/13 3:27 PM 304 Chapter 6 trimmers down to one minute? (You
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 able to accommodate the queue all the time, not just during “average” times).
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 scenario and select the best in terms of lowest average time in system. In retrospect, is your choice
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 same as before, and observe statistics on the average time in system by customer type (frequent f
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 your .doe f le, or paste in a partial screenshot that provides the requested results.
In Exercise 5-14, make 30 replications, and estimate the expected difference between this and the model of Exercise

Showing 200 - 300 of 385

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

Step by Step Answers