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business process management

Business Process Modeling Simulation And Design 1st Edition Laguna Manuel, Marklund, Johan - Solutions

Inventory System-A large discount store is planning to install a system to control the inventory of a particular video game system. The time between demands for a video game system is exponentially distributed with a mean time of 0.2 weeks. In the case where customers demand the system when it is
Airline Ticket Counter-At an airline ticket counter, the current practice is to allow queues to form before each ticket agent. Time between arrivals to the agents is exponentially distributed with a mean of 5 minutes. Customers join the shortest queue at the time of their arrival. The service time
A bank with five tellers opens its doors at 9 A.M. and closes its doors at 5 P.M., but it operates until all customers in the bank by 5 P.M. have been served. Assume that the interarrival times of customers are exponentially distributed with a mean of 1 minute and that the service times of
A service facility consists of two servers in series (tandem), each with its own FIFO queue.(See Figure 7.31.) A customer completing service at server 1 proceeds to server 2, and a customer completing service at server 2 leaves the facility. Assume that the interarrival times of customers to server
For the single-server queuing system in exercise 1b, suppose the queue has room for only three customers, and that a customer arriving to find that the queue is full just goes away.(This is called balking.) Simulate this process for 5,000 minutes, and estimate the same quantities as in part b of
Consider a single-server queuing system for which the interarrival times are exponentially distributed. A customer who arrives and finds the server busy joins the end of a single queue. Service times of customers at the server are also exponential random variables.Upon completing service for a
A process manager is considering automating a bottleneck operation. The operation receives between three and nine jobs per hour in a random fashion. The cost of waiting associated with the jobs is estimated at $2.20 per hour. The team's equipment choices are specified in Table 6.10.Develop a
At Letchworth Community College, one person, the registrar, registers students for classes. Students arrive at a rate of 10 per hour (Poisson arrivals), and the registration process takes 5 minutes on the average (exponential distribution). The registrar is paid $5 per hour, and the cost of keeping
The chief of staff in the emergency room of problem 22 is considering the computerization of the admissions process. This change will not reduce the lO-minute service time, but it will make it constant. Develop a spreadsheet simulation to compare the performance of the proposed automated process
A railroad company paints its own railroad cars as needed. The company is about to make a significant overhaul of the painting operations and needs to decide between two alternative paint shop configurations.Alternative 1: Tho "wall-to-wall" manually operated paint shops, where the painting is done
The manager of a grocery store is interested in providing good service to the senior citizens who shop in his store. The manager is considering the addition of a separate checkout counter for senior citizens. It is estimated that the senior citizens would arrive at the counter at an average of 30
A case team completes jobs at a rate of two per hour, with actual processing times following an exponential distribution. Jobs arrive at rate of about one every 32 minutes, and the arrival times also are considered exponential. Use queuing theory to answer the following questions.a. What is the
Truckloads of seasonal merchandise arrive to a distribution center within a 2-week span.Because of this, merchandised-filled trucks waiting to unload have been known to back up for a block at the receiving dock. The increased cost caused by unloading delays including truck rental and idle driver
The arrival and service rates in Table 6.9 pertain to telephone calls to a technical support person in a call center on a typical day. The interarrival times and the service times are exponentially distributed.a. Determine the average time the callers wait to have their calls answered for each
Consider a cashier at a grocery store. Customers arrive at this cashier's station according to a Poisson process with a mean of 25 customers per hour. The cashier's service times are exponentially distributed with a mean of 2 minutes. By hiring a person to help the cashier bag the groceries and
A fast food chain is opening a new restaurant in a shopping mall. The restaurant needs to hire a cashier and has two prime candidates. Candidate 1 is experienced and fast but demands a higher salary. Candidate 2 is inexperienced and slower but also has more modest salary requests. The question is
Most arrivals to a hospital emergency room are not considered emergencies in that the patients can wait to see a doctor until they complete the proper forms. At County Hospital, emergency patients arrive at a rate of six per hour. This process is, to no one's surprise, a Poisson arrival process. It
A process has a bottleneck resource that consists of specialized equipment. Jobs arrive tothis machine at a rate of 40 per hour (according to a Poisson arrival process). The processing times average 1 minute and are exponentially distributed. Compare the performance (e.g., average cycle time
The manager of a movie theater would like to predict the consequences of adding a second ticket clerk. Data show that arrivals to the theater are Poisson distributed at a rate of 250 per hour, and service times are exponentially distributed with a mean of 12 seconds. The manager has also estimated
A company has a central document-copying service. Arrivals can be assumed to follow the Poisson probability distribution, with a mean rate of 15 per hour. It can be assumed that service times are exponentially distributed. With the present copying equipment, the average service time is 3 minutes. A
A facility management company has recently acquired a number of new commercial properties within the city of Greenfield. They are faced with the problem of hiring a number of oncall janitors, who are responsible for fixing emergency problems that arise at these different facilities. The question is
Plans are being made to open a small gas station in a central location in Springfield. The owner must decide how much space should be provided for waiting cars. This is an important decision because land prices are high. It is assumed that customers (cars) arrive according to a Poisson process with
A workstation has enough storage space to store three jobs in addition to the one being processed. Excess jobs are routed to another workstation, which is used solely to handle this overflow of jobs from the regular workstation. Jobs arrive to the regular workstation according to a Poisson process
Consider the description of problem 14.a. Identify an appropriate queuing model that adequately describes the queuing process.Use the corresponding formulae to determine: Pn , n = 0,1, 2, 3, ... , L, Lq, W, and Wq•b. Determine the fraction of time that the mechanic is busy.c. Determine the
A mechanic is responsible for keeping two machines in working order. The time until a working machine breaks down is exponentially distributed with a mean of 12 hours. The mechanic's repair time is exponentially distributed with a mean of 8 hours.a. Show that this queuing process is a
A telecommunications company receives customer calls at a rate of 25 per hour. The interarrival times are exponentially distributed. Each call requires an average of 20 minutes. The times for each call also follow an exponential distribution.a. What is the minimum number of customer service agents
A pharmaceutical company has formed a team to handle FDA applications for approval of new drugs. Requests for applications arrive at a rate of one every year. The arrivals follow a Poisson distribution. On average, the team processes an application in 9 months. The company estimates that the
Consider an M/M/2 model. Derive the following expressions by constructing the rate diagram and solving the balance equations.
A small machine shop consists of three sensitive machines that break down frequently but independently from each other. The company has two service technicians on standby to repair the machines as soon as they break down. For each fully functional machine, the breakdown rate is 0.1 times per hour,
A gas station has a single automated car wash. Cars arrive to the gas station according to a Poisson process with an average of 30 cars per hour. One third of the customers also want a car wash, so for every customer there is a 33.33 percent chance it desires a car wash. The mean service rate is 10
The mean service and arrival rates for a birth-and-death process describing a queuing system with two parallel servers are given in Table 6.7.a. Construct the corresponding rate diagram.b. Develop the balance equations and solve them to determine the stationary probabilities for finding n customers
Consider a birth-and-death process with mean birth rates and death rates, An and ILm shown in Table 6.6.a. Construct a rate diagram.b. Calculate the stationary probabilities for finding the process in state n, n = 0,1,2,3, . . ..c. If a queuing process with two identical servers fits this
A queuing process is modeled as a birth-and-death process with mean arrival rates Ao = 2, A) = 4, ~ = 3, .1..3 = 1, and Ii" = 0 for n > 3 and mean service rates ILl = 2, J.L2 = 4, IL3 = 1, IL4 = 1 and ILn = 0 otherwise.a. Construct a rate diagram.b. Develop the balance equations and solve them to
It has been concluded that a single-server queuing system with exponentially distributed service and interarrival times can be modeled as a birth-and-death process with statedependent mean service and arrival rates, ILn and Ii", respectively.f1 = {n for n = 0,1,2,3 n 0 otherwise I\. = {3 -n n 0a.
A small branch office of a local bank has two tellers for which customers line up in a single queue. The customers are being served on a first-come-first-served basis. It has been determined that the steady-state probability distribution for finding exactly n customers in the system, lPn, n = 0,1,2
Purchasing requests arrive to an agent at a rate of six per day. The time between arrivals is exponentially distributed. The agent typically requires 1 hour to process a request. The processing time is also exponentially distributed. Assuming 8-hour working days:a. What is the cycle time (the
A mechanic, Bob, requires on average 3 hours to complete a repair. Furthermore, the repair time closely follows an exponential distribution. Bob realizes that by hiring his nephew Bill as an assistant, he can reduce the average repair time to 2 hours. The repair time would still be exponential
Demonstrate that each of the following situations can be represented as a basic queuing process by identifying its components. How would you define the corresponding queuing system?a. The checkout stations in a supermarket.b. The tollbooth at a road-toll checkpoint.c. An auto shop or garage.d. An
Warehouse .tlficiency: A distribution system for a large grocery chain consists of 25 warehouses. The director of logistics and transportation would like to evaluate the relative efficiency of each warehouse. Warehouses have a fleet of trucks to deliver grocery items to a set of stores within their
Consider the linear programming model for process D shown in Section 11.2. The manager of process D has suggested the use of the following weight values: wout(1) = 0.4, wout(2) = 0.75, and win = 1.The manager argues that if each process is allowed to choose weights in order to maximize its
In some applications of DEA, it has been suggested to impose limits on the weight values for all the processes; that is, the application considers that each weight must be between some specified bounds. Under which circumstances would it be necessary to impose such a range?
Do you think it is possible for a process to appear efficient simply because of its pattern of inputs and outputs and not because of any inherent efficiency? Give a numerical example to illustrate this issue.
One major concern with the DEA approach is that with a judicious choice of weights, a high proportion of processes in the set will turn out t6 be efficient and DEA will thus have little discriminatory power. Can this happen when a process has the highest ratio of one of the outputs to one of the
Use the graphical approach to data envelopment analysis and the data in Table 11.5 to determine the efficiency of each process.
The management of a mortgage company has decided, with limited information, that the company can save money if it reduces its staff size. Before downsizing, management asks you to model the credit application process to provide reassurance that service will not be severely affected by the reduction
(Adapted from Khoshnevis, 1994) The management of a major ski resort wants to simulate the rental program during the high season. The resort has two types of customers: people who pay cash and people who use a credit card. The interarrival times of these customers is exponentially distributed with
With a preliminary simulation of 10 days of operation of an emergency room; an analyst found the results, shown in Table 9.24, in terms of the average number of patients waiting.Suppose the analyst would like to estimate the average number of patients waiting with a 95 percent confidence interval
An analyst has suggested a new design for the process in Exercise 14.A simulation of the proposed process yielded the WIP values in Table 9.23. Test the hypothesis that the new process has a mean WIP that is less than the average of the old process. Assume a 5 percent significance level.
The data set in Table 9.22 represents the work-in-process (WIP) at the end of a day for a 40-day simulation of a given business process. Find a 99 percent confidence interval for the mean WIP.
Use the data in Exercise 4 to generate random variates from an Exponential distribution with a mean of 25.
Use the data in Exercise 4 to generate random variates from the discrete probability distribution function in Table 9.2l.
Perform the following tests on the numbers generated in Exercise 10.a. Test for randomness using Kolmogorov-Smirnov with a significance level of 0.05.b. Test for independence using the runs test with a 0.05 level of significance.
Use the linear congruential method with parameters Zo = 79, a = 56214, c = 17, and m = 999 to generate 10 three-digit random numbers.
Starting with a seed of 3,461, generate 10 four-digit random numbers using the mid-square method.
The data set in Table 9.20 consists of cycle times of jobs in a given process. Perform the runs test to determine with a 99 percent confidence level whether or not the cycle times (ordered by columns) are independent.
Consider the data in Exercise 4.Perform the runs test to determine with a 95 percent confidence level whether or not the numbers in the sequence (ordered by rows) are independent.
Apply the Kolmogorov-Smirnov test to the data in Exercise 2.
Apply the Kolmogorov-Smirnov test to the data in Exercise 1.
Use the Kolmogorov-Smirnov test to examine under the significance level of 0.01 whether the observations in Table 9.19 are random numbers uniformly distributed between 0 and 1.
An analyst is interested in determining whether the Weibull distribution with parameters a = 6 and 13 = 10 is a good fit to the data set in Table 9.18. Use Microsoft Excel to perform a chi-square goodness-of-fit test to help the analyst make a decision.
Use the chi-square goodness-of-fit test and a significance level of 0.05 to test the set of service times in Table 9.17 for possible fit to the Normal distribution.
Use the chi-square goodness-of-fit test and a significance level of 0.1 to test the set of interarrival times in Table 9.16 for possible fit to the Exponential distribution.
The raw material arrives by truck once every week on Monday morning. Each shipment contains 15 units each of the five necessary components. The internal logistics within the factory are such that the transportation times for the incomplete cabinets can be neglected. However, to transport the fully
Identify the bottleneck and add the new employee to the bottleneck. Compare the utilization of clerks and accounting personnel before and after adding the new employee. Also compare the frequency distribution of cycle times before and after adding the new employee. Include line graphs for the
Discuss the performance of the current process based on the collected data. Include the following exhibits to support your arguments: queue statistics, line graphs of resource utilization, a histogram of cycle times, and the WIP value at the end of the 15 days.
Set the random seed value to 34 in the Simulation Setup of the Run menu. Run the model for 15 working days and collect the waiting time at the queues, cycle time, resource utilization, and work-in-process. (A working day consists of 8 hours.)
Using the flowchart as a guideline, develop a simulation model of this process. Because only two resource types are in this process (the clerks and the accounting personnel), your model should have only two queues. Include an exhibit consisting of the simulation model.
The first task is to understand this process, so you should develop a flowchart. This chart should be the first exhibit in your written report.
The hospital is willing to allocate up to $2,000 per day for labor associated with the X-ray process. The hourly salaries for each labor resource are shown in Table 8.13.Management also is considering adding two more facilities, which can be a combination of X-ray labs, dark rooms, or changing
Assess the performance of the process using the values calculated in question 2.
Simulate 10 days of operation and compute the cycle time and resource utilization statistics.Assume a working day has 8 hours.
Develop a simulation model of this process.Hourly Salary$12$25$20$8
Refer to the grocery store described in problem 8 in Chapter 7 to answer the following questions.a. To make the model more realistic, Safeway also wants to include the time customers spend in the store walking around and picking up their groceries. Empirical investigation has shown that there are
Figure 8.49 shows the flowchart of a business process that receives an average of one job every 10 minutes with a standard deviation of 2.5 minutes. The actual interarrival times approximately follow a normal distribution. The processing times are exponentially distributed with the mean values (in
Priority Queues- A business process consists of six activities, as shown in the flowchart of Figure 8.48. The activity times are normally distributed with mean values of 15, 10, 8,8, 13, and 7, respectively, for activities A through F. Similarly, the standard deviations are 3,2.5,2, 3,3.5, and
Multiple Queues-The order-fulfillment process of an entrepreneurial catalog business operates as follows. Orders arrive with exponential interarrival times with a mean of 10 minutes.A single clerk accepts and checks the orders and processes payment. These activities require a random time that is
Variable Resource Availability-Travelers arrive at the main entrance door of an airline terminal according to an exponential interarrival time distribution with a mean of 1.6 minutes.The travel time from the entrance to the check-in is distributed uniformly between 2 and 3 minutes. At the check-in
Assessing Process Performance-The process of insuring a property consists of four main activities: review and distribution, underwriting, rating, and policy writing. Four clerks, three underwriting teams, eight raters, and five writers perform these activities in sequence. The time to perform each
Investigating the Effect of Rework Rates-A proposed business process consists of five serial workstations. One caseworker is positioned in each workstation. The processing times at each workstation are exponentially distributed with mean values of 11, 10, 11, 11, and 12 minutes, respectively. The
Investigating the Effect of Pooling Resources-Three types of jobs arrive to a process at a rate that randomly varies between two and five jobs per hour; that is, the interarrival times are governed by a uniform distribution with mean equal to three and a half jobs per hour.The process is currently
Measuring Cycle Times of Different Types of Jobs-Three types of jobs arrive to a process at a rate of four jobs per hour. The interarrival times are exponentially distributed. The arrivals are not equally likely for each job type. Typically, 40 percent of the jobs are type 1,35 percent are type II,
Grocery Store-You are hired by Safeway to help them build a number of simulation models to better understand the customer flows and queuing processes in a grocery store setting.The pilot project at hand focuses on an off-peak setting where at most two checkouts are open. To better understand the
Bank Tellers--Consider a banking system involving two inside tellers and two drive-in tellers. Arrivals to the banking system are either for the drive-in tellers or for the inside tellers. The time between arrivals to the drive-in tellers is exponentially distributed with a mean of 1 minute. The
Inventory System-A large discount store is planning to install a system to control the inventory of a particular video game system. The time between demands for a video game system is exponentially distributed with a mean time of 0.2 weeks. In the case where customers demand the system when it is
Airline Ticket Counter-At an airline ticket counter, the current practice is to allow queues to form before each ticket agent. Time between arrivals to the agents is exponentially distributed with a mean of 5 minutes. Customers join the shortest queue at the time of their arrival. The service time
A bank with five tellers opens its doors at 9 A.M. and closes its doors at 5 P.M., but it operates until all customers in the bank by 5 P.M. have been served. Assume that the interarrival times of customers are exponentially distributed with a mean of 1 minute and that the service times of
A service facility consists of two servers in series (tandem), each with its own FIFO queue.(See Figure 7.31.) A customer completing service at server 1 proceeds to server 2, and a customer completing service at server 2 leaves the facility. Assume that the interarrival times of customers to server
For the single-server queuing system in exercise 1b, suppose the queue has room for only three customers, and that a customer arriving to find that the queue is full just goes away.(This is called balking.) Simulate this process for 5,000 minutes, and estimate the same quantities as in part b of
Consider a single-server queuing system for which the interarrival times are exponentially distributed. A customer who arrives and finds the server busy joins the end of a single queue. Service times of customers at the server are also exponential random variables.Upon completing service for a
A process manager is considering automating a bottleneck operation. The operation receives between three and nine jobs per hour in a random fashion. The cost of waiting associated with the jobs is estimated at $2.20 per hour. The team's equipment choices are specified in Table 6.10.Develop a
At Letchworth Community College, one person, the registrar, registers students for classes. Students arrive at a rate of 10 per hour (Poisson arrivals), and the registration process takes 5 minutes on the average (exponential distribution). The registrar is paid $5 per hour, and the cost of keeping
The chief of staff in the emergency room of problem 22 is considering the computerization of the admissions process. This change will not reduce the lO-minute service time, but it will make it constant. Develop a spreadsheet simulation to compare the performance of the proposed automated process
A railroad company paints its own railroad cars as needed. The company is about to make a significant overhaul of the painting operations and needs to decide between two alternative paint shop configurations.Alternative 1: Tho "wall-to-wall" manually operated paint shops, where the painting is done
The manager of a grocery store is interested in providing good service to the senior citizens who shop in his store. The manager is considering the addition of a separate checkout counter for senior citizens. It is estimated that the senior citizens would arrive at the counter at an average of 30
A case team completes jobs at a rate of two per hour, with actual processing times following an exponential distribution. Jobs arrive at rate of about one every 32 minutes, and the arrival times also are considered exponential. Use queuing theory to answer the following questions.a. What is the
Truckloads of seasonal merchandise arrive to a distribution center within a 2-week span.Because of this, merchandised-filled trucks waiting to unload have been known to back up for a block at the receiving dock. The increased cost caused by unloading delays including truck rental and idle driver
The arrival and service rates in Table 6.9 pertain to telephone calls to a technical support person in a call center on a typical day. The interarrival times and the service times are exponentially distributed.a. Determine the average time the callers wait to have their calls answered for each
Consider a cashier at a grocery store. Customers arrive at this cashier's station according to a Poisson process with a mean of 25 customers per hour. The cashier's service times are exponentially distributed with a mean of 2 minutes. By hiring a person to help the cashier bag the groceries and
A fast food chain is opening a new restaurant in a shopping mall. The restaurant needs to hire a cashier and has two prime candidates. Candidate 1 is experienced and fast but demands a higher salary. Candidate 2 is inexperienced and slower but also has more modest salary requests. The question is
Most arrivals to a hospital emergency room are not considered emergencies in that the patients can wait to see a doctor until they complete the proper forms. At County Hospital, emergency patients arrive at a rate of six per hour. This process is, to no one's surprise, a Poisson arrival process. It

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