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Question:An enterprising student has set up an internship clearinghouse for business students. Each student who uses the service fills out a form and lists up to 10 companies that he or she would like to have contacted. The clearinghouse has a choice of two methods to use for processing the forms. The traditional method requires about 20 minutes to review the form and arrange the information in the proper order for processing. Once this setup is done, it takes only two minutes per company requested to complete the processing. The other alternative uses an optical scan/retrieve system, which takes only a minute to prepare but requires five minutes per company for completing the processing. If it costs about the same amount per minute for processing with either of the two methods, when should each be used?

A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.

a. How many customers would you expect to see on the average at the coffee urn?

b. How long would you expect it to take to get a cup of coffee?

c. What percentage of time is the urn being used?

d. What is the probability that three or more people are in the cafeteria?

e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 15 seconds, how does this change your answers to (a) and (b)?

Question: The flow of materials through eight departments is shown on the next page. Even though the table shows flows into and out of the different departments, assume that the direction of flow is not important. In addition, assume that the cost of moving material depends only on the distance moved.

a. Construct a schematic layout where the departments are arranged on a 2 x 4 grid with each cell representing a 10 x 10-meter square area.

b. Evaluate your layout using a distance-times-flow measure. Assume that distance is measured rectilinearly (in this case, departments that are directly adjacent are 10 meters apart and those that are diagonal to one another are 20 meters apart).

An engineering firm retains a technical specialist to assist four design engineers working on a project. The help that the specialist gives engineers ranges widely in time consumption. The specialist has some answers available in memory, others require computation, and still, others require significant search time. On average, each request for assistance takes the specialist one hour. The engineers require help from the specialist on average of once each day. Because each assistance takes about an hour, each engineer can work for seven hours, on average, without assistance. One further point: Engineers needing help do not interrupt if the specialist is already involved with another problem. Treat this as the finite queuing problem and answer the following questions:

a. How many engineers, on average, are waiting for the technical specialist for help?

b. What is the average time that an engineer has to wait for the specialist?

c. What is the probability that an engineer will have to wait in line for the specialist?

L. Winston Martin (an allergist) has an excellent system for handling his regular patients who come in just for allergy injections. Patients arrive for injection and fill out a name slip, which is then placed in an open slot that passes into another room staffed by one or two nurses. The special injections for a patient are prepared, and the patient is called through a speaker system into the room to receive the injection. At certain times during the day, patient load drops, and only one nurse is needed to administer the injections. Let’s focus on the simpler case of the two—namely when there is one nurse. Also, assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentially distributed. During this slower period, patients arrive with an inter-arrival time of approximately three minutes. It takes the nurse an average of two minutes to prepare the patients’ serum and administer the injection.

a.What is the average number you would expect to see in Dr. Martin’s facilities?

b.How long would it take for a patient to arrive, get an injection, and leave?

c.What is the probability that there will be three or more patients on the premises?

d.What is the utilization of the nurse?

e.Assume three nurses are available. Each takes an average of two minutes to prepare the patients’ serum and administer the injection. What is the average total time of a patient in the system?

A local market research firm has just won a contract for several thousand small projects involving data gathering and statistical analysis. In the past, the firm has assigned each project to a single member of its highly trained professional staff. This person would both gather and analyze the data. Using this approach, an experienced person can complete an average of 10 such projects in an eight-hour day. The firm’s management is thinking of assigning two people to each project in order to allow them to specialize and become more efficient. The process would require the data gatherer to i ll out a matrix on the computer, check it, and transmit it to the statistical analysis program for the analyst to complete. Data can be gathered on one project while the analysis is being completed on another, but the analysis must be complete before the statistical analysis program can accept the new data. After some practice, the new process can be completed with a standard time of 20 minutes for the data gathering and 30 minutes for the analysis.

a.What is the production (output per hour) for each alternative? What is the productivity (output per labor hour)?

b.How long would it take to complete 1,000 projects with each alternative? What would be the labor content (total number of labor hours) for 1,000 projects for each alternative?

Customers enter the camera department of a store at the average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation.

a. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)?

How long would a customer expect to spend in the camera department (total time)?

b. What is the utilization of the clerk?

c. What is the probability that there are more than two people in the camera department (excluding the clerk)?

d. Another clerk has been hired for the camera department who also takes an average of six minutes to serve each arrival. How long would a customer expect to spend in the department now?

Wally’s Widget Warehouse takes orders from 7 a.m. to 7 p.m. The manager wants to analyze the process and has provided the process flow diagram shown below. There are three steps required to ship a customer order. The first step is to take the order from a customer. The second step is to pick the order for the customer, and then they have to pack the order ready for shipping. Wally promises that every order placed today gets shipped tomorrow. That means that the picking and packing operations must finish all orders before they go home.

Wally wants to figure out the following.

a. What is the current maximum output of the process assuming that no one works overtime?

b. How long will the picking and packing operations have to work if we have a day where the order taker works at his maximum capacity?

c. Given b, what is the maximum number of orders waiting to be picked?

d. Given b, what is the maximum number of orders waiting to be packed?

e. If we double the packing capacity (from 60 to 120 orders per hour), what impact does this have on your answers in parts (b), (c), and (d)?

Question: The customer order decoupling point determines the position of what in the supply chain?

What is the objective of assembly-line balancing? How would you deal with the situation where one worker, although trying hard, is 20 percent slower than the other 10 people in a line?