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DMS2030

Individual Assignment 1

Due Date: 11:59 pm, October 14th, 2024

1. A fertilizer company from San Diego has provided the following data.

(a) Compute the labor, raw material, and total productivity for each year. (5 points)

(b) Compute the overall labor, raw material, and total productivity for the two years. (5 points)

2. The inventory of a supermarket turns 46 times a year. The manager of the supermarket says that everything that the store receives from vendors is, on average, sold in two weeks. Are these statements consistent? Assume there are 52 weeks in a year. (5 points)

3. A truck rental company serves 30 rental requests per week on average.  Each truck on average is rented for 3 weeks. The rental fee is $1,000 per truck per week. How many trucks are on renton average?  What is the average weekly revenue? (5 points)

4. A hospital emergency room (ER) is currently organized so that all patients register through an initial check-in process. At his or her turn, each patient is seen by a doctor and then exits the process, either with a prescription or with admission to the hospital. Currently, 55 people per hour arrive at the ER, 10% of who are admitted to the  hospital. On average, 7  people are waiting to  be  registered and  34  are registered and waiting to see a doctor. The registration process takes, on average, 2 minutes per patient. Among patients who receive prescriptions, average time spent with a doctor is 5 minutes. Among those admitted to the hospital, average time is 30 minutes. On average, how long does a patient spend in the ER? On average, how many patients are being examined by doctors? On average, how many patients are there in the ER? Assume the process to be stable; that is, average inflow rate equals average outflow rate.

Please refer to the diagram next page.

(a) On average, how long does a patient spend in the ER? (5 points)

(b) On average, how many patients are being examined by doctors? (5 points)

(c) On average, how many patients are there in the ER? (5 points)

Note: In the last stage (seeing a doctor), there are two types of patients,i.e. two types of flows. When you consider the average time in the last stage, you should take the weighted average because these two types of patients have different measures.

5. Elaine owns a computer rental store.  The rental process can be depicted by the following process flow diagram.

Return rate R

Customer arrivals to the store with an average rate of R = 20 per week and each customer requests for one computer. The rental time is 3 weeks on average. The rental fee is $300 per week. At the end of the rental  period, the customer returns his/her rented  computer to the store. Elaine will inspect every returned computer. The inspection time is negligible. On average 10% of the returned computers need to be repaired by a technician (repair actually means re-configuration and minor repair). A computer that needs repair spends an average time of 1 week in the repair stage, including waiting and repair. After repair work is completed, the computer will be put into the stock for rental. Returned computers that don’t need repair will  be put immediately into the stock for rental. To ensure that there are always computers available to satisfy customer requests, Elaine has to keep an average of 10 computers in the stock for rental.

(a) What is the total number of computers that Elaine needs for her rental business? (5 points)

(b) With an average of 10 computers in the stock for rental, on average how much time does a computer spend in the stock for rental before it is rented by a customer? (5 points)

(c) Elaine estimates that the average rental time will become 2 weeks if she increases the rental fee to $500 per week. The customer arrival rate, the repair time and the percentage of returned computers that need repair will remain the same. Again, she needs to have an average of 10 computers in the stock for rental. Should she increase the rental fee? Justify your answer by considering the number of computers required and the expected revenue per week. (5 points)

6. Bandai has a production line which produces Doraemon toys. There are three steps: in the molding step, workers transfer plastic into the white figures; in the painting step, worker transfer the white figures into painted figures; in the packing step, workers transfer the painted figures into final boxed toys. Currently, the number of workers and the time needed for each step is listed as follows:

(a) Draw a flowchart to depict the toy production process. (5 points) (b) What is the bottleneck of the process? (5 points)

(c) Suppose the demand for toys is 60 units per hour. What is the flow rate of the process? What is the capacity utilization for each step? What is the implied utilization for each step? (5 points)

(d) Bandai plans to hire 17 new workers for the Doraemon production line. How should Bandai train and allocate these workers to different steps in order to maximize the capability of the production line? What if there are 34 new workers? (5 points)

7. Vernon, Andy, and Sean are getting ready for their last period in the exchange study in CBS. Following the final exams, they intend to throw a big party with many of their friends from back home. Presently, they have identified the following set of activities that need to be completed. They decide to not spend any work on preparing the party until all final exams are over. Moreover, they aim to spend a 3-day beach vacation as early as possible, but not before all party planning activities are completed.

On June 10, they will enter the final exam week, which will take 5 days. They then want to arrange for live music (which will take 5 days), evaluate a number of potential party sites (6 days), and prepare a guest list, which includes inviting their friends and receiving the RSVPs (7 days).  They want to visit their two most promising party sites, which they expect to take 4 days. However, this can only be done once they have completed the list of party sites. Once they have finished the guest list and received the RSVPs, they want to book hotel rooms for their friends and created a customized T-shirt with their names on it as well as the name of the guest. Hotel room reservation (3 days) and T-shirt creation (6 days) are independent from each other, but both of them require the guest list to be completed. Once they have picked the party site, they want to have a meeting onsite with an event planner, which they expect to take 4 days. And then, once all work is completed, they plan to takeoff to the beach.

(a) Draw a table to list all the activities, their immediate predecessors, and their durations. Draw the network based on the table. (5 points)

(b) What is the critical path? (5 points)

(c) For each activity, compute the slack time. (5 points)

8. The following table represents a project that should be scheduled using CPM:

(a) Draw the network. (5 points)

(b) What is the critical path? (5 points)

(c) What is the probability of completing this project within 16 days? (5 points)

9. Any suggestions/comments for the class so far? (Optional)


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