OM - CH3 HW

Throughput is a

rate

Which of these in not an approach to capacity planning? Tracking Leading Forecasting Following

Forecasting

Capacity is directly related to:

Output Machines Time Processes

Consider a four-step serial process with processing times given in the following list. There is one machine at each step of the process, and this is a machine-paced process. Step 1: 30 minutes per unit Step 2: 8 minutes per unit Step 3: 24 minutes per unit Step 4: 17 minutes per unit Assuming that the process starts out empty, how long will it take (in hours) to complete a batch of 95 units? (Do not round intermediate calculations. Round your answer to nearest hour.)

Step 1 is the bottleneck step of the process, so the machine-paced process will be set at a speed of 0.5 hour per unit at each step. The first unit will take 4 × 0.5 = 2 hours to complete. The remaining 94 units will have a cycle time of 0.5 hour. The total time required to complete a batch of 95 units is 2 + 94 × 0.5 = 49 hours

Consider a four-step serial process with the number of workers at each step and processing times given in the following table. Assuming that the process starts out empty and is worker-paced, how long will it take (in minutes) to serve 15 customers?

The bottleneck is step 1 of the process, which means that the cycle time for all customers other than the first one is 8 minutes. The first customer takes 8 + 12 + 9 + 9 = 38 minutes to complete service. As a result, it takes a total of 38 + 14 × 8 = 150 minutes to serve 15 customers.

Which of the following are required for a capacity calculation Time between process starts Time between process completions Total Time spent in the process Length of the time horizon in question

Time between process starts Time between process completions Length of the time horizon in question

Consider a process consisting of three resources. Assume there exists unlimited demand for the product. Resource 1 has a processing time of 9 minutes per unit. Resource 2 has a processing time of 7 minutes per unit. Resource 3 has a processing time of 6 minutes per unit. The three resources are staffed by different workers individually. The flow diagram is shown above. a - What is the capacity of resource 2? b - What is the bottleneck in the process? c - What is the utilization of resource 2? d - How long does it take the process to produce 196 units starting with an empty system, assuming this is a worker-paced process?

a. 1 unit / 7 minutes per unit = 0.143 units per minute. b. Resource 1 has the longest processing time. c. Flow rate = 60/9 = 6.667 units/hour. Resource 2 capacity = 60/7 = 8.571 units/hour.Resource 2 Utilization = Flow Rate / Capacity = 6.667/8.571 = 78%. d. (196 units × 9 minutes) + 7 minutes + 6 minutes = 1777 minutes.

Glenn Dental Clinic provides general dental care to residents of Philadelphia on a walk-in basis. The clinic has started receiving complaints from patients that the waiting time is too long and has asked you to investigate whether this problem can be solved. Upon arrival, customers first receive a series of paperwork from the receptionist and fill out relevant information such as personal health records and insurance provider. The form is then handed back to the receptionist who enters the information into the computer system for the dentist to see. A dental assistant then takes an X-ray from the patient. A dentist then performs the checkup and discusses any issues with the patient. Based on conversations with staff members at the clinic, you have obtained the following information on the process: It takes about 5 minutes for a customer to fill out the paperwork. Entry of information on the paperwork into the system and verification with past records takes another 5 minutes for a receptionist. There are two receptionists. It takes 15 minutes, on average, for the dental assistant to take an X-ray. There are three dental assistants on shift at any moment. There are 10 dentists working at the clinic. Each checkup takes 30 minutes, on average. The following table summarizes the process data collected above. What is the capacity (patients/hour) at the resource "Dentist"? What is the bottleneck in the process? Assuming unlimited demand, what would be the flow rate? Assuming unlimited demand, what would be the utilization at resource "Receptionists"? If demand is 12 patients per hour, what would be the cycle time (minutes)? If demand is 11 patients per hour, what would be the cycle time (minutes)? Assume the process started empty. How long would it take to serve 20 patients?

a. 10 workers × (60 minutes per hour/30 minutes per patient) = 20 patients per hour. b. The dental assistants have the lowest capacity of 12 patients per hour, 3 dental assistants × (60 minutes per hour / 15 minutes per patient) = 12 patients per hour. c. The Flow Rate = 12 patients per hour, 3 dental assistants × (60 minutes per hour / 15 minutes per patient) = 12 patients per hour. d. Receptionists capacity = 2 receptionists × (60 minutes per hour / 5 minutes per patient) = 24 patients per hour.Utilization = 12 patients per hour at the bottleneck / 24 patients per hour capacity = 50% e. Flow rate is 12 per hour, which yields a cycle time of 60 /12 = 5 minutes. f. The process is demand constrained. Flow rate is 11 per hour, which yields a cycle time of 60/11 = 5.45 minutes. g. Time to produce N units when starting with an empty worker-paced system = Sum of processing times + (N − 1) × Cycle time, where Cycle time = 1 / Flow rate, which in this case is 1 / (12 patients per hour) = 1 / (0.2 patients per minute). Therefore, time to serve 20 patients = (5 min + 5 min + 15 min + 30 min) + (20 − 1) × (5 min) = 150 minutes.

A community health system's nurse team consists of 17 nurses working in the local community. It takes a nurse 1.5 hours to complete one patient visit (including travel time and breaks). Nurses work 9 hours per workday. a.What is the capacity of the nurse team over the course of a 9-hour workday? b.Assuming the demand for the nurses is 60 patients per day, what is the utilization of the nurse team? c.Assuming the demand for the nurses is 60 patients per day, what is the cycle time?

a. 17 nurses × 9 hours / 1.5 hours per visit = 102.0 visits b. 60 demand / 102.0 capacity = 59% utilization. c. (9 hours × 60 minutes) / 60 patients = 9.0 minutes per patient

It takes a barber 5 minutes to serve one customer a.What is the capacity of the barber expressed in customers per hour? b.Assuming the demand for the barber is 7 customers per hour, what is the flow rate? c.Assuming the demand for the barber is 7 customers per hour, what is the utilization? d.Assuming the demand for the barber is 7 customers per hour, what is the cycle time?

a. 60 minutes / 5 minutes = 12 customers per hour c. 7 demand / 12 capacity = 58.33% d. Cycle time = 1/flow rate, 7/60 minutes = 8.57 minutes per customer

A small, privately owned Asian company is producing a private-label soft drink called Yoggo. A bottling line puts the soft drinks into plastic bottles and then packages the bottles into boxes holding 10 bottles each. The bottling line is comprised of the following four steps: (1) the bottling machine takes 1 second to fill a bottle, (2) the lid machine takes 3 seconds to cover the bottle with a lid, (3) a labeling machine takes 3 seconds per bottle, and (4) the packaging machine takes 4 seconds to place a bottle into a box. When a box has been filled with 10 bottles, a worker tending the packaging machine removes the filled box and replaces it with an empty box. Assume that the time for the worker to remove a filled box and replace it with an empty box is negligible and hence does not affect the capacity of the line. Problem data are summarized in the following table. What is the capacity (bottles/hour) at the resource "Apply a lid"? What is the bottleneck in the process? Assuming unlimited demand, what would be the flow rate? Assuming unlimited demand, what would be the utilization at resource "Apply a lid"? If demand were 12 bottles per minute, what would be the utilization of bottling? If demand were 12 bottles per minute, what would be the cycle time (seconds) of the process? Assume the process started empty and that this is a machine-paced process. How long would it take to produce 500 bottles?

a. 60 seconds / 3 seconds × 60 minutes per hour = 1,200 bottles b. Packaging is the bottleneck with a capacity = 3600 seconds / 4 seconds per unit = 900 units per hour. c. The Flow Rate = 15 bottles per minute at the bottleneck location × 60 minutes = 900 bottles per hour. d. Apply a lid capacity = 60 seconds / 3 seconds per lid × 60 minutes = 1,200Utilization = Flow Rate / Capacity, 900 / 1,200 = 75% e. Flow rate is 1/5 bottle per second. Capacity is 1 bottle per second. Utilization is 1/5 / 1 = 20% f. This is demand constrained with a flow rate of 1/5 bottle per second. Cycle time is 1 / (1/5) = 5 seconds. g. Since it is a machine-paced line, the first unit will take 4 stations × 4 secs = 16 seconds. The remaining 499 units will take 499 × 4 secs = 1,996 seconds, Therefore, 16 + 1,996 = 2,012 seconds.

Consider the following production process for manufacturing biscuits. The first step of the process is mixing, where all of the ingredients are combined in the correct proportion to form dough. In the next step of the process, the dough is formed into sheets and cut into pieces in preparation for baking. The cut dough is then baked into biscuits and subsequently must be cooled. The final step of the process is packaging the biscuits for the consumer. The following table summarizes the production process along with the processing times at each step of the process. The process is highly automated, so assume that this is a machine-paced process with one machine available at each step. a.What is the capacity of the baking process step (in batches per hour)? b.What is the bottleneck of the manufacturing process?c.Assuming unlimited demand, what is the process flow rate (in batches per hour)? Assuming unlimited demand, what is the utilization of the mixing process step? If demand is 3 per hour, what is the utilization of the packing step? f.If demand is 3 per hour, what is the cycle time (minutes) of the process? If the manufacturing process is currently full of work-in-process inventory, how long would it take to complete 50 batches of biscuits?

a. Since there is only one machine at each process step, the capacity is the reciprocal of the activity time. The capacity of the baking process step is 1 / 12 batches per minute × 60 minutes per hour = 5 batches per hour. b. Cooling; since there is only one machine at each process step, the bottleneck is the step with the most work to do. c. The process flow rate is the capacity of the bottleneck, which is the cooling process. The process flow rate is 1 / 18 batches per minute × 60 minutes per hour = 3.33 batches per hour. d. The capacity of the mixing process step is 1 / 15 batches per minute × 60 minutes per hour = 4 batches per hour. The process flow rate is 3.33 batches per hour. The utilization is the flow rate divided by the capacity of the process step = 3.33 batches per hour / 4 batches per hour = 83%. e. Flow rate is 3 per hour, capacity is 6 per hour, so utilization is 3/6 = 50% f. Flow rate is 3 per hour (because the process is demand constrained), so cycle time is 60 min/hr / 3 per hour = 20 minutes g. The time to complete X units in a full system is X × Cycle time. The cycle time is 1 / 3.33 hours, so it takes 50 / 3.33 = 15 hours to complete 50 batches.

The local driver's license center processes applications for driver's license renewals through the following three steps. First, the customer registers with the receptionist, who updates the customer's information in the database. This first step takes 4 minutes per customer. Then, the customer visits one of 3 cashiers to pay the associated fees for the license renewal. This takes 9 minutes per customer because several forms must be printed from the computer and signed by the customer. Finally, the customer visits one of 3 license processing stations where the customer's picture is taken and the license is printed. This final step takes 15 minutes per customer. a.Assuming unlimited demand, what is the flow rate of the process in customers per hour? b.If demand is 7 customers per hour, what is the utilization of the receptionist? c.If demand is 7 customers per hour, what is the cycle time (minutes) of the process? d.If the system starts empty and operates worker paced, how long does it take to complete the processing of 9 customers? e.Assuming unlimited demand, what would the new flow rate be if the center added one server to the bottleneck resource?

a. The bottleneck resource is the license processing station. Each machine can process 16 customers per hour, and there are three machines; thus, the flow rate through this stage (and the process as a whole) is 12 customers per hour. All of the other steps have higher capacities. b. The process is demand constrained with a flow rate of 7 per hour. The receptionist's capacity is 60 / 4 = 15 per hour. Utilization is 7 / 15 = 0.47 c. The process is demand constrained with a flow rate of 7 per hour. Cycle time is 1 / 7 hour or 60 / 7 = 8.57 minutes d. The first customer takes 28 minutes. The other 8 customer appear with a cycle time of 5 minutes. Total time is 28 + 8 × 5 = 68 minutes. e. Since the bottleneck is processing, adding an extra server there will increase its capacity to 16 while the capacities of registering and paying will remain at 15 and 20 respectively. Thus the new flow rate will be 15 customers per hour.

A small mortgage lender has one receptionist, four loan officers, and two office managers. When applicants apply for a new loan in person, they first fill out paperwork with the receptionist. Then the applicants meet with one of the loan officers to discuss their needs. The loan officer spends additional time processing the application after the applicants leave the office. Finally, the application must be reviewed by an office manager before it can be approved. The following table lists the processing times at each stage. The office is open for 8 hours per day, 5 days per week. a.What is the bottleneck of the process? b.Assuming unlimited demand, what is the process flow rate (in loans per week)? c.If customer demand is 18 loans per week, what is the utilization of the office managers resource? d.If customer demand is 18 loans per week, what is the cycle time (hours) of the process? e.If customer demand is 24 loans per week, what is the utilization of the loan officers? f.If customer demand is 24 loans per week, what is the cycle time (hours) of the process?. Assuming that the office currently has no backlog of loans that it is processing, how long will it take to complete 10 loans?

a. The capacity of each resource is the number of employees / activity time. The capacity for the office managers is 2 / 4 = 0.50 loans per hour, which is less than the capacities of either of the other two resources. b. The flow rate is the capacity of the bottleneck, which is 2 / 4 = 0.50 loans per hour × 8 hours per day × 5 days per week = 20 loans per week. c. If the demand is 18 loans per week, this is the process flow rate because it is lower than the process capacity. The utilization of the office managers' resource is Flow rate / Resource capacity = 18 loans per week / 20 loans per week = 90%. d. The process is demand constrained with a flow rate of 18 per week. The cycle time is 40 hr/week / 18 per week = 2.22 hours e. The process is supply constrained with a flow rate of 20 per week. Capacity of loan officers is 4 × 40 / 7 = 22.85 per week. Utilization is 20 / 22.85 = 0.875 f. The process is supply constrained with a flow rate of 20 per week. The cycle time is 40 hr/week / 20 per week = 2 hours. g. This is a worker-paced process, so the first loan will take 1 + 7 + 4 = 12 hours to complete. The remaining loans have a cycle time of 1 / 0.50 = 2 hours per loan. This means that the remaining loans will take an additional 9 × 2 = 18 hours to complete. The total time to complete 10 loans is 12 + 9 × 2 = 30 hours.

An automated car wash serves customers with the following serial process: pretreat, wash, rinse, wax, hand dry. Each of these steps is performed by a dedicated machine except for the hand-dry step, which is performed manually on each car by one of three workers. The steps of the process have the following processing times: Pretreat: 4 minute per car Wash: 6 minutes per car Rinse: 3 minutes per car Wax: 2 minutes per car Hand dry: 4 minutes per car a.Which resource is the bottleneck of this process? b.If the car wash has a demand of 13 cars per hour, what is the flow rate of the process? c.If the car wash has a demand of 13 cars per hour, what is the utilization of the machine that performs the Wax process? d.If the car wash has a demand of 9 cars per hour, what is the utilization of hand dry? e.If the car wash has a demand of 9 cars per hour, what is the cycle time of the process (minutes)? f.Now assume demand is 13 cars per hour. Starting from an empty system (and assuming the stations can work independently), how long would it take (minutes) to wash 4 cars?

a. Wash has the lowest capacity b. The bottleneck is the Wash process, with a capacity of 10 cars per hour. The flow rate is the minimum of the capacity of the bottleneck and the demand. c. Utilization is the flow rate divided by the capacity of the process step. If the demand is 13 cars per hour, the flow rate is 10 cars per hour, because the flow rate is the minimum of the capacity of the bottleneck and the demand. The capacity of the machine that performs the Wax process is 1 / 2 × 60 = 30 cars per hour. The utilization of this machine is 10 / 30 = 33.33%. d. The flow rate is 9 cars per hour and the capacity of hand dry is 45 cars per hour. So utilization is 9 / 45 = 20.00% e. The process is demand constrained, so the flow rate is 9 cars per hour. The cycle time is 1 / 9 hours, or 60 / 9 = 6.67 minutes f. The first unit requires 4 + 6 + 3 + 2 + 4 = 19 minutes. The other 3 require 3 × 6 minutes = 18 minutes. Total time is 19 + 18 = 37 minutes.

Throughput is generally equal to which thing?

arrival rate

You observe a long line at the airport security. The process currently is

capacity-constrained

Which of the following items would be considered resources in a restaurant? Recipes Food Brand image Chefs

chefs

s the capacity of the bottleneck larger than, equal to, or smaller than the capacity of the process?

equal to

SmartPhones are made on a 40-step assembly process. All 40 steps are connected through a conveyor belt and all of the 40 steps must work at the same rate even if some of them have more capacity than others. Is this process a machine-paced process or a worker-paced process?

machine-oaced

You are sitting in a restaurant and the waiter brings you the food you ordered a while ago. If you think about you being the flow unit in the process of the restaurant, which step of this process will be downstream relative to your current position in the process? Waiting to order Being seated at a table Paying the bill Reviewing the menu

paying the bill

You observe a vehicle registration department at your local township. Assume that all employees are ready to work at 9 a.m. You arrive at 9 a.m. sharp and are the first customer. Is your time through the empty process longer or shorter than the flow time averaged across all customers that arrive over the course of the day?

shorter than the average flow time

To get capacity from time between completions you do which mathematical operation?

take the inverse

What is the maximum utilization a resource can achieve?

1.00