HW1Solutions for operation management class PDF

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Operations Management Homework 1 Solutions Suppose that loading a tray of cookies into the oven takes Kristen’sroommate 3 minutes instead of 1 minute as in the case discussed in class. What is the minimum amount of time it will take Kristen and her roommate to complete a rush order of 2 dozen cookie...

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Operations Management Homework 1 Solutions 1. Suppose that loading a tray of cookies into the oven takes Kristen’s roommate 3 minutes instead of 1 minute as in the case discussed in class. What is the minimum amount of time it will take Kristen and her roommate to complete a rush order of 2 dozen cookies? Use a Gantt chart to find your answer. Please submit your Gatt chart. The minimum amount of time will be 40 minutes. See below for one possible Gantt chart.

Figure 1: Gantt chart for Question 1. 2. Suppose that Jeff, Anna, and Paul are working in a bicycle factory. The bicycle making process consists of four activities: assembling the handlebars, placing the handlebars on the frame, attaching the wheels, and finally placing a kickstand on the bike. Jeff is responsible for the handlebars activity, Anna is responsible for the frames and kickstand activities, and Paul is responsible for the wheels activity. The process flow diagram looks as follows.

Figure 2: Process Flow Diagram for Question 2.

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a. Calculate the capacity of each resource. We create the following chart to calculate the capacity of each resource. Resource Jeff Anna Paul

Activities Handlebars Frames and Kickstand Wheels

Total time per job (min) 2 6+2=8 3

Capacity (per/hour) 30 7.5 20

b. What is the bottleneck of the process, and what is the capacity of the process? Anna is the bottleneck of the process since she can only process 7.5 bicycles per hour. Therefore, the capacity of the process is 7.5 bicycles per hour. c. Calculate the utilization of each resource assuming that the process is operating at maximum capacity. If we assume that the process is operating at its maximum capacity of 7.5 bicycles per hour, then the utilization of each resource is given as follows. Resource Jeff Anna Paul

Capacity (per hour) 30 7.5 20

Process Capacity (per hour) 7.5 7.5 7.5

Utilization 25% 100% 37.5%

d. Suppose that Jeff is paid $20 per hour but only for the amount of time that he actually works, that Anna is paid $30 per hour but only for the amount of time that she actually works, and that Paul is paid $16 per hour but also only for the amount of time that he actually works. Suppose also that each bicycle sold generates a revenue of $200 and has raw materials cost of $60. Assuming that the bicycle factory is operating at its maximum capacity, what is the profit per hour after paying Jeff, Anna, and Paul their salaries? The bicycle factory can make 7.5 bicycles per hour, and each bicycle generates a profit of $200 - $60 = $140 before labor costs. Therefore, it yields a profit of 7.5 × $140 = $1, 050 per hour before accounting for labor costs. Labor costs for each hour can be computed as follows. Resource Jeff Anna Paul Total

Labor Cost per hour $20 $30 $16 -

Utilization 25% 100% 37.5% -

Salary per hour $5 $30 $6 $41

Since the total labor costs are $41 per hour, the profit (per hour) after paying Jeff, Anna, and Paul their salaries is $1,050 - $41 = $1,009 per hour.

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