Q3. Consider a process consisting of five resources that are operated for eight hours per day. The process works on three different products (A, B and C): (Flow time in minutes) #Workers Flow Time for A Flow Time for B Flow Time for C Resource 1 2 5 5 5 2 2 3 4 5 3 1 15 0 0 4 1 0 3 3 5 2 6 6 6 Demand for product A is 40 units/day, demand for product B is 50 units/day and demand for product C is 60 units/day. What is the bottleneck? What is the flow rate for each unit assuming that demand must be served in the mix described above (i.e. for every 4 units of A there are 5 units of B and 6 units of C)? Inventory Buildup Q4. The Western Pennsylvania Milk Company is producing milk at a fixed rate of 5,000 gallons/hour. The company's clients request 100,000 gallons of milk over the course of one day. This demand is spread uniformly from 8am to 6pm. If there is no milk available, clients will wait until enough is produced to satisfy their requests. The company starts producing at 8am with 25,000 gallons in finished goods inventory. At the end of the day, after all demand has been fulfilled, the plant keeps on producing until the finished goods inventory has been restored to 25,000 gallons. (NOTE: For the following questions, treat trucks/milk as a continuous flow process. Begin by drawing a graph indicating how much milk is in inventory and how much milk is "back-ordered" over the course of the day.) a. b. C. d. At what time during the day will the clients have to start waiting for their requests to be filled? At what time will clients stop waiting? Assume that the milk is picked up in trucks that hold 1,250 gallons each. What is the maximum number of trucks that are waiting? Assume the plant is charged $50/hour per waiting truck. What are the total waiting time charges on a day? Little's Law Q5. The total number and gender mix of employees in a certain company remains constant. Due to turnover, on average the company hires 150 men and 200 women each year. It is estimated that on average a woman stays 50% longer than a man. What proportion of the employees are women? Q6. The Internal Revenue Service Department of Tax Regulations writes regulations in accord with laws passed by Congress. On average, the department completes 300 projects per year. The Wall Street Journal reports that, as of October 11, 1997, the number of projects currently "on the Department's plate" is 588. Nevertheless, the department head claims that average time to complete a project is under six months. Do you have any reason to disagree? Why or why not? Q7. Checking accounts at a local bank carry an average balance of $3,000. The bank turns over its balance six times a year. On average, how many dollars flow through the bank each month? Q3. Consider a process consisting of five resources that are operated for eight hours per day. The process works on three different products (A, B and C): (Flow time in minutes) #Workers Flow Time for A Flow Time for B Flow Time for C Resource 1 2 5 5 5 2 2 3 4 5 3 1 15 0 0 4 1 0 3 3 5 2 6 6 6 Demand for product A is 40 units/day, demand for product B is 50 units/day and demand for product C is 60 units/day. What is the bottleneck? What is the flow rate for each unit assuming that demand must be served in the mix described above (i.e. for every 4 units of A there are 5 units of B and 6 units of C)? Inventory Buildup Q4. The Western Pennsylvania Milk Company is producing milk at a fixed rate of 5,000 gallons/hour. The company's clients request 100,000 gallons of milk over the course of one day. This demand is spread uniformly from 8am to 6pm. If there is no milk available, clients will wait until enough is produced to satisfy their requests. The company starts producing at 8am with 25,000 gallons in finished goods inventory. At the end of the day, after all demand has been fulfilled, the plant keeps on producing until the finished goods inventory has been restored to 25,000 gallons. (NOTE: For the following questions, treat trucks/milk as a continuous flow process. Begin by drawing a graph indicating how much milk is in inventory and how much milk is "back-ordered" over the course of the day.) a. b. C. d. At what time during the day will the clients have to start waiting for their requests to be filled? At what time will clients stop waiting? Assume that the milk is picked up in trucks that hold 1,250 gallons each. What is the maximum number of trucks that are waiting? Assume the plant is charged $50/hour per waiting truck. What are the total waiting time charges on a day? Little's Law Q5. The total number and gender mix of employees in a certain company remains constant. Due to turnover, on average the company hires 150 men and 200 women each year. It is estimated that on average a woman stays 50% longer than a man. What proportion of the employees are women? Q6. The Internal Revenue Service Department of Tax Regulations writes regulations in accord with laws passed by Congress. On average, the department completes 300 projects per year. The Wall Street Journal reports that, as of October 11, 1997, the number of projects currently "on the Department's plate" is 588. Nevertheless, the department head claims that average time to complete a project is under six months. Do you have any reason to disagree? Why or why not? Q7. Checking accounts at a local bank carry an average balance of $3,000. The bank turns over its balance six times a year. On average, how many dollars flow through the bank each month?