#### Transcript OM3 C07 Solved Problems

Solved Problem An inspection station for assembling printers receives 40 printers/hour and has two inspectors, each of whom can inspect 30 printers per hour. What is the utilization of the inspectors? What service rate would be required to have a target utilization of 85 percent? Solution The labor utilization at this inspection station is calculated to be 40/(2 × 30) = 67%. If the utilization rate is 85%, we can calculate the target service rate by solving the equation: 85% = 40/(2 × SR) 1.7 × SR = 40 SR = 23.5 printers/hour Process Design and Resource Utilization • The average number of entities completed per unit time— the output rate—from a process is called throughput. – • Throughput might be measured as parts per day, transactions per minute, or customers per hour, depending on the context. A bottleneck is the work activity that effectively limits throughput of the entire process. – Identifying and breaking process bottlenecks is an important part of process design and improvement, and will increase the speed of the process, reduce waiting and work-in-process inventory, and use resources more efficiently. Little’s Law • Flow time, or cycle time, is the average time it takes to complete one cycle of a process. • Little’s Law is a simple formula that explains the relationship among flow time (T ), throughput (R ), and work-in-process (WIP ). Work-In-Process = Throughput × Flow Time or WIP = R × T [7.3] • If we know any two of the three variables, we can compute the third. Solved Problem Suppose that a voting facility processes an average of 50 people per hour and that, on average, it takes 10 minutes. What is the average number of voters in the process? for each person to complete the v Solution WIP = R T = 50 voters/hr (10 minutes/60 minutes per hour) = 8.33 voters Solved Problem Suppose that the loan department of a bank takes an average of 6 days (0.2 months) to process an application and that an internal audit found that about 100 applications are in various stages of processing at any one time. Using Little’s Law, we see that T = 0.2 and WIP = 100. What is the throughput? the v Solution R = WIP/T = 100 applications/0.2 months = 500 applications per month Solved Problem Suppose that a restaurant makes 400 pizzas per week, each of which uses one-half pound of dough, and that it typically maintains an inventory of 70 pounds of dough. In this case, R = 200 pounds per week of dough and WIP = 70 pounds. What is the average flow time? Solution T = WIP/R = 70/200 = 0.35 weeks, or about 21/2 days.