OPIM101 - Spring 2012 - R2 exercise - solutions

OPIM101 - Spring 2012 - R2 exercise - solutions - OPIM 101...

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Unformatted text preview: OPIM 101 - Spring 2012 Recitation 2 Exercise - Solutions Section # (201,202,…,214): _____________ Instructor (circle): Balas Fishman Horowitz Saunders Shah Zhang PennCard Last Name: PennCard First Name: PennID: Place your answers in the boxes provided. Espress IM Some enterprising students decided to open "EspressOPIM". Although there are grand plans for expansion, the plan is to start small with a single product, espresso. As the business grows, the revenue generated from espresso will provide funds for expanding the product line. The espresso operation is very simple and only takes two employees: A cashier to take orders and a person to operate the espresso machine. There is only one drink, espresso, and there is only one way to make it – the EspressOPIM way. Having taken OPIM, our entrepreneurs have carefully timed this two‐step process: Step 1, taking orders and operating the cash register, takes 30 seconds per customer. Step 2, making the espresso and pouring the drinks takes 1 minute and 10 seconds. To promote fairness in the face of the tremendous demand forecast for EspressOPIM, customers may only order one beverage for each turn that they wait in line (queue). The expected demand is 50 customers per hour. Q1 What is the implied utilization of the cashier (as a %)? (%) 41.67 A cashier can process a customer in 30 seconds. In 1 hour, which is 3600 seconds, a cashier can process 3600/30 = 120 customers. If the cashier can process 120 customers/hour, and demand is 50 customers/hour, then implied utilization of the cashier is 50/120=41.67%. Q2 Assume that there is a line of 9 customers waiting when the store opens at 7AM. From the time that the store opens, how many minutes after that will the 15th customer of the morning get his/her EspressOPIM? (e.g. to have the drink in their hand, not to get to the front of the line) (minutes) The question is actually potentially much trickier than it appears. 18 The short way to calculate this is to assume that the process is supply constrained, i.e., the drink maker (barista) always has work. The first customer takes 100 seconds (30 cashier + 70 barista) and the subsequent 14 customers take 70 seconds each. The barista making the drink is the bottleneck step, which constrains the process. This adds up to 1,080 seconds, or 18 minutes. However, we can check whether our initial assumption is correct – that the process is supply constrained and that the barista is continuously checking out drinks for the first 15 people starting at 7am. To complete the processing of the initial 9 customers requires 100+ 8*70 = 660 seconds. So the 9th customer is finished at 7:11am. The 15th customer is the 6th customer to arrive after the 9th. Those new customers arrive every 3600/50=72 seconds, so the 6th new customer arrives after 432 seconds, or at 7:07:12am exactly. Hence, by the time the 15th customer arrives, the process hasn’t even finished with the initial 9. So the 15th customer finds a queue and waits for service. Hence, our assumption that the process is supply constrained is correct. Q3 How many customers per hour will EspressOPIM serve on average? (Assume their demand rate is 50 customers per hour even though in Q2 they had 9 customers waiting at 7AM.) (customers/hr) 50 Average hourly capacity: 3600sec / 70sec=51.4 customers > hourly demand 50 customers The process is demand constrained, so only 50 customers can be served per hour. Q4 EspressOPIM is concerned with how many customers they can serve per hour. They will add two employees and two espresso machines. With this plan, one employee will be dedicated to the cash register and three will make drinks. Those new employees also take 1 minute and 10 seconds to complete a drink order. What is the maximum number of customers per hour EspressOPIM could serve with this plan? (customers/hr) We re‐examine the process capacity of EspressOPIM. 120 The cashier, as in question Q1, can process 120 customers/hour. With three baristas and three machines, on average, the capacity to make drinks has tripled. They can serve 3600/70 * 3=154.3 customers/hour The bottleneck of the process is now the cashier, which processes customers at 120/hour. (However – that doesn’t mean they are actually serving that many – if demand is 50 customers/hour then they are still serving 50 customers/hour.) Q5 A process has three tasks that are performed in sequence. The activity times for the three tasks are 50 minutes, 55 minutes and 60 minutes. Company A assigns one person to each task. Company B has three employees that are capable of doing all of the tasks. Furthermore, they are able to complete each task in the same amount of time as the employees at Company A. What is the ratio of A’s maximum flow rate to B’s maximum flow rate? Company A’s maximum flow rate is simple to calculate. The bottleneck activity is the one that takes 60 minutes to complete. So, per hour, exactly 1 process can be completed. Company B, however, is at a great advantage. For example, workers 1, 2 and 3 could work on 3 separate processes, from beginning to end (50, 55, 60) in parallel! For one worker, it takes 50+55+60=165 minutes from beginning to end to finish an entire process. Three workers finish a total of three processes at the end of 165 minutes, which means they average 165/3 minutes per process. This translates to or 60/(165/3) = 1.091 per hour. Company A’s maximum flow rate is (165/3)/60=165/180=0.917 times as fast as Company B’s maximum flow rate. 165/180 or 0.917 Consider the following process that involves three types of jobs (A, B and C) and two tasks (1 and 2): For example, type A jobs are processed by tasks 1, but not by 2. Inventory is allowed before each task, but triangles are not included to simplify the presentation of the process. Additional data regarding the process is provided in the tables. For example Task 1 has 6 workers and task 2 has 4 workers. Q6. What is the implied utilization of task 1 (as a %)? (%) 75% Q7. What is the implied utilization of task 2 (as a %)? (%) 100% Start with the capacity of the resource. We will use minutes of capacity per work‐hour. Resource Number of Workers Task 1 6 Task 2 4 Minutes of capacity per work‐hour 6 x 60 = 360 4 x 60 = 240 Now create a demand table for each of the three types of jobs, A, B, and C Resource Workload for A Workload for B Workload for C 10 jobs/work‐hour * 15 * 10 = 150 30 * 0 = 0 Task 1 Task 2 12 min/job = 120 min/work‐hour 10 * 0 = 0 15 * 4 = 60 30 * 6 = 180 Total Workload 120+ 150 = 270 min/work‐hour 0 + 60 + 180 = 240 min/work‐hour To get implied utilization, we divide workload by available capacity. Thus, the implied utilization of Task 1 is 270/360 = 75%. The implied utilization of Task 2 is 240/240 = 100% ...
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This note was uploaded on 04/04/2012 for the course OPIM 101 taught by Professor Lee during the Spring '08 term at UPenn.

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