ISyE 6201: Manufacturing Systems Instructor : Spyros Reveliotis Fall 2006 Solutions for Homework #3
C. Four-station assembly line case study
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C. Four-station assembly line case study: To identify good candidates for consideration, we first look at the performances and prices of each option. We can rule out some options from further consideration since they are dominated by some other candidate(s). For instance, among the options for station 1, option 3 is obviously slower than option 1 and option 2 and it operates with high variance and with a much higher cost. A similar situation arises at station 4, where option 2 can be eliminated. Next, we attempt to find a good configuration that meets the demand and performance requirements while minimizing the deployment cost. The easiest way to solve this problem is to build a spreadsheet. The tricky parts are converting rate in piece/hour to batch process times and computing the SCV (squared coefficient of variation) for the batch processing. Let: b = batch size te = effective processing time for one piece ts = time to perform a setup (to be taken equal to 0 in our case) tb = effective processing time for a batch Ce2 = SCV for the processing time for a piece Cb2 = SCV for the processing time for a batch ra = arrival rate (equals to throughput, TH, in our case) We compute the mean effective processing time for a batch as: tb = b * te + ts = b * te = 50 * (1/ speed) e.g., for option 1 of station 1, tb = 50 / 42 = 1.19 hr/batch Similarly, the fact that the batch processing time is the sum of the processing times of the b pieces in the batch, which are identically distributed, implies that b2 = b * e2. Since C2 = t2, we have that Cb2 = b2 / tb2 = (b * e2) / (b * te)2 = Ce2/ b e.g., for option 1 of station 1, Ce2 = (2.0)2 / 50 = 0.08 We get the arrival rate in batches per hour as (assume that there are 8 working hrs/day): ra = (1000 prt/day) / (50 prt/batch)(8 hr/day) = 2.5 batches / hour We can now start our calculation as follows: Min. machines required = ra * tb Actual machine required, m = roundup (ra * tb) Utilization, u = ra * tb / m Average time in queue, 
Total waiting time at the station, 
Since the SCV for inter-departure time, Cd2 , of previous station is the SCV for the arrivals, Ca2, to the next station. The linking equation for multiple machine station is 
We must also determine the SCV Directory: ~spyros -> courses courses -> Production & Capacity Planning at McGuinness & Co. Microbrewery courses -> ISyE 3104: Introduction to Supply Chain Modeling: Manufacturing and Warehousing Instructor: Spyros Reveliotis Summer 2002 Homework #4 Due Date: Monday, 7/1/02 Problem set courses -> ISyE 3104: Introduction to Supply Chain Modeling: Manufacturing and Warehousing Instructor : Spyros Reveliotis Spring 2006 Solutions for Homework #3 Problem set Download 324.14 Kb. Share with your friends:
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