Station 2 Has 11 Identical Machines with Average Processing Times of 30 Minutes Per Job

HW3

OSCM 424

Due Thursday, Feb. March 9 by 5:00

1. Consider the following three-station production line with a single product that must visit the stations in sequence.

Station 1 has four identical machines with average processing times of 15 minutes per job

Station 2 has 11 identical machines with average processing times of 30 minutes per job.

Station 3 has 5 machines with average processing time of 3 minutes per job

The line currently has a cycle time of 7 hours and work in process inventory averages 100 jobs.

a.) Compare present performance to the Best Case, Worst Case, and Practical Worst case. Is there room for improvement?

Station rates (jobs/minute)

Station 1 rate: 4/15 = .267

Station 2 rate: 11/30 = .367

Station 3 rate: 5/3 = 1.67

rb = .267 , To = 15 + 30 + 3 = 48, Wo = rbTo = 48(.267) = 12.8

Note: Current WIP much higher than critical WIP. This is to be expected since we have parallel machine stations.

Performance of the current line:

CT = 420 minutes

WIP (w) = 100 jobs

TH = 100/420 = .2381 (Little’s Law)

Internal Benchmarks

Cycle Time:

CTbest = w/rb = 100/.2667 = 375

CTworst = wTo = 100(48) = 4800

CTPWC = To + (w-1)/rb = 48 + 99/.267 = 419.25

Interpretation: Current cycle time is at the practical worst case

Throughput:

THbest = rb = .267

THworst = 1/To = 1/48 = .02

THPWC = wrb/(Wo -1 + w) = 100(.267)/(12.8-1+100) = .2388

Interpretation: Current throughput is at the practical worst case

Also, since TH and CT are at PWC we know that WIP is at PWC from Little’s Law.

Conclusion: There is some room for improvement since: 1) we are right at the practical worst case and 2) we expect unbalanced lines with parallel machines to perform better than the balanced, single machine station line we used to derive the practical worst case (and other benchmarks).

2. Create a spreadsheet to model a serial production line with 5 stations. The inputs will be the mean and standard deviation of arrival time, processing time, time to failure, and time to repair. The number of machines at each station is input as well. Since we want the flexibility to model multi machine stations, you must use the equations for the multi machine case throughout. I have posted a sheet (without the formulas) that you can use to check your answers.

Once your spreadsheet has been created use it to verify the principles of variability propagation outlined in the Power Point Slides.