Homework

Homework 1

1. Compute the capacity in parts per hour of the following:

a) A station with three machines operating in parallel with 20‐minute process times at each station.

b) A balanced line with single –machine stations, all with average processing times of 15 minutes.

c) A four‐station line with single‐machine stations, where the average processing times are 15, 20, 10, 12 minutes, respectively for stations 1, 2, 3, 4.

d) A four‐station line with multiple‐machine stations, where the number of (parallel) machines at stations 1, 2, 3, 4 is 2, 6, 10, 3 respectively. The average processing times at the stations are 10, 24, 40, 18 minutes, respectively.

e) A three‐station line with ample equipment at all stations (i.e. don’t worry about machines—you only need to make calculations for the labor) staffed by six operators who are identical with regard to average processing times and require 10, 15, 5 minutes, respectively on stations 1, 2, 3.

f) The same line as in part e), except that station 2 now consists of only two parallel machines. Stations 1 and 3 still have ample capacity.

2. Is it possible for a line to have the same throughput with both high WIP and high cycle time or low WIP and low cycle time? Which would you rather have? Why?

3. Consider the following three‐station line with multi‐machine stations, where the number of machines at stations 1, 2, and 3 is 5, 12, and 1 respectively; the average processing times are 15, 30, and 3 minutes, respectively.

a) Find rb, T0, and W0 for this line.

b) Suppose WIP = 20. Compute TH in the Best, MEP, and Worst Cases.

4. Positively Rivet Inc. is a small machine shop that produces sheet metal products. It had one line dedicated to the making of light‐duty vent hood shells, but because of strong demand it recently added a second line. The new line makes use of higher‐capacity automated equipment and is all single‐machine workstations, but consists of the same basic four processes as the old line. See table.

Over the past three months, the old line has averaged 315 parts per 8 hour shift with an average WIP level of 400 parts. The new line has averaged 680 parts per 8 hour shift with an average WIP level of 350 parts. Management is dissatisfied with the old line because it is achieving a lower throughput rate with a higher WIP level compared to the new line. Is this thinking correct? Your job is to evaluate both lines relative to their potential.

a) Find rb, T0, and W0 for both lines. Why do you think the old line has larger Critical WIP?

b) Compare the performance of each line to its respective MEP performance. Is management correct in criticizing the old line for its inefficiency?

c) If you were the manager and needed more throughput, what would you consider first to get more throughput (answer the question separately for each line). (Short answers)