Written Assignment 3: Line Balancing

Be sure you have read the material on designing product layouts (Chapter 6) before you begin this assignment.

Background

Refer to the top of page 263. Suppose each station represents a worker-machine that does one step of a five-step operation to make a widget. The first workstation takes 0.1 minutes to complete the first step of the operation. The worker is employed for 8 hours, but one hour of productive time is lost for lunch and planned breaks during the day. Thus the worker is actually working for 7 hours or 420 minutes. Since an operation takes 0.1 minutes, the worker can do 4,200 operations in a day (420 minutes/0.1 minute per operation).

How many operations can the second workstation do in the course of the day? The third? The fourth? The fifth?

Since this is a sequential operation, where the input of any workstation is the output of the previous workstation, the output of the system is determined by the worker-machine with the lowest output. In this case, system output is constrained by the third worker-machine, whose output is only 420 per day. This is similar to the hiking speed of a group of Cub Scouts. The slowest-walking Cub Scout determines the speed of the group. If you want to speed up the group, then something has to be done to increase the hiking speed of the slowest Cub Scout, such as having someone else carry his knapsack.

Since system output is constrained by the third workstation, the first workstation is essentially 90 percent idle. It no longer matters how rapid the first workstation is and how many widgets it can produce, because the third workstation can only process 420 widgets per day.

Assignment Question

Suppose the system is required to produce 800 widgets per day. Rounding up as there can be no fractional worker-machines, you would have to have two worker-machines for the third workstation. As long as the outputs for the other workstations are above 800 per day, one worker-machine for each is adequate. If not, then another worker-machine has to be added.

How many worker-machines do you need for the other workstations?

How many worker-machines would you need if the system output has to be 1,200?