Lab 6

Faculty Notes

The Big Chill Refrigerator Factory

Most of the work in this lab requires the students to organize and schedule. The mathematics involved requires working with scale drawings and using the distance-equation, distance = rate * time. This lab provides a setting where there is no clear-cut solution or unique answer. The solution to this problem involves addition, subtraction, multiplication, division, manipulation of the distance formula, as well as creating timing diagrams.

If you are concerned that solutions will be passed from one class to another, this lab can be readily adapted for use in multiple sections by changing the line speed, shape of the assembly line, or the layout of the plant. The basic problem is the same, but these changes result in different solutions.

Much of the computation can be simplified by the using the LIST function on a TI-82™ or TI-83™. However, the calculator solution described below will yield results that need to be adjusted to account for the fact that the outside ends of the stations at the ends of the lines have no buffer space. Thus, when you use the list-based solution that follows, remember to adjust the results to get the correct answers. When computing the total distance required for each station, have the students enter the time required in L1. This is done by first pressing STAT, then pressing 1, EDIT. If the list already contains data, it can be cleared by pressing the up arrow until L1 is highlighted. Then press CLEAR and ENTER. Next, have the students enter the times in L1. Be sure to press ENTER after each time is entered. To get the total distance required, you will want to multiply each of these times by 6 and then add 10 if working on the door, or 20 if working on the refrigerator. This can all be done with one set of entries. Move the cursor so L2 is now highlighted. While the cursor is on L2 press L1*6+20 then press ENTER. The "L1" is the yellow keystroke on the number 1 on the keypad. When ENTER is pressed, this set of operations will be performed on all of the data in L1. These times can then be entered in Table 2. If a TI-82™ or TI-83™ is not available, a spreadsheet can be used in a similar fashion.

When laying out the routes for FTOs to follow for delivering parts, be sure to have the students draw the routes, perhaps color-coded, on a scale drawing of the plant. They may want to layout the FTO routes on an enlarged copy of the plant drawing.

When discussing the number of bins required, some students will want to round down the required number of bins if the number is something like 3.2. This will not work. If only 3 bins are delivered, that station will be short part of a bin required to complete the work for the day. This station requires 4 bins per day. When four bins are delivered each day to this station a build up of parts will occur. At some point the delivery schedule will need to be modified to accommodate this build up. This was not addressed in this lab. Including this in the scheduling can be done if a more sophisticated solution is desired.

As you read through the students' solutions, be careful to note the number of parts at each workstation before an FTO goes on break. If the number of parts is inadequate to cover the 15-minute break, the line will stop. This is not good! It may be that while one FTO is on break a second FTO will need to deliver a bin of parts on the first person's route. Be sure to have students mention things like this in their model portfolios. These fine points in scheduling can be difficult to spot.

As part of the students' research, it would be beneficial if they could tour at least one plant in your area that uses an assembly line. When arranging a tour, be sure to follow all of your college's policies and procedures.

You may have students generate a glossary of terms used in the model portfolio. In addition to the terminology specific to this particular lab (FTOs, FSL, DAL, etc.), they may include other terms such as rectilinear distance.

Spinoffs

There are numerous modifications that can be made to expand this problem according to the amount of time available. Some are listed below.

1. What specific changes could be made to reduce the number of FTOs required? Is this reasonable in this industrial setting?
2. In warehouses it is possible for an FTO to carry two or even three bins at a time. While there is some additional time required to stack and unstack the additional bins (about 15 seconds per bin to stack or unstack), overall time can be saved in some cases by scheduling an FTO to carry multiple bins. Students may examine if this makes a significant change in the number of FTOs required.
3. The company is going to build a new plant.
   1. Give each group a different floor plan and have them design the layout to achieve the same production rate as this problem with the same or fewer FTOs.
   2. Have each group develop its own original floor plan that will allow for the same rate of production and minimize the number of FTOs required.
4. The students are starting a new company. Have them choose the product, determine the parts and assembly time, design the layout of the plant, and schedule the FTOs. To help in choosing a product in which students could determine the parts required and how long it takes to assemble the product, have them actually make a product. It may be as simple as assembling video tapes (put label on box, insert tape, insert advertisement, seal tape, box in sets of 12) or actually constructing a model. Students could use a product like LEGOs® or another building material to make a structure of some kind.