a. How many possible solutions are there to this problem?

b. Design a spreadsheet model for this problem. How many pieces of stock would have to be cut to produce the windows in this half-hour of production if Wella processes the windows and parts in the order given (in WellaData.xls)? How much scrap is generated by this solution?

c. Use Solver to optimize the problem. How many pieces of stock would have to be cut to produce the windows in this half-hour of production if Wella processes the windows and parts in the order Solver identifies? How much scrap is generated by this solution?

d. Assume that Wella pays $4 for each 16-foot piece of stock. If the results identified in the previous question are representative of the results that could be obtained on all of Wella’s production lines, how much money could Wella save over the course of a year?

e. What other suggestions/issues (if any) do you think Wella should consider before implementing your solution on their factory floor?

Wella Corporation is a privately held manufacturer of doors and windows with annual sales in excess of $900 million. Some of the company’s products are “standard size” and sold through wholesale and retail building material centers. However, much of their business involves manufacturing custom windows that can vary in size from 12 inches to 84 inches in quarter-inch increments.

The company has two plants, in Iowa and Pennsylvania. Each plant has five production lines devoted to custom window manufacturing. Each of these production lines operates eight hours a day, five days a week and produces 50 windows per hour.

Sash and frame parts for the windows are cut from standard size “stock” pieces of lumber 16 feet in length. These stock pieces are purchased from a supplier who takes various pieces of lumber of various lengths, cuts out the defects (knotholes, cracks, etc.) and finger-joins the pieces together to create the 16-foot stock pieces that are basically free of defects.

Wella cuts all the sash and frame parts for a particular window and then immediately passes that set of parts to the next operation in the production process for further assembly (i.e., it does not carry inventories of parts of various length). However, the parts for any particular window may be cut in any order.

The demand for custom windows varies such that no two days (or even hours) of production are ever the same. Currently, line workers take a 16-foot piece of stock and start cutting parts for a window in the same order as they are listed on the bill of materials (BOM) until the remaining piece of stock is too short to cut the next required part.

As a simplified example, suppose the first window being produced has a BOM listing two 3-foot parts and two 4-foot parts (in that order). (Most of Wella’s windows actually require 8 or 9 parts.) Those parts might be cut from a 16-foot stock piece and leave a 2-foot piece of scrap.

Now suppose that the next window has a BOM that requires two 3-foot pieces and two 1-foot pieces (in that order). Because the 3-foot pieces can’t be cut from the 2-foot scrap leftover from the first piece of stock, Wella would start cutting a new piece of stock. It seems to make more sense to use the 2-foot piece of scrap from the first piece of stock to cut the two 1-foot pieces required by the second window. However, reordering the pieces for the second window to eliminate the 2-foot piece of scrap could lead to the creation of a 3-foot piece of scrap later in the production process. (Any pieces of “scrap” at the end of one stock piece that cannot be used in the next job are scrapped, as moving these scrap pieces into and out of inventory becomes a logistical nightmare.)

Being able to “look ahead” to see the downstream impacts of reordering decisions is beyond the capability of most humans—especially when this must be repeated on an ongoing basis. As a result, Wella wants to develop a system to optimize the production on each line on an hour-by-hour basis.

The file WellaData.xls contains data for a half-hour of production on one of Wella’s lines. (This line produces windows that require 8 sash/frame parts per window.) Assume Wella wants to produce the windows in the order indicated, but the parts for each window can be produced in any order. Wella wants to determine the optimal partcutting sequence that would allow them to minimize the amount of scrap (and the number of stock pieces required to fill all the orders).