Chapter Two Linear Programming: Basic Concepts
2.1 A CASE STUDY: THE WYNDOR GLASS CO. PRODUCT-MIX PROBLEM
Jim Baker is excited. The group he heads has really hit the jackpot this time. They have had some notable successes in the past, but he feels that this one will be really special. He can hardly wait for the reaction after his memorandum reaches top management. Jim has had an excellent track record during his seven years as manager of new product development for the Wyndor Glass Company. Although the company is a small one, it has been experiencing considerable growth largely because of the innovative new products developed by Jim’s group. Wyndor’s president, John Hill, has often acknowledged publicly the key role that Jim has played in the recent success of the company. Therefore, John felt considerable confidence six months ago in asking Jim’s group to develop the following new products: • An 8-foot glass door with aluminum framing. • A 4-foot 6-foot double-hung, wood-framed window. Although several other companies already had products meeting these specifications, John felt that Jim would be able to work his usual magic in introducing exciting new features that would establish new industry standards. Now, Jim can’t remove the smile from his face. They have done it.
The Wyndor Glass Co. produces high-quality glass products, including windows and glass doors that feature handcrafting and the finest workmanship. Although the products are expensive, they fill a market niche by providing the highest quality available in the industry for the most discriminating buyers. The company has three plants. Plant 1 produces aluminum frames and hardware. Plant 2 produces wood frames. Plant 3 produces the glass and assembles the windows and doors. Because of declining sales for certain products, top management has decided to revamp the company’s product line. Unprofitable products are being discontinued, releasing production capacity to launch the two new products developed by Jim Baker’s group if management approves their release. The 8-foot glass door requires some of the production capacity in Plants 1 and 3, but not Plant 2. The 4-foot 6-foot double-hung window needs only Plants 2 and 3. Management now needs to address two issues: 1. Should the company go ahead with launching these two new products? 2. If so, what should be the product mix—the number of units of each produced per week— for the two new products?
Management’s Discussion of the Issues
Having received Jim Baker’s memorandum describing the two new products, John Hill now has called a meeting to discuss the current issues. In addition to John and Jim, the meeting includes Bill Tasto, vice president for manufacturing, and Ann Lester, vice president for marketing. Let’s eavesdrop on the meeting. John Hill (president): Bill, we will want to rev up to start production of these products as soon as we can. About how much production output do you think we can achieve? Bill Tasto (vice president for manufacturing): We do have a little available production capacity, because of the products we are discontinuing, but not a lot. We should be able to achieve a production rate of a few units per week for each of these two products. John: Is that all? Bill: Yes. These are complicated products requiring careful crafting. And, as I said, we don’t have much production capacity available.
An Application Vignette
Swift & Company is a diversified protein-producing business based in Greeley, Colorado. With annual sales of over $8 billion, beef and related products are by far the largest portion of the company’s business. To improve the company’s sales and manufacturing performance, upper management concluded that it needed to achieve three major objectives. One was to enable the company’s customer service representatives to talk to their more than 8,000 customers with accurate information about the availability of current and future inventory while...