Wyndor Glass Co. Research Paper

18 Chapter Two Linear Programming Basic Concepts 2. 1 A grimace STUDY THE WYNDOR GLASS CO. PRODUCT-MIX PROBLEM Jim baker is excited. The assembly he heads has sincerely hit the jackpot this age. They have had just about not up to(p) successes in the past, that he feels that this one impart be really picky. He infract the sack hardly wait for the reaction after his memorandum reaches top forethought. Jim has had an magnificent track record during his seven years as manager of revolutionary output bourgeonment for the Wyndor crank Company.Although the company is a small one, it has been experiencing extensive growth largely because of the innovative sensitive products real by Jims group. Wyndors professorship, magic Hill, has often ack at a timeledged publicly the key component part that Jim has played in the recent success of the company. Therefore, John felt grand confidence six months ago in asking Jims group to develop the following youthful products An 8- foot glass door with aluminum framing. A 4-foot 6-foot double-hung, wood-framed window.Although several otherwise companies already had products meeting these specifications, John felt that Jim would be able to work his usual magic in introducing exciting new device characteristics that would establish new industry standards. Now, Jim grasst remove the grin from his face. They have done it. Background The Wyndor Glass Co. produces high- timber glass products, including windows and glass doors that feature handcrafting and the finest workmanship. Although the products atomic number 18 expensive, they fill a market niche by providing the highest quality accessible in the industry for the most discriminating buyers. The company has 3 plants. go down 1 produces aluminum frames and hardware. build 2 produces wood frames. Plant 3 produces the glass and assembles the windows and doors. Because of declining sales for certain products, top counsel has decided to regenerate the com panys product line. Un economic products are be discontinued, evacuant merchandise capacity to launch the twain new products developed by Jim bakers group if management approves their release. The 8-foot glass door requires almost of the doing capacity in Plants 1 and 3, but not Plant 2. The 4-foot 6-foot double-hung window necessitate only Plants 2 and 3. counselling now enquires to address deuce come forwards 1.Should the company go ahead with launching these two new products? 2. If so, what should be the product mixthe number of units of each produced per work workweek for the two new products? Managements Discussion of the Issues Having received Jim Bakers 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 step Tasto, vice president for manufacturing, and Ann Lester, vice president for marketing. lets eavesdrop on the meeting. John Hill (president) Bill, we forget inadequacy to rev up to start production of these products as soon as we can.About how practically production output do you think we can touch? Bill Tasto (vice president for manufacturing) We do have a little useable 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 complex products requiring careful crafting. And, as I said, we dont have a lot production capacity procurable. An Application Vignette Swift &038 Company is a diversified protein-producing business based in Greeley, Colorado.With annual sales of all e genuinelywhere $8 billion, beef and related products are by far the largest dower of the companys business. To improve the companys sales and manufacturing performance, swiftness management concluded that it compulsory to achieve three major objectives. adept was to enable the companys customer service representatives to talk to their more(prenominal) than 8,000 customers with accurate information about the availability of current and future history while turning requested delivery discovers and maximum product age upon delivery. A second was to produce an efficient shift-level schedule for each plant over a 28-day horizon.A third was to accurately determine whether a plant can ship a requested order-line-item quantity on the requested date and time given the availability of cattle and constraints on the plants capacity. To meet these three challenges, a management science team developed an integrated system of 45 linear programming examples based on three model formulations to dynamically schedule its beef-fabrication operations at quint plants in real time as it receives orders. The total audited benefits realized in the first year of operation of this system were $12. 74 one thousand million, including $12 million due to optimizing the product mix.Other benefits include a reduction in orders lost, a reduction in price discounting, and better on-time delivery. Source A. Bixby, B. Downs, and M. Self, A scheduling and Capable-to-Promise Application for Swift &038 Company, Interfaces 36, no. 1 (JanuaryFebruary 2006), pp. 6986. The issue is to arise the most payable mix of the two new products. John Ann, depart we be able to sell several of each per week? Ann Lester (vice president for marketing) Easily. John OK, considerably. I would like to set the launch date for these products in six weeks. Bill and Ann, is that feasible? Bill Yes.Ann Well have to scramble to give these products a proper marketing launch that soon. But we can do it. John Good. Now theres one more issue to re drub. With this limited production capacity, we need to decide how to split it between the two products. Do we want to produce the same number of both products? Or mostly one of them? Or even just produce as untold as we can of one and postpone launching t he other one for a little while? Jim Baker (manager of new product development) It would be dangerous to hold one of the products back and give our opposition a chance to scoop us. Ann I agree.Furthermore, launching them together has some advantages from a marketing standpoint. Since they share a lot of the same special features, we can combine the advertising for the two products. This is going to make a big splash. John OK. But which mixture of the two products is going to be most profitable for the company? Bill I have a suggestion. John Whats that? Bill A couple times in the past, our Management Science sort has helped us with these same kinds of product-mix decisions, and theyve done a good job. They ferret out all the relevant data and so dig into some detailed analysis of the issue.Ive found their input very helpful. And this is right down their alley. John Yes, youre right. Thats a good idea. Lets get our Management Science concourse operative on this issue. Bill, will you coordinate with them? The meeting ends. The Management Science Group Begins Its Work At the outset, the Management Science Group spends considerable time with Bill Tasto to clarify the general problem and specific issues that management wants addressed. A particular concern is to ascertain the appropriate objective for the problem from managements viewpoint.Bill points out that John Hill posed the issue as determining which mixture of the two products is going to be most profitable for the company. 19 20 Chapter Two Linear Programming Basic Concepts Therefore, with Bills concurrence, the group fructifys the key issue to be addressed as follows. Question Which combination of production rates (the number of units produced per week) for the two new products would maximize the total profit from both of them? The group also concludes that it should consider all possible combinations of production rates of both new products permitted by the available production capacities in the thre e plants.For example, one alternative (despite Jim Bakers and Ann Lesters objections) is to forgo producing one of the products for now (thereby setting its production rate equal to zero) in order to produce as much as possible of the other product. (We must not neglect the opening that maximum profit from both products might be attained by producing none of one and as much as possible of the other. ) The Management Science Group neighboring identifies the information it needs to gather to tolerate this study 1. Available production capacity in each of the plants. 2.How much of the production capacity in each plant would be call for by each product. 3. Profitability of each product. Concrete data are not available for any of these quantities, so estimates have to be made. Estimating these quantities requires enlist the help of key personnel in other units of the company. Bill Tastos staff develops the estimates that involve production capacities. Specifically, the staff estimate s that the production facilities in Plant 1 indispensable for the new kind of doors will be available approximately four mos per week. (The rest of the time Plant 1 will continue with current products. The production facilities in Plant 2 will be available for the new kind of windows about 12 mos per week. The facilities needed for both products in Plant 3 will be available approximately 18 hours per week. The amount of each plants production capacity actually used by each product depends on its production rate. It is estimated that each door will require one hour of production time in Plant 1 and three hours in Plant 3. For each window, about two hours will be needed in Plant 2 and two hours in Plant 3. By analyzing the cost data and the pricing decision, the Accounting Department estimates the profit from the two products.The projection is that the profit per unit will be $300 for the doors and $ five hundred for the windows. Table 2. 1 summarizes the data now gathered. The Man agement Science Group recognizes this as being a classic product-mix problem. Therefore, the next step is to develop a mathematical modelthat is, a linear programming modelto represent the problem so that it can be solved mathematically. The next four sections focus on how to develop this model and then how to solve it to find the most profitable mix between the two products, assume the estimates in Table 2. 1 are accurate.Review Questions 1. 2. 3. 4. 5. What is the market niche being filled by the Wyndor Glass Co.? What were the two issues addressed by management? The Management Science Group was asked to help analyze which of these issues? How did this group define the key issue to be addressed? What information did the group need to gather to conduct its study? TABLE 2. 1 Data for the Wyndor Glass Co. Product-Mix Problem Plant 1 2 3 Unit profit Production Time Used for Each Unit Produced Doors 1 hour 0 3 hours $300 Windows 0 2 hours 2 hours $ d Available per Week 4 hours 12 hour s 18 hours