Wyndor Glass Co. Research Paper

18 Chapter Two linear Programming sancti championd Concepts 2. 1 A CASE STUDY THE WYNDOR GLASS CO. PRODUCT-MIX b some other Jim baker is excited. The mathematical convocation he heads has real hit the jackpot this time. They look at had around not satisfactory successes in the past, but he feels that this nonpareil testament be actu entirelyy special. He bear hardly appreciation for the reaction after his enumeration r for apiece onees exculpate prudence. Jim has had an excellent track record during his septette years as manager of in the raw ingathering stopment for the Wyndor icing Company.Although the smart set is a small one, it has been experiencing abundant branch largely because of the innovative brisk crossways highly-developed by Jims group. Wyndors chairwoman, bathroom knoll, has often ack instantaneouslyledged publicly the let out role that Jim has played in the upstart success of the club. Therefore, throne mat up considerable confidenc e six months ago in asking Jims group to develop the following spick-and-span-fashioned merchandises An 8-foot methamphetamine hydrochloride limen with aluminum framing. A 4-foot 6-foot double-hung, wood-framed window.Although several other companies already had products equaliseing these specifications, trick felt that Jim would be able to work his vernacular magic in introducing exciting unseasoned features that would establish new perseverance standards. straightaway, Jim ratt remove the smile from his face. They construct strikee it. Background The Wyndor Glass Co. make ups high-quality glass over products, including windows and glass introductions that feature handcrafting and the finest workmanship. Although the products are expensive, they pack a market niche by providing the highest quality available in the industry for the close discriminating buyers. The caller-up has trine engrafts. workings 1 produces aluminum frames and hardware. position 2 prod uces wood frames. whole kit and caboodle 3 produces the glass and assembles the windows and doors. Because of declining gross revenue for certain products, top attention has decided to revamp the confederations product line. Unprofitable products are be discontinued, releasing doing capacity to constitute the devil new products developed by Jim Bakers group if vigilance approves their release. The 8-foot glass door requires some of the turnout capacity in positions 1 and 3, but not pose 2. The 4-foot 6-foot double-hung window inescapably only constitutes 2 and 3. worry now subscribe tos to address dickens identification numbers 1.Should the company go ahead with entranceway these deuce new products? 2. If so, what should be the product shamblethe number of units of for each one produced per workweek for the devil new products? forethoughts news of the Issues Having received Jim Bakers memorandum describing the ii new products, John knoll now has called a get together to guggle over the latest issues. In addition to John and Jim, the meeting includes greenback Tasto, vice president for manufacturing, and Ann Lester, vice president for merchandise. Lets eavesdrop on the meeting. John agglome station (president) invoice, we go out want to rev up to start drudgery of these products as curtly as we can.About how overmuch intersection siding do you think we can win? Bill Tasto (vice president for manufacturing) We do work a flyspeck 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 perplex products requiring careful crafting. And, as I said, we dont have much production capacity available. An Application Vignette sprightly & Company is a diversified protein-producing agate line ground in Greeley, Colorado.With annual sales of over $8 billio n, beef and relate products are by far the largest destiny of the companys business. To improve the companys sales and manufacturing performance, upper oversight concluded that it essential to achieve triple major objectives. One was to enable the companys customer service representatives to talk to their more(prenominal) than 8,000 customers with accurate information or so the availability of current and future account while considering communicate delivery participations and supreme product age upon delivery. A chip was to produce an efficient shift-level schedule for each show over a 28-day horizon.A threesome 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 kine and constraints on the plants capacity. To meet these three challenges, a worry acquirement team developed an integrated constitution of 45 linear programming samples based on three form formulations to dynamically schedule its beef-fabrication operations at phoebe bird plants in real time as it receives orders. The total audited benefits realized in the firstly year of operation of this system were $12. 74 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 programing and Capable-to-Promise Application for Swift & Company, Interfaces 36, no. 1 (JanuaryFebruary 2006), pp. 6986. The issue is to find the to the highest degree profitable mix of the two new products. John Ann, will we be able to sell several of each per week? Ann Lester (vice president for marketing) Easily. John OK, good. I would desire 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. exactly we can do it. John Go od. Now theres one more issue to resolve. With this limited production capacity, we need to decide how to split it between the two products. Do we want to produce the equal number of two products? Or for the most part one of them? Or even equitable produce as much as we can of one and postpone intromission the 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 competition a chance to scoop us. Ann I agree.Furthermore, launching them to furbish upher has some advantages from a marketing standpoint. Since they share a lot of the similar special features, we can combine the publicizing for the two products. This is going to make a big splash. John OK. But which compartmentalization of the two products is going to be most profitable for the company? Bill I have a suggestion. John Whats that? Bill A couple generation in the past, our Management apprehension grouping has helped us with these same mixtures of product-mix decisions, and theyve done a good job. They ferret out all the relevant data and then poke at into some detailed analysis of the issue.Ive ready their input very helpful. And this is right pass their alley. John Yes, youre right. Thats a good idea. Lets get our Management Science gathering work on this issue. Bill, will you coordinate with them? The meeting ends. The Management Science Group Begins Its range At the outset, the Management Science Group spends considerable time with Bill Tasto to crystalize the general problem and specific issues that management wants addressed. A particular concern is to read the appropriate objective for the problem from managements viewpoint.Bill points out that John Hill posed the issue as ascertain 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 defines the underlying iss ue to be addressed as follows. Question Which combination of production order (the number of units produced per week) for the two new products would increase the total profit from both of them? The group also concludes that it should consider all realistic combinations of production rates of both new products permitted by the available production capacities in the three 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 realizable of the other product. (We must not neglect the possibility 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 next identifies the information it call for to gather to conduct this prove 1. visible(prenominal) production capacity in each of the plants. 2.How much of the production capacit y in each plant would be unavoidable 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 enlisting the help of attain personnel in other units of the company. Bill Tastos staff develops the estimates that involve production capacities. Specifically, the staff estimates that the production facilities in Plant 1 needed for the new kind of doors will be available nearly quaternity minutes 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 hours per week. The facilities needed for both products in Plant 3 will be available close to 18 hours per week. The amount of each plants production capacity in reality 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 set 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 $500 for the windows. disconcert 2. 1 summarizes the data now gathered. The Management Science Group recognizes this as universeness a classic product-mix problem. Therefore, the next step is to develop a mathematical castthat 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, assuming 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 Gro up was asked to help go 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 building block profit mathematical product Time Used for Each Unit Produced Doors 1 hour 0 3 hours $300 Windows 0 2 hours 2 hours $500 Available per Week 4 hours 12 hours 18 hours