PLEASE REVIEW THE CASE EVALUATION INFORMATION AND CASE EVALUATION CRITERIA SECTIONS. A management (executive) summary is a summary of the written report. You should write the report first, and then prepare the management summary. For your case, three components should be included in the summary: (1) problem identification, (2) brief description of alternatives, and (3) specific recommendation. This summary lets the reader know what to expect in the report. Do not place formulations in the text of a report. Formulae, formulations, variables should appear in an appendix for the reader to review as needed. The report should be written in such a manner that a person without knowledge of the techniques and jargon could understand the general idea and recommendations. Remember that the objective function is not your problem statement. For example, in the sample case shown below, maximizing profits may be a consideration of management, and it may be one of the goals, but it is not the problem. The problem in the Lake Saddleback case is about determining the best allocation of the land among the various products and plans. They wanted to focus on the right mix while keeping in mind the goals, restrictions, and other concerns. Your alternatives should match your problem statement. For example, in the sample case one alternative could be to build the products under the plans originally described with all acreage being devoted to houses, greenbelts, parking, etc. A second alternative may be to add the sports complex which would reduce the total acreage for the houses, etc. Still a third alternative might involve reviewing the sensitivity analysis and concluding that 2 - 4 acres were not used, but could be allocated to the sports complex or additional housing. In an LP problem, you want to use the sensitivity analysis to help you think about additional alternatives. You have a great deal of leeway in developing your alternatives as long as you do not include something completely infeasible. In addition, you want to be sure that you point out the pros and cons of each alternative. The recommendation section should clearly justify why you are selecting a specific alternative. This is extremely important. The following case report is included for your examination. It is not an “A” case. One, it only included two alternatives. This report is an example from a student. The student followed most of the directions. I am hesitant to include any report as an example because you should develop your own ideas. However, it may help you think about the format and formulation information. Again, it is suggested that you review the case evaluation information and criteria provided under assignment information. Table of Contents I. Management Summary……………………………………………………3 II. Background Information…………………………………………………..4 III. Problem Statement……………………………………………………….…5 IV. Alternatives………………………………………………………………………5 V. Analysis of Alternatives…………………………………………………….5 VI. Detailed Recommendations……………………………………………..6 VII. Implementation………………………………………………………………..7 VIII. Appendices………………………………………………………………………8 I have made some comments throughout this report to help you think about how the case could be improved. 2 Management Summary Lake Saddleback Development Corporation needs to determine the number of houses of each product to build in order to maximize its profit on its new 300-acre development on Lake Saddleback, Texas. LSDC has the option of building only homes on all of the property, or using 10-acres to build a sports/recreation complex which will cost $8,000,000 but increase the value of the homes. Upon detailed analysis, it is in the best interest of LSDC to go ahead and build the sports complex because this will increase its net profit by almost 9%. Comments: Notice the management summary contains the (a) identification of the problem: need to determine the houses of each product to build [you might have said determine the product mix for the development, or something similar]. Then the (b) alternatives were identified: (1) use all of the property for homes and (2) use part of the property for a sports complex. The guidelines for the report indicate that at least three alternatives be identified and considered. Also, the description of the alternatives should have provided more details about the alternatives. Finally, the (c) recommendation was stated. Remember: there should been at least three alternatives, and it should be clear what the alternatives involve – don’t say alternative 1, 2 and 3 and then fail to describe them. However, the management summary for short reports does not need to be lengthy. For cases in this course, usually one page or 1 ½ pages is sufficient. If you were writing a 50-page report, your management summary might be 5 pages for example. The management summary is there to help the readers have some idea of what to expect when, and if, they decide to read the entire report. You might think of as being somewhat similar to an abstract for an article. Business reports should include a management or an executive summary. In addition, remember you are to assume a role. Do not refer to the write-up as a case. 3 Background Information XYZ’s Consulting has been asked to evaluate the current situation facing Lake Saddleback Development Corporation (LSDC). LSDC owns 300 acres near Lake Saddleback, Texas which it is planning to develop into homes and condominiums. The idea is to establish a planned community offering a variety of home plans and products while maximizing profits from the development. An option of a 10-acre sports/recreational complex is also being evaluated. Table 1 outlines the different product and floor plan options. Table 1 Product Grand Estates Grand Estates Grand Estates Grand Estates Grand Estates Grand Estates Grand Estates Grand Estates Glen Wood Glen Wood Glen Wood Glen Wood Glen Wood Lakeview Lakeview Lakeview Lakeview Lakeview Country Condos Country Condos Country Condos Plan Trump Trump – Premium Vanderbilt Vanderbilt – Premium Hughes Hughes – Premium Jackson Jackson – Premium Grand Cypress Grand Cypress – Premium Lazy Oak Wind Row Orangewood Bayview Bayview – Premium Shoreline Docks Edge Golden Pier Country Stream Weeping Willow Picket Fence The total land requirements for each option vary. Each home has its lot size which consists of the ground area of the home, the yard size, and the garage size. In addition to lot size, outside parking and road/greenbelt requirements vary from house to house. LSDC wants the Lake Saddleback development to have a variety of products and floor plans. The marketing department has established guidelines to ensure that this 4 variety is attained. Also, in accordance with federal government mandates, at least 15% of the project must be affordable housing selling for no more than $200,000. Profit margins on each of the four product lines vary from 18% to 25%. Table 2, in the appendix, offers more background information on each plan. The Introduction does not need to be lengthy, but it should provide some background for identifying the problem and alternatives. Think about what the reader might want to consider as they read the report. Problem Statement Lake Saddleback Development Corporation needs to determine the number of houses of each product and plan in order to maximize its profit on the development. Comment: Again the problem or opportunity identified here is the need to determine the best way to develop this property -- product mix. After you have identified the problem, you may include the idea of profit or other criteria that you may use in discussing the alternatives. However, do not define your problem in terms of the objective function. That is, do not simply indicate you want to maximize profit or minimize cost. There will be other criteria that you will want to consider, including some discussion of qualitative criteria. Try to be clear in defining your problem and match the alternatives to the problem. Alternatives (1) The first alternative is to only build homes in the 300-acre community. (2) The second alternative is to build a 10-acre sports/recreation complex on the property. The $8,000,000 complex would reduce the amount of usable acreage for home development, but it will enhance the value of the homes allowing LSDC to increase the selling prices of the homes. 5 Comment: Alternatives are identified. You may include more details in this section when you are describing the alternatives or you may elaborate in the analysis section. However, be sure to describe the alternatives completely. You describe the alternatives and then present results. Don’t give results and indicate that the results constitute the alternative. However, in some cases, a look at sensitivity analysis may help you develop additional alternatives. Remember this report did not contain an adequate number of alternatives. Analysis of Alternatives Based on the land requirements and selling price data and information in Table 2 of the Appendix, a profit maximization model was developed to analyze each alternative for LSDC. The step-by-step set up of the linear program can be found in Appendix A. Utilizing the linear programming module of the WINQSB software, the following table shows the number of each house plan that should be built in order to maximize profit under each alternative. Table 3 shows the rounded results for Alternative 1 – no sports complex and Alternative 2 – with a sports complex. Table 3 Alternative 1 Plan Trump Trump – Premium Vanderbilt Vanderbilt – Premium Hughes Hughes – Premium Jackson Jackson – Premium Grand Cypress Grand Cypress - Premium Lazy Oak Wind Row Orangewood Bayview Bayview – Premium Shoreline Docks Edge Golden Pier Country Stream Weeping Willow Picket Fence Alternative 2 # of Homes to Build 63 26 56 8 43 8 43 8 156 52 148 119 119 86 29 71 65 76 174 183 166 Net Profit $154,000 $211,200 $149,600 $205,480 $143,000 $196,900 $129,800 $179,740 $75,600 $131,600 $68,400 $57,600 $50,400 $60,000 $100,000 $54,000 $48,000 $40,000 $55,000 $40,000 $35,000 Profit on Plan $9,702,000 $5,491,200 $8,377,600 $1,643,840 $6,149,000 $1,575,200 $5,581,400 $1,437,920 $11,793,600 $6,843,200 $10,123,200 $6,854,400 $5,997,600 $5,160,000 $2,900,000 $3,834,000 $3,120,000 $3,040,000 $9,570,000 $7,320,000 $5,810,000 Plan Trump Trump - Premium Vanderbilt Vanderbilt - Premium Hughes Hughes - Premium Jackson Jackson - Premium Grand Cypress Grand Cypress - Premium Lazy Oak Wind Row Orangewood Bayview Bayview - Premium Shoreline Docks Edge Golden Pier Country Stream Weeping Willow Picket Fence # of Homes to Build 63 26 56 8 43 8 43 8 208 0 148 119 119 74 25 65 62 57 198 198 170 Net Profit $189,000 $251,200 $183,600 $245,480 $175,500 $236,900 $159,300 $219,740 $88,200 $147,600 $79,800 $67,200 $58,800 $69,000 $116,000 $62,100 $55,200 $40,000 $65,000 $50,000 $45,000 Profit on Plan $11,907,000 $6,531,200 $10,281,600 $1,963,840 $7,546,500 $1,895,200 $6,849,900 $1,757,920 $18,345,600 $0 $11,810,400 $7,996,800 $6,997,200 $5,106,000 $2,900,000 $4,036,500 $3,422,400 $2,280,000 $12,870,000 $9,900,000 $7,650,000 6 Total Profit: Total Profit: $122,324,160 $142,048,060 The analysis section for this case is inadequate. Each alternative must be described, the results of the analysis of each alternative provided, and the pros and cons of each alternative stated. The alternatives should be in separate subsections under the analysis section. You need to use subheadings to identify the alternatives. Comment: This case was not a complex case that required the introduction of many pros and cons. However, in the analysis section, you frequently want to include some qualitative viewpoints. For example, do you think the amenities might add to the overall marketing of the homes in the long-run regardless of the exact profit? Do you think that it might be better to have less premium homes based upon some market research you have conducted? That is, try to think of other possibilities for the development. One of the benefits of looking at sensitivity analysis, is that it may provide additional information for other alternatives. Depending upon a specific formulation, one may have noticed that all of the 15 acres for parking was not used. Thus, one could adjust that constraint and include more area in the 300 acres for homes. The analysis section is one of the most important sections because it will help you determine your recommendation. This report should have contained more details in both the analysis and recommendation sections. Detailed Recommendations Based on the profit information below in Table 4, XYZ’s Consulting recommends that LSDC commit to Alternative 2 in order to maximize profits on the development. Table 4 Gross Profit Less Sports Complex Cost Net Profit Alternative 1 $122,324,160 $0 $122,324,160 Alternative 2 $142,048,060 - $8,000,000 $134,048,060 Alternative 2 will have a net profit of $134,048,060 as opposed to the net profit of Alternative 1 of $122,324,160. This is an increase of $11,723,900. Table 5 presents the solutions again for Alternative 2. Table 5 Plan Trump # of Homes to Build 63 7 Trump - Premium Vanderbilt Vanderbilt - Premium Hughes Hughes - Premium Jackson Jackson - Premium Grand Cypress Grand Cypress Premium Lazy Oak Wind Row Orangewood Bayview Bayview - Premium Shoreline Docks Edge Golden Pier Country Stream Weeping Willow Picket Fence 26 56 8 43 8 43 8 208 0 148 119 119 74 25 65 62 57 198 198 170 A stronger justification for the recommendation should have been made. Comment: Solutions among student cases may not have the same values because of different formulations. The differences may occur because of interpretation or assumptions made. In this case, either the differences could be explained in the text [maybe under assumptions section] or in the appendix. For example, profits on the homes when the complex was included varied depending upon an individual’s interpretation. One might have read the adding 5% to homes not on the lake [Grand Estates] as follows: take Trump not on lake – selling price $700,000, when you multiplied that by .22 you obtained a profit of $154,000. If you added 5% as suggest in the sentence “add $35,000 to profit for Trumps,” you would have a profit of $189,000. However, the sentence above referred to raise the “selling price of the home by the following amounts:” Thus, if you used that criterion, you would take the selling price of $700,000 and add $35,000 to obtain a selling price of $735,000, and then taking 22% of the selling price, you would obtain a profit of $161,700. When there may be more than one interpretation, just be sure to indicate which interpretation you used. Either would be okay here. What is important is that you make your assumptions clear. Be sure that you include a discussion of sensitivity analysis in the analysis or recommendation section. Only one alternative may be recommended. 8 Implementation Due to the formulation of the linear programming model, the number of homes was rounded off. These slight rounding adjustments require that the amount of land to build homes on must either increase slightly, the size of the sports complex must be reduced slightly, or the allotted greenbelts and small parks must be reduced slightly. The land estimates are off by 22,864 ft2 or about ½ acre. It is the recommendation of XYZ’s Consulting to decrease the acreage of the sports complex to 9 ½ acres instead of 10. By doing this, LSDC will save on the cost of the sports complex, and the decrease in acreage should not affect home values. Comment: The need to round was addressed here and accommodations made. Linear Programming gives the optimal answer, but when the variables need to be integers, adjustments must be made. However, it was not the formulation of the linear programming model that caused the number of houses to be rounded. Rather it was the results – needed to use integer, but due to the algorithm for integer programming problems, you are allowed to use the linear programming module. Another consideration for LSDC is the ongoing increase in building costs for its development. It is projected that this development will take approximately 5-7 years to complete. In that time period, the cost of lumber, concrete, labor, etc. are likely to increase. Given this fact, it is necessary to evaluate the profit maximization for LSDC long term. Table 6 presents part of the sensitivity analysis for Alternative 2 solutions. Table 6 Plan Trump Trump - Premium Vanderbilt Vanderbilt - Premium Hughes Hughes - Premium Net Profit $189,000 $251,200 $183,600 $245,480 $175,500 $236,900 Allowable Max $189,320.00 M $186,800.10 $245,800.00 $176,700.00 $237,700.00 9 Jackson Jackson - Premium Grand Cypress Grand Cypress - Premium Lazy Oak Wind Row Orangewood Bayview Bayview - Premium Shoreline Docks Edge Golden Pier Country Stream Weeping Willow Picket Fence $159,300 $219,740 $88,200 $147,600 $79,800 $67,200 $58,800 $69,000 $116,000 $62,100 $55,200 $40,000 $65,000 $50,000 $45,000 $174,491.10 $221,500.00 $404,502.40 $153,441.60 $83,853.77 $77,583.80 $70,680.98 $83,850.85 $291,787.50 $63,300.00 $62,100.00 $83,301.81 $397,117.50 $382,117.50 $50,000.00 The “Allowable Max” in Table 6 is the largest amount that the net profit could increase to on each plan without affecting the recommended number of houses to build within that plan thus altering the maximization model. Therefore, if LSDC is faced with increased building costs, this table can help guide them in adjusting their selling prices on homes. Your formulation, input, output files, and large tables should be placed in the Appendix of the report. You want the body of the report to flow. Only a portion of the appendix is included in this sample. You want to be sure that your input and output are available to the reader, if needed. Appendix Table 2 Plan Selling Price Size Bed rooms Stories Garage Size Lot Size Ground Area Yard Size Garage size Parking Spaces Required Parking Sq. Ft. Total Land Per House Alt. 1 Net Profit Alt. 2 Net Profit Trump $700,000 4,000 5 2 3 21,780 2 400 23,180 $154,000 $189,000 Trump - Premium $960,000 4,000 5 2 3 21,780 2 400 23,180 $211,200 $251,200 Vanderbilt $680,000 3,600 4 2 3 21,780 1 200 22,980 $149,600 $183,600 Vanderbilt - Premium $934,000 3,600 4 2 3 21,780 1 200 22,980 $205,480 $245,480 Hughes $650,000 3,000 4 1 3 21,780 1 200 22,980 $143,000 $175,500 Hughes - Premium $895,000 3,000 4 1 3 21,780 1 200 22,980 $196,900 $236,900 Jackson $590,000 2,600 3 1 3 21,780 0 0 22,780 $129,800 $159,300 Jackson - Premium $817,000 2,600 3 1 3 21,780 0 0 22,780 $179,740 $219,740 10 Grand Cypress $420,000 2,800 4 2 3 4,950 2,100 2,100 750 1 200 6,150 $75,600 $88,200 Grand Cypress - Premium $504,000 2,800 4 2 3 10,890 Lazy Oak $380,000 2,400 4 2 2 4,356 1,800 1,800 500 1 200 12,090 $131,600 $147,600 2 400 5,756 $68,400 Wind Row $320,000 2,200 3 2 2 4,356 1,650 1,650 $79,800 500 1 200 5,556 $57,600 $67,200 Orangewood $280,000 1,800 3 Bayview $300,000 2,000 4 1 2 4,356 1,800 2 2 4,356 1,500 1,200 500 1 200 5,556 $50,400 $58,800 1,350 500 2 400 5,756 $60,000 Bayview - Premium $360,000 2,000 4 2 2 7,260 $69,000 2 400 8,660 $100,000 $116,000 Shoreline $270,000 1,800 3 2 2 4,356 1,350 1,275 500 1 200 5,556 $54,000 $62,100 Docks Edge Golden Pier $240,000 1,500 3 1 2 4,356 1,500 $200,000 1,200 2 1 2 4,356 1,200 900 500 1 200 5,556 $48,000 $55,200 900 500 0 0 5,356 $40,000 Country Stream $220,000 1,600 3 2 0 $40,000 1,500 3 600 3,100 $55,000 $65,000 Weeping Willow $160,000 1,200 2 1 Picket Fence $140,000 1,000 2 1 0 1,500 2 400 2,900 $40,000 $50,000 0 1,500 2 400 2,900 $35,000 $45,000 Appendix A - Lake Saddleback LP Set Up Part 1 Step 1: Define decision variables. Variable X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 Product Grand Estates Grand Estates Grand Estates Grand Estates Grand Estates Grand Estates Grand Estates Grand Estates Glen Wood Glen Wood Glen Wood Glen Wood Glen Wood Lakeview Lakeview Lakeview Lakeview Lakeview Country Condos Country Condos Country Condos Total # of Homes Plan Trump Trump – Premium Vanderbilt Vanderbilt – Premium Hughes Hughes – Premium Jackson Jackson – Premium Grand Cypress Grand Cypress – Premium Lazy Oak Wind Row Orangewood Bayview Bayview – Premium Shoreline Docks Edge Golden Pier Country Stream Weeping Willow Picket Fence 11 X23 X24 X25 X26 Total # of Grand Estates Total # of Glen Wood Total # of Lakeview Total # of Country Condos Step 2: State the objective function. MAX p (profit) $154,000X1 + $211,200X2 + $149,600X3 + $205,480X4 + $143,000X5 + $196,900X6 + $129,800X7 + $179,740X8 + $75,600X9 + $131,600X10 + $68,400X11 + $57,600X12 + $50,400X13 + $60,000X14 + $100,000X15 + $54,000X16 + $48,000X17 + $40,000X18 + $55,000X19 + $40,000X20 + $35,000X21 Step 3: Identify content constraints. Land Limit 23,180X1 + 23,180X2 + 22,980X3 + 22,980X4 + 22,980X5 + 22,980X6 + 22,780X7 + 22,780X8 + 6,150X9 + 12,090X10 + 5,756X11 + 5,556X12 + 5,556X13 + 5,756X14 + 8,660X15 + 5,556X16 + 5,556X17 + 5,356X18 + 3,100X19 + 2,900X20 + 2,900X21 ≤ 13,068,000 ft 2 GE 50 Prem X2 + X4 + X6 + X8 = 50 GE Mix X2 ≥ 8 X4 ≥ 8 X6 ≥ 8 X8 ≥ 8 GCypress .25X9 - .75X10 ≥ 0 Bayview .25X14 - .75X15 ≥ 0 Parking 400X1 + 400X2 + 200X3 + 200X4 + 200X5 + 200X6 + 0X7 + 0X8 + 200X9 + 200X10 + 400X11 + 200X12 + 200X13 + 400X14 + 400X15 + 200X16 + 200X17 + 0X18 + 600X19 + 400X20 + 400X21 ≤ 653,400 ft 2 2BR Max 2BR Min X18 + X20 + X21 - .25X22 ≤ 0 X18 + X20 + X21 - .15X22 ≥ 0 3BR Max 3BR Min X7 + X8 + X12 + X13 + X16 + X17 + X19 - .40X22 ≤ 0 X7 + X8 + X12 + X13 + X16 + X17 + X19 - .25X22 ≥ 0 4BR Max 4BR Min X3 + X4 + X5 + X6 + X9 + X10 + X11 + X14 + X15 - .40X22 ≤ 0 X3 + X4 + X5 + X6 + X9 + X10 + X11 + X14 + X15 - .25X22 ≥ 0 5BR Max 5BR Min X1 + X2 - .15X22 ≤ 0 X1 + X2 - .05X22 ≥ 0 Product Constraints GE Max X23 - .35X22 ≤ 0 GE Min X23 - .15X22 ≥ 0 GW Max X24 - .35X22 ≤ 0 GW Min X24 - .15X22 ≥ 0 12 L Max X25 - .35X22 ≤ 0 L Min X25 - .15X22 ≥ 0 C Max X26 - .35X22 ≤ 0 C Min X26 - .15X22 ≥ 0 Plan Constraints X1 & X2 Max X1 + X2 - .35X23 ≤ 0 X1 & X2 Min X1 + X2 - .20X23 ≥ 0 X3 & X4 Max X3 + X4 - .35X23 ≤ 0 X3 & X4 Min X3 + X4 - .20X23 ≥ 0 X5 & X6 Max X5 + X6 - .35X23 ≤ 0 X5 & X6 Min X5 + X6 - .20X23 ≥ 0 X7 & X8 Max X7 + X8 - .35X23 ≤ 0 X7 & X8 Min X7 + X8 - .20X23 ≥ 0 X9 & X10 Max X9 + X10 - .35X24 ≤ 0 X9 & X10 Min X9 + X10 - .20X24 ≥ 0 X11 Max X11 - .35X24 ≤ 0 X11 Min X11 - .20X24 ≥ 0 X12 Max X12 - .35X24 ≤ 0 X12 Min X12 - .20X24 ≥ 0 X13 Max X13 - .35X24 ≤ 0 X13 Min X13 - .20X24 ≥ 0 X14 & X15 Max X14 + X15 - .35X25 ≤ 0 X14 & X15 Min X14 + X15 - .20X25 ≥ 0 X16 Max X16 - .35X25 ≤ 0 X16 Min X16 - .20X25 ≥ 0 X17 Max X17 - .35X25 ≤ 0 X17 Min X17 - .20X25 ≥ 0 X18 Max X18 - .35X25 ≤ 0 X18 Min X18 - .20X25 ≥ 0 X19 Max X19 - .35X26 ≤ 0 X19 Min X19 - .20X26 ≥ 0 X20 Max X20 - .35X26 ≤ 0 X20 Min X20 - .20X26 ≥ 0 X21 Max X21 - .35X26 ≤ 0 X21 Min X21 - .20X26 ≥ 0 2 Story X1 + X2 + X3 + X4 + X9 + X10 + X11 + X12 + X14 + X15 + X16 - .70X22 + .70X19 + .70X20 + .70X21 ≤ 0 13 Affordable X18 + X20 + X21 - .15X22 ≥ 0 Step 4: Identify the non-negative constraint X(1-26) ≥ 0 Part 2 (changes from part 1) Step 2: State the objective function. MAX p (profit) $189,000X1 + $251,200X2 + $183,600X3 + $245,480X4 + $175,500X5 + $236,900X6 + $159,300X7 + $219,740X8 + $88,200X9 + $147,600X10 + $79,800X11 + $67,200X12 + $58,800X13 + $69,000X14 + $116,000X15 + $62,100X16 + $55,200X17 + $40,000X18 + $65,000X19 + $50,000X20 + $45,000X21 Step 3: Identify content constraints. Land Limit 23,180X1 + 23,180X2 + 22,980X3 + 22,980X4 + 22,980X5 + 22,980X6 + 22,780X7 + 22,780X8 + 6,150X9 + 12,090X10 + 5,756X11 + 5,556X12 + 5,556X13 + 5,756X14 + 8,660X15 + 5,556X16 + 5,556X17 + 5,356X18 + 3,100X19 + 2,900X20 + 2,900X21 ≤ 12,632,400 ft 2 14
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