TIỂU LUẬN formulate a linear programming model and write down the mathematical model for this problem

ĐẠI HỌC UEH TRƯỜNG KINH DOANH KHOA KINH DOANH QUỐC TẾ - MARKETING TIỂU LUẬN BỘ MÔN KHOA HỌC QUẢN TRỊ NGUYỄN PHƯƠNG UYÊN TP Hồ Chí Minh, ngày 24 tháng 11 năm 2021 ĐẠI HỌC UEH TRƯỜNG KINH DOANH KHOA KINH DOANH QUỐC TẾ - MARKETING TIỂU LUẬN Môn học: Khoa học quản trị (Management Sciene) Giảng viên: Nguyễn Thị Hồng Thu Mã lớp học phần: 21C1BUS50306804 Sinh viên: Nguyễn Phương Uyên Khóa – Lớp: K46 - FTC01 MSSV: 31201024693 TP Hồ Chí Minh, ngày 24 tháng 11 năm 2021 TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem ENDORSEMENT I hereby declare that the data and research results in this thesis are my own construction, processing, not copied from any articles of any other organizations and individuals INSTRUCTOR’S COMMENT SCORES TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TABLE OF CONTENT PART I: LINEAR PROGRAMMING PROBLEM Formulate a linear programming model and write down the mathematical model for this problem Way to solve this problem using QM and SOLVER If the company want to maximize revenue while ignoring client preferences and consultant compatibility, will the solution in b change or not ? Create a sensitivity report Find out about the shadow price in this case ? 10 If consultant A and E change their hourly wage from $155 to $200 (A) and from $270 to $200, will the solution change ? 15 If the capacity for consultant B and E for every project now minimum start from three instead of or 2, will the shadow price change ? 16 PART II: DECISION MAKING PROBLEM Draw a decision tree to help Petrolimex choose what’s best for the profit 21 PART III: FORECASTING Calculate the forecasting demand using Weighted Moving Average Method, with the weighted factor of 0,40; 0,20; 0,40 26 Calculate the forecast using 3-month average method 27 Calculate the forecast using last-value method 27 Explain methods of forecast Which one is better and more accurate ? 28 TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem PART 1: LINEAR PROGRAMMING PROBLEM UDT is a consulting firm that develops e-commerce project, systems and websites for its clients It has six available consultants and eight clients project is under contract The consultants have different technical abilities and experience, and as a result, the company charges different hourly rates for its services Also, the consultant’s skill are more suited for some projects than others, and clients sometimes prefer some consultants over others The suitability of a consultant for a project is rated according to a 5-point scale, in which is the worst and is the best The following table shows the rating for each consultant for each project, as well as the hours available for each consultant and the contracted hours and maximum budget for each project : Project Consultant Hourly wage Available hours A $155 3 5 3 3 550 B $140 3 5 3 600 C $165 3 500 D $300 1 2 400 E $270 1 2 3 710 F $150 3 860 510 240 420 475 350 460 290 200 90 80 110 90 65 85 50 55 Project Hours Contract budget (x1000 USD) The company wants to know how many hours to assign each consultant to each project in order to best utilize their skill while meeting clients needs TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem a Formulate a linear programming model and write down the mathematical model for this problem b Solve this problem using QM and SOLVER c If the company want to maximize revenue while ignoring client preferences and consultant compatibility, will this change the solution in b ? d Create a sensitivity report What is the shadow price in this case ? e If consultant A and E change their hourly wage from $155 to $200 (A) and from $270 to $200, will the solution change ? f By exprerience, consultant B and E is getting better at their ability, which mean their capacity for every project now minimum start from instead of or 2, will the shadow price change ? *** a.) Formulate a linear programming model and write down the mathematical model for this problem In order to formulate a linear programming model for this problem, we have to start with defining the decision variables *These variables are defined below: Hence let Hi: the hour used by each consultant (i=A,B…F) HWi: the hourly wage for each consultant (i=A,B F) HAi: the hour available for each consultant (i=A,B F) WPj: the wage per hours of each project (j=1,2 8) PHj: the contracted hours for every project (j=1,2, 8) CBJ: the contract budget for every project (j=1,2 8) Then Hij: the hour used by each consultant for every project where (i=A,B…F) and (j=1,2 8) 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TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem PART FORECASTING The monthly demand of a water bottle extracted from a supermarket is shown below: Month Demand 25 24 28 25 29 28 a Using Weighted Moving Average Method, with the weighted factor of 0,40; 0,20; 0,40 What is the forecasting demand b Using 3-month average method, calculate the forecast c Using last-value method, calculate the forecast d Explain methods of forecast Which one is better and more accurate according to you? You can explain however you want *** a) Using Weighted Moving Average Method, with the weighted factor of 0,40; 0,20; 0,40 the forecasting demand is: TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem b) Using 3-month average method, calculate the forecast TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem c) Using last-value method, calculate the forecast d) Explain three method of forecast * 3-Month Average Method: The -month average forecasting method provides a middle ground between the last-value and averaging method by using the average of the monthly sales for the three most recent months as the forecast for the next month For example, a three-month moving average forecast for the supermarket in the 4th month is being calculated by: Forecast = 25 + 24+ 28 = 25,666666667 *Last-Value Method: The last-value forecasting method is calculated simply by using the last month’s sales as the forecast for the next month For example, the last-value method forecast for the supermaket in the 2nd month is being calculated by Forecast = 25 * Weighted Moving Average Method: The weighted average is employed when there is a need to place more importance on some periods over others In most cases, we place more TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem TIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problemTIEU.LUAN.formulate.a.linear.programming.model.and.write.down.the.mathematical.model.for.this.problem importance on recent data Therefore in this case, the 0.4 will be placed on the most recent value (3th month) , the 0,2 on the next most recent (2nd month) and so on For example, we can now calculate the weighted moving average method for the 4th month using the given weights 0.4; 0.2; 0.4: Forecast = 0.4*28 + 0.2*24 + 0.4* 25 = 26 + Which method is better and more accurate according to you? - The key factor in choosing a forecasting method is how stable the time series is and the value of MAD It is known that + Last-value method is suitable for a time series that is so unstable that even the next-to-last value is not considered relevant for forecasting the next value In this last-value forecasting problem, MAD =2,6 + Averaging method: Suitable for a very stable time series where even its first few values are considered relevant for forecasting the next value In this 3-month average method, MAD = 1.555555556 + Weighted moving-average method: Suitable for a moderately stable time series where the last few values are considered relevant for forecasting the next value In this weight moving-average method, MAD = 1.66666667 -> In this case, It is clear that 3-month average method is the best method among the three since it has the lowest MAD (1.56