MANAGEMENT SCIENCE INDIVIDUAL PROJECT formulate a linear programming model and write down the mathematical model for this problem

UEH UNIVERSITY COLLEGE OF BUSINESS SCHOOL OF INTERNATIONAL BUSINESS AND MARKETING MANAGEMENT SCIENCE INDIVIDUAL PROJECT Subject: Management Science Class ID: 21C1BUS50304001 Lecturer: Ph.D Ha Quang An Full Name: Nguyen Phuoc Loc Student ID: 31201025486 Class: IBC04 Major: International Business MARK LECTURER’S COMMENT Question 1: ………… ………………………………………………… Question 2: ………… ………………………………………………… Question 3: ………… Sum: ……………… ………………………………………………… ………………………………………………… LECTURER’S SIGNATURE (Full Name and Signature) Ha Quang An TABLE OF CONTENT Linear Programming Question a Question b Question c Question d Question e Question f Decision Making Forecasting 10 Question a 10 Question b 10 Question c 10 Question d 11 1 Linear Programming a Formulate a linear programming model and write down the mathematical model for this problem Decision variables are number of hours assigned to each consultant for respective project xij = Number of hours consultant i is assigned to project j i = A,B,C,D,E,F (Consultants) j = 1,2,3,4,5,6,7,8 (Projects) Objective is to maximize utilization of consultant skills and meeting clients’ needs based on ratings This can be accomplished by maximizing the product of the number of hours assigned and the ratings Since higher ratings are better, maximize the objective F Maximize Z = ∑ ∑ R x (x ij ) i− A j=1 Where Z is the ratings adjusted hours and R is the rating provided Subject to constraints: Hours availability: Consultant A: ∑ x Aj < 450 j=1 Consultant B: ∑ x Bj < 600 j=1 Consultant C: ∑ x Cj < 500 j=1 Consultant D: ∑ x Dj < 300 j=1 Consultant E: ∑ x Ej < 710 j=1 Consultant F: ∑ x Fj < 860 j=1 Project hours: F Project 1: ∑ xi = 500 i= A F Project 2: ∑ xi = 240 i= A F Project 3: ∑ xi = 400 i= A F Project 4: ∑ xi = 400 i= A F Project 5: ∑ xi = 350 i= A F Project 6: ∑ xi = 460 i= A F Project 7: ∑ xi = 290 i= A F Project 8: ∑ xi = 200 i= A Budget constraint: F Project 1: ∑ xi × ( Hourly Rate)i < 100,000 i= A F Project 2: ∑ xi × (Hourly Rate)i < 80,000 i= A F Project 3: ∑ xi × (Hourly Rate)i < 120,000 i= A F Project 4: ∑ xi × (Hourly Rate)i < 90,000 i= A F Project 5: ∑ xi × (Hourly Rate)i < 65,000 i= A F Project 6: ∑ xi × ( Hourly Rate)i < 85,000 i= A F Project 7: ∑ xi × ( Hourly Rate)i < 50,000 i= A F Project 8: ∑ xi × ( Hourly Rate)i < 55,000 i= A Non-negativity constraint Xij > 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? When the company maximize revenue while ignoring client preferences and consultant compatibility, the solution in B will change 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? When consultant A and E change their hourly wage from $155 to $200 (A) and $270 to $200, the solution will change f By experience, 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? The shadow price will not change The shadow price of Q.F: The shadow price of Q.B: Decision making EMV of Local gas company ¿ 60 % × 300.000+ 40 % × 150.000=240.000 EMV of Provider ¿ 60 %× (−100.000 ) +40 % × 600.000=180.000 EMV of Corporation ¿ 60 % × 120.000+ 40 % × 170.000=140.000 The maximum profit is related to Locas gas company, so the decision must be Locas gas company Forecasting a Weighted Moving Average Method The weight of April is 0.4 The weight of May is 0.2 The weight of June is 0.4 The forecasting demand for July ¿ 15 ×0.4 +19× 0.2+18 ×0.4=17 10 b 3-month average method The forecasting demand for July ¿ 18+ 19+15 =17.33 c Exponential Smoothing The forecast for June is 16 and ∝=0.4 The forecasting demand for July ¿ DJune × ∝+ F June ×(1−∝) ¿ 18 ×0.4 +16 × ( 1−0.4 )=16.8 d Weighted Moving Average Method averages the data for only the most recent time periods with the weight factor of 0,4; 0,2; 0,4 3-month average method averages the data of lastest months Exponential Smoothing modifies the moving-average method by placing the greatest weight on the last value in the time series and then progressively smaller weights on the older values This formula for forecasting the next value in the time series combines the last value and the last forecast (the one used one time period ago to forecast this last value) For me, the best and most accurate is 3-month average method Because, the moving-average method is somewhat slow to respond to changing conditions and Exponential Smoothing choosing the value of ∝ amounts to using this pattern to choose the desired progression of weights on the time series values 11 ... Programming a Formulate a linear programming model and write down the mathematical model for this problem Decision variables are number of hours assigned to each consultant for respective project xij... combines the last value and the last forecast (the one used one time period ago to forecast this last value) For me, the best and most accurate is 3-month average method Because, the moving-average... method by placing the greatest weight on the last value in the time series and then progressively smaller weights on the older values This formula for forecasting the next value in the time series