Info3010, Week 4 notes
Info3010, Week 4 notes Info3010
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This 3 page Class Notes was uploaded by Rebecca Evans on Friday February 12, 2016. The Class Notes belongs to Info3010 at Tulane University taught by Srinivas Krishnamoorthy in Spring 2016. Since its upload, it has received 35 views. For similar materials see Business Modeling in Business at Tulane University.
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Date Created: 02/12/16
st Notes from Class on February 1 A Review & some Vocab Bland Brewery, Flakey Cereals and Grand Prix are all linear optimization models with continuous decision variables o Bland Brewery: produce ale and lager (x1 and x2) and objective is 13x1 + 23 x2; is st a liner model because decisions (x1 and x2) are to the 1 power=linear Today: linear optimization model with binary decision variables Tatham Investments Tatham Investments is considering 7 investments. The cash required for each investment and the net present value (NPV) of each investment are listed in the table below. The cash available for investment is $15,000. Tatham wants to find the investment portfolio that maximizes its NPV. The crucial aspect to note is that if Tatham wants to take part in an investment then it must go all the way. It cannot, for instance, go halfway in investment 1 by investing $2,500 and realizing an NPV of $8,000. Inv. 1 Inv. 2 Inv. 3 Inv. 4 Inv. 5 Inv. 6 Inv. 7 Cash $5,000 $2,500 $3,500 $6,000 $7,000 $4,500 $3,000 require d NPV $16,00 $8,000 $10,000 $19,50 $22,000 $12,000 $7,500 0 0 Linear Optimization with binary decision variables 1. Decision: Which investment opportunities to choose a. X = 1, if investment 1 is selected and X = 0 otherwise 1 1 b. X =71, if investment 1 is selected and X7= 0 otherwise 2. Objective: maximize NPV of portfolio a. NPV=net present value (measure value of investment) b. Portfolio NPV= 16,000X +18,000 X +210,000 X +319,500 X 4 22,000 X 5 12,000 X 6 + 7,500X 7 3. Constraints: a. Budget constraint: 5,000X 1 2,5000 X 2 3,5000 X 3+ 6,000 X 4+ 7,000 X5 + 4,5000 X6 + 3,000X ≤ $15,000 7 b. X ,1X 2… X 7re binary i. Binary constraint takes care of nonnegativity constraint Excel 1. Decision: binary so 1=invest and 0=don’t invest 2. Objective: portfolio npv =sumproduct(decision row, NPV row) 3. Constraint: total investment cost =sumproduct(decision row, investment cost row) a. ALWAYS use comma with sumproduct 4. Solver a. Changing variable cells: decision row b. Constraints: total investment cost ≤ budget (single cells not row) c. Constraint: binary constraint investment decision row and in middle box select “bin” for binary i. BINARY CONSTRAINT: in constraint area of solver instead of ≤ or ≥ select “bin” ii. Excel will NOT create sensitivity report for binary decision 5. New Constraint: at least 4 investments must be selected a. Conceptual: 1 +2 +.… 7 ≥ 4 b. Add constraint in solver c. Result: use 4 investments, use total budget and portfolio NPV decreased Notes from Class on February 3 rd Paddy Projects The modeling group at Paddy Projects wants to create an optimal portfolio of projects. The list of projects, their NPVs and the funds required for lab research and field development are given in the table below. Right now, lab research has $200M in funds available while field development has $130M. Project Project Project Project Project 1 2 3 4 5 NPV ($M) $10 $17 $13 $9 $14 Lab research funds $28 $50 $45 $20 $44 required ($M) Field development $20 $46 $35 $12 $24 funds required ($M) In addition to developing an optimal portfolio, the modeling group wants to know if they should recommend Paddy Projects to seek more funds from the parent company. What is your recommendation in this regard? Also, the modeling group wishes to know what the optimal portfolio would be if the following constraints were imposed: Both project 3 and project 4 must be accepted or neither of them. Project 1 must be accepted if project 5 is accepted. Note that the group wants to maintain the linearity of the model. Conceptual Model 1. Decisions a. Which projects to include in the portfolio. b. X =1 if project 1 is included, =0 if otherwise… c. X =5, if project included, =0 if otherwise 2. Objective a. Maximize NPV(net present value) of project portfolio b. Portfolio NPV= 10X + 17X + 13X + 9X + 14X 1 2 3 4 5 3. Constraints a. Lab Research funds limitation i. 28X 1 50X +2 + 44X ≤ 2005 b. Field development funds limitation i. 20 X 1 46X +2 + 24X ≤ 135 c. Binary constraint i. X 1 X 2… X a5e binary Excel 1. Portfolio project NPV =sumproduct(decision,NPV) 2. Lab research funds used =sumproduct(decision, lab research funds required) 3. Field development funds used =sumproduct(decision, field development funds required) 4. Solver a. Objective: Portfolio project NPV b. Max c. By changing variable cells: decision cells **select before constraints bc binary d. Constraints: i. Lab research funds and field development funds used ≤ funds available ii. Binary constraint 1. Select decision cells middle row select “bin” for binary More Constraints 1. If reallocated some money from lab research to field development, then can afford all the projects, or make a common pool of funds a. If pool all money: use $324 out of $330, so still under total budget b. Common issue in companies: dividing money, but has enough funds overall 2. Extra constraint: both project 3 and 4 must be accepted or neither of them a. X =3 or 4 X 3 0 4 3. Project 1 must be accepted if project 5 is accepted a. If use “if statement” then become nonlinear b. X ≥1 (be5 use if X is 05then X can b1 anything, but if X is 1 then5X must be 11 as well) X 1 X 5 1 1 1, 0 0
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