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CapBudg: Getting Started

CapBudg: Getting Started. TABLES NPV (4) ! Net Present Value of investment Cost (4) ! Investment required DATA NPV(1) = 16, 22, 12, 8 Cost(1) = 5, 7, 4, 3 VARIABLES x(4) CONSTRAINTS Yield: SUM(i=1:4) NPV(i)*x(i) $ Budget: SUM(i=1:4) Cost(i)*x(i) < 14 BOUNDS x(i=1:4) .BV.

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CapBudg: Getting Started

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  1. CapBudg: Getting Started • TABLES • NPV (4) ! Net Present Value of investment • Cost (4) ! Investment required • DATA • NPV(1) = 16, 22, 12, 8 • Cost(1) = 5, 7, 4, 3 • VARIABLES • x(4) • CONSTRAINTS • Yield: SUM(i=1:4) NPV(i)*x(i) $ • Budget: SUM(i=1:4) Cost(i)*x(i) < 14 • BOUNDS • x(i=1:4) .BV.

  2. Other Constraints • Cannot invest in more than two projects • MaxProjects: SUM(i=1:4)x(i) < 2 • If we invest in project 2, we must invest in project 1 • If2Then1: x(2) < x(1) • If we invest in project 3, we cannot invest in project 4 • If3ThenNot4: x(3) + x(4) < 1 • If we invest in two projects, we must invest in project 1 • IfTwoThen1: SUM(i=2:4) x(i) < 1

  3. Dish Wash: Fixed Charge • 3 Kinds of Dishwashers • Limited amounts of • Steel • Labor • If we make a product there’s a minimum quantity we can make economically • Otherwise, we don’t make the product • Maximize Profit

  4. The Parameters (Tables) • LET NProd = 3 ! Number of products • TABLES • P(NProd) ! Unit profit • ST(NProd) ! Steel used per unit • STAVL ! Steel available • HR(NProd) ! Hours used per unit • HRAVL ! Hours available • UB(NProd) ! Upper bound on x - calculated • LB(NProd) ! Lower bound on x

  5. The Model • ASSIGN • UB(p=1:NProd) = min(STAVL/ST(p), HRAVL/HR(p)) • VARIABLES • x(NProd) ! Amount of product made • mkx(NProd) ! 1 if any product made • CONSTRAINTS • Profit: SUM(p=1:NProd) P(p)*x(p) $ • SteelMax: SUM(p=1:NProd) ST(p)*x(p) < STAVL • HoursMax: SUM(p=1:NProd) HR(p)*x(p) < HRAVL • UBx(p=1:NProd): x(p) < UB(p)*mkx(p) • LBx(p=1:NProd): x(p) > LB(p)*mkx(p) • BOUNDS • mkx(p=1:NProd) .BV.

  6. The Data • DATA • P = 25, 27, 35 • ST = 10, 13, 17 • STAVL = 90 • HR = 7, 5, 5 • HRAVL = 40 • LB = 2, 2.5, 2

  7. Ambulance 2: Set Covering • 6 cities • Travel times between • Minimum number of ambulances so that one is within 20 minutes of every city

  8. Parameters (TABLES) • LET NTown = 6 ! No. towns • LET TimeLimit = 20 ! Max time allowed to reach any town • TABLES • TIME(NTown,NTown) ! Time taken between each pair of towns • SERVE(NTown,NTown) ! 1 if time within limit, 0 otherwise

  9. The Model • ASSIGN • SERVE(s=1:NTown,t=1:NTown) = & if (TIME(s,t) <= TimeLimit, 1, 0) • VARIABLES • open(NTown) ! 1 if ambulance at town; 0 if not • CONSTRAINTS • MinAmb: & Minimise number ambulances • SUM(t=1:NTown) open(t) $ • Serve(s=1:NTown): & Serve each town • SUM(t=1:NTown) SERVE(s,t) * open(t) > 1 • BOUNDS • open(t=1:NTown) .bv.

  10. The Data • DATA • TIME(1,1) = 0,15,25,35,35,25 • TIME(2,1) = 15, 0,30,40,25,15 • TIME(3,1) = 25,30, 0,20,30,25 • TIME(4,1) = 35,40,20, 0,20,30 • TIME(5,1) = 35,25,35,20, 0,19 • TIME(6,1) = 25,15,25,30,19, 0

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