CapBudg: Getting Started

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(i14) NPV(i)x(i)
• Budget SUM(i14) Cost(i)x(i) lt 14
• BOUNDS
• x(i14) .BV.

2
Other Constraints

• Cannot invest in more than two projects
• MaxProjects SUM(i14)x(i) lt 2
• If we invest in project 2, we must invest in
  project 1
• If2Then1 x(2) lt x(1)
• If we invest in project 3, we cannot invest in
  project 4
• If3ThenNot4 x(3) x(4) lt 1
• If we invest in two projects, we must invest in
  project 1
• IfTwoThen1 SUM(i24) x(i) lt 1

3
Dish Wash Fixed Charge

• 3 Kinds of Dishwashers
• Limited amounts of
• Steel
• Labor
• If we make a product theres a minimum quantity
  we can make economically
• Otherwise, we dont 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(p1NProd) min(STAVL/ST(p), HRAVL/HR(p))
• VARIABLES
• x(NProd) ! Amount of product made
• mkx(NProd) ! 1 if any product made
• CONSTRAINTS
• Profit SUM(p1NProd) P(p)x(p)
• SteelMax SUM(p1NProd) ST(p)x(p) lt STAVL
• HoursMax SUM(p1NProd) HR(p)x(p) lt HRAVL
• UBx(p1NProd) x(p) lt UB(p)mkx(p)
• LBx(p1NProd) x(p) gt LB(p)mkx(p)
• BOUNDS
• mkx(p1NProd) .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(s1NTown,t1NTown)
• if (TIME(s,t) lt TimeLimit, 1, 0)
• VARIABLES
• open(NTown) ! 1 if ambulance at
  town 0 if not
• CONSTRAINTS
• MinAmb Minimise number
  ambulances
• SUM(t1NTown) open(t)
• Serve(s1NTown) Serve each town
• SUM(t1NTown) SERVE(s,t) open(t) gt 1
• BOUNDS
• open(t1NTown) .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