# Solving binary integer optimization problem

2 messages
Open this post in threaded view
|
Report Content as Inappropriate

## Solving binary integer optimization problem

 Hi, I am new to R for solving optimization problems, I have set of communication channels with limited capacity with two types of costs, fixed and variable cost. Each channel has expected gain for a single communication. I want to determine optimal number of communications for each channel maximizing ROI)return on investment) with overall budget as constraint.60000 is the budget allocated. Channel Fixed_Cost Variable_Cost Capacity Expected_Gain C1 400 2.5 5000 0.25 C2 10000 0 30000 0.3 C3 4000 0.15 20000 0.15 C4 2000 2 10000 0.36 C5 100 3 4000 0.09 Channel_Select <-data.frame(Channel=c('c1','c2','c3','c4','c5'),                        Fixed_Cost=c(400,5000,4000,2000,100),                                     Variable_Cost=c(2.5,0,0.15,2,3),                                     Capacity=c(5000,30000,20000,10000,4000),                                     Expected_gain=c(0.25,0.3,0.15,0.36,0.09)) Let  x1,x2,x3,x4,x5 are the decision variables  for c1,c2,c3,c4,c5 channel and z1,z2,z3,z4,z5 are the indicator binary variables if channel has allocated communication if any. max((0.25*x1+0.30*x2+0.15*x3+0.36*x4+0.09*x5)-(2.5*x1+0*x2+0.15*x3+2*x4+3*x5+400*z1+10000*z2+4000*z3+2000*z4+100*z5)/( 2.5*x1+0*x2+0.15*x3+2*x4+3*x5+400*z1+10000*z2+4000*z3+2000*z4+100*z5)) Constraints: (2.5*x1+0*x2+0.15*x3+2*x4+3*x5+400*z1+10000*z2+4000*z3+2000*z4+100*z5)) <= 60000 ##Budget Constraint x1-5000*z1<=0 x2-30000*z2<=0 x3-20000*z3<=0 x4-10000*z4<=0 x5-4000*z5<=0 x1 >= 200 x2 >= 100 x3>=100 x4>=500 x5>=0 I had tried lp function from lpsolve but not able to set objective.in for objective function. Any help or hint is welcomed!