#************************************************************************
# Scrap Removal Assignment, "Mathematical Programming Modelling" (42112)
using JuMP
using HiGHS
#************************************************************************

#************************************************************************
# PARAMETERS
Items = ["S1","S2","S3","S4","S5","S6","S7","S8","S9","S10",
         "S11","S12","S13","S14","S15","S16","S17","S18","S19","S20"]
I=length(Items)
ItemWeight=[35,10,45,53,37,22,26,38,63,17,44,54,62,42,39,51,24,52,46,29]
BigBags=[1,2,3,4,5,6,7,8,9,10]
B=length(BigBags)
BigBagCost=50
BigBagWeightLimit=100
#************************************************************************

#************************************************************************
# Model
SR = Model(HiGHS.Optimizer)

@variable(SR, x[i=1:I,b=1:B], Bin) # x[i,b]=1 if item i is in big-bag b
@variable(SR, y[b=1:B], Bin)

# Minimize transporatation cost
@objective(SR, Min,
           sum( BigBagCost*y[b] for b=1:B)
           )

@constraint(SR, [b=1:B],
            sum( ItemWeight[i]*x[i,b] for i=1:I) <= BigBagWeightLimit*y[b]
            )

@constraint(SR, [i=1:I],
            sum( x[i,b] for b=1:B) == 1
            )
#************************************************************************


#************************************************************************
# solve
optimize!(SR)
println("Termination status: $(termination_status(SR))")
#************************************************************************


#************************************************************************
# Report results
let
println("-------------------------------------");
if termination_status(SR) == MOI.OPTIMAL
    println("RESULTS:")
    println("objective = $(objective_value(SR))")
else
  println("  No solution")
end
println("--------------------------------------");
end
#************************************************************************