Re: Warehouse location

Sorry. I realized thanks to Mark Wallace that I hade made xij's integer 
in the strong version and not in the aggregated, which is not necessary 
since the constraint matrix for integer y's are unimodular. What then 
happens I gues is that CPLEX begins branching on the xij's before yj's 
making the B&B tree unecessarily large. Now I can solve the problem in 
42 sec., which is however still much longer than the aggregated version.

Jesper Hansen wrote:

> Hi eclipsers
>
> I made this small warehouse location model based on the CLP one in the 
> ECLiPSe example section (I snipped the cost matrix). I tried to solve 
> it with the XRESS version included in 5.5, but it aborts with too many 
> B&B nodes. If the commented out constraint is readded it takes 0.2 
> sec. I also tried another formulation where the xij =< yj are 
> aggregated, which is a weaker formulation shown below the ***** line. 
> It solves the problem in less than 0.1 sec!
> Does anyone have any idea why this is? I haven't access to CPLEX. 
> Perhaps someone could try to see if it is an XPRESS problem?
>
> Thanks
>
> Jesper
>
> :- lib(ic).
> :- lib(ic_eplex_cplex).
> :- eplex_instance(eplex).
>
> solve(SupplyMatrix, BuiltWarehouses, Cost) :-
>       lp_set(result_channel, +output),
>       lp_set(log_channel, +log_output),
>
>    % get the data
>    setup_cost(SetupCost),
>        get_capacity(WareHouseCapacity),
>    supply_cost_matrix(SupplyCostMatrix),
>    dim(SupplyCostMatrix, [NCustomers, NWareHouses]),
>      % model
>        length(BuiltWarehouses,NWareHouses),
>        BuiltWarehouses :: 0..1,
>        eplex: (integers(BuiltWarehouses)),
>        dim(SupplyMatrix, [NCustomers, NWareHouses]),
>        SupplyMatrix[1..NCustomers,1..NWareHouses] :: 0..1,
> %        eplex: (sum(BuiltWarehouses) >= 
> NCustomers//WareHouseCapacity+1),
>        (
>            for(CustomerId, 1, NCustomers),
>            foreach(CustCost, CustCosts),
>            
> param(BuiltWarehouses,SupplyCostMatrix,NWareHouses,SupplyMatrix)
>        do
>            SupplyVars is SupplyMatrix[CustomerId, 1..NWareHouses],
>            eplex: (sum(SupplyVars) =:= 1),
>            eplex: (integers(SupplyVars)),
>            CostTable is SupplyCostMatrix[CustomerId, 1..NWareHouses],
>            (
>                foreach(BW,BuiltWarehouses),
>                foreach(SV,SupplyVars),
>                foreach(SC,CostTable),
>                foreach(CC,CustCost)
>            do
>                CC = SV*SC,
>                eplex: (SV =< BW)
>            )
>        ),
>        (
>            for(WareHouseID,1,NWareHouses),
>            param(SupplyMatrix,NCustomers,WareHouseCapacity) do
>                SupplyVars is SupplyMatrix[1..NCustomers, WareHouseID],
>                eplex: (sum(SupplyVars) =< WareHouseCapacity)
>        ),
>    % objective
>       flatten(CustCosts,CCosts),
>    Objective = sum(BuiltWarehouses)*SetupCost + sum(CCosts),
>
>    % search
>        optimize(min(Objective),Cost).
>
> setup_cost(50000).
>
> get_capacity(2).
>
> ****************************************
>
>  (
>            for(CustomerId, 1, NCustomers),
>            foreach(CustCost, CustCosts),
>            param(SupplyCostMatrix,NWareHouses,SupplyMatrix)
>        do
>            SupplyVars is SupplyMatrix[CustomerId, 1..NWareHouses],
>            eplex: (sum(SupplyVars) =:= 1),
> %            eplex: (integers(SupplyVars)),
>            CostTable is SupplyCostMatrix[CustomerId, 1..NWareHouses],
>            (
>                foreach(SV,SupplyVars),
>                foreach(SC,CostTable),
>                foreach(CC,CustCost)
>            do
>                CC = SV*SC
>            )
>        ),
>        (
>            for(WareHouseID,1,NWareHouses),
>            foreach(BW,BuiltWarehouses),
>            param(SupplyMatrix,NCustomers,WareHouseCapacity) do
>                SupplyVars is SupplyMatrix[1..NCustomers, WareHouseID],
>                eplex: (sum(SupplyVars) =< WareHouseCapacity*BW)
>        ),
>

-- 
_______________________________________
Jesper Hansen         
Ph.D. student         
Telephone: (+45) 45 25 33 88 
Telefax.:  (+45) 45 25 26 73
E-mail: mailto:jha@imm.dtu.dk 
Homepage: http://www.imm.dtu.dk/~jha/
Department of Mathematical Modelling 
Building 305                      
Technical University of Denmark
DK-2800 Lyngby