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Loading and cutting problems Description
Further explanation of this example: 'Applications of optimization with Xpress-MP', Chapter 9: Loading and cutting stock problems
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Data Files
d3tanks.mos (!****************************************************** Mosel Example Problems ====================== file d3tanks.mos ```````````````` Loading of liquid chemicals into tanks Five tanker ships filled with liquids must be unloaded into storage tanks. The 5 liquids must not be mixed. (1) How should the ships be unloaded to maximize the capacity of unused tanks? (2) How should they be unloaded to maximize the number of unused tanks? The storage tanks are defined as a range of consecutive integers whereas the liquids are identified by their names. Entries of the decision variable array 'load' are created dynamically depending on the initial configuration data. This problem calls the custom 'printsol' procedure after minimizing each objective. (c) 2008-2022 Fair Isaac Corporation author: S. Heipcke, Mar. 2002, rev. Mar. 2022 *******************************************************!) model "D-3 Tank loading" uses "mmxprs" forward procedure printsol declarations TANKS: range ! Set of tanks LIQ: set of string ! Set of liquids CAP: array(TANKS) of integer ! Tank capacities TINIT: array(TANKS) of string ! Initial tank contents type QINIT: array(TANKS) of integer ! Quantity of initial contents ARR: array(LIQ) of integer ! Arriving quantities of chemicals REST: array(LIQ) of integer ! Rest after filling part. filled tanks ifload: dynamic array(LIQ,TANKS) of mpvar ! 1 if liquid loaded into tank, ! 0 otherwise end-declarations initializations from 'd3tanks.dat' CAP ARR [TINIT, QINIT] as 'FILLED' end-initializations finalize(LIQ) forall(t in TANKS | QINIT(t)=0, l in LIQ) do create(ifload(l,t)) ifload(l,t) is_binary end-do ! Complete the initially partially filled tanks and calculate the remaining ! quantities of liquids forall(l in LIQ) REST(l):= ARR(l) - sum(t in TANKS | TINIT(t)=l) (CAP(t)-QINIT(t)) ! Objective 1: total tank capacity used TankUse:= sum(l in LIQ, t in TANKS) CAP(t)*ifload(l,t) ! Objective 2: number of tanks used TankNum:= sum(l in LIQ, t in TANKS) ifload(l,t) ! Do not mix different liquids forall(t in TANKS) sum(l in LIQ) ifload(l,t) <= 1 ! Load the empty tanks within their capacity limits forall(l in LIQ) sum(t in TANKS) CAP(t)*ifload(l,t) >= REST(l) ! Solve the problem with objective 1 minimize(TankUse) ! Solution printing printsol ! Solve the problem with objective 2 minimize(TankNum) ! Solution printing printsol !----------------------------------------------------------------- ! Solution printing procedure printsol writeln("Used capacity: ", getsol(TankUse) + sum(t in TANKS | QINIT(t)>0) CAP(t), " Capacity of empty tanks: ", sum(t in TANKS) CAP(t) - getsol(TankUse) - sum(t in TANKS | QINIT(t)>0) CAP(t)) writeln("Number of tanks used: ", getsol(TankNum) + sum(t in TANKS | QINIT(t)>0) 1) forall(t in TANKS) if(QINIT(t)=0) then write(t, ": ") forall(l in LIQ) write( if(getsol(ifload(l,t))>0 , l, "")) writeln else writeln(t, ": ", TINIT(t)) end-if end-procedure end-model | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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