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Using multi-objective solving

Description
lexgoalprog.mos: lexicographic goal programming for solving a small production planning example
• configuration of multiple objectives via 'objconfig' constructors in list form
• list combining 'mpvar' and 'linctr' types
• detailed status check via XPRS_SOLVESTATUS and XPRS_SOLSTATUS
markowitzmo.mos: Markowitz portfolio optimization, multi-objective quadratic programming example
• list combining 'nlctr' and 'linctr' types
• display of the optimal frontier as SVG graph
multiobjknapsack.mos: Knapsack problem with two objectives
• configuration of multiple objectives in array structure using priorities
• multi-objective logging settings
Further explanation of this example: 'Mosel User Guide', Section 12.2 Goal Programming

Source Files
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lexgoalprog.mos

(!*******************************************************
Mosel Example Problems
======================

file lexgoalprog.mos

An example of lexicographic goal programming using the
Xpress multi-objective functionality

Problem description:
A company produces two electrical products, A and B. Both require
two stages of production: wiring and assembly.
The production plan must meet several goals:
1. A profit of $200 2. A contractual requirement of 40 units of product B 3. To fully utilize the available wiring department hours 4. To avoid overtime in the assembly department (c) 2022 Fair Isaac Corporation author: S. Heipcke, June 2022 *******************************************************!) model "lexGP" uses "mmxprs" public declarations ! Decision variables for the number of products to make of each type produceA,produceB: mpvar ! Deviational variables: ! There is a penalty for both under- and over-utilizing each department surfeit_wiring, deficit_wiring: mpvar surfeit_assembly, deficit_assembly: mpvar ! There is no penalty for surfeit in profit or in production of product B, ! only for deficits deficit_profit, deficit_productB: mpvar Goals: list of linctr or mpvar ! or also: list of any end-declarations produceA is_integer; produceB is_integer ! **** Production constraints: ! Meet or exceed profit goal of$200
! Profit for products A and B are $7 and$6 respectively
Profit:= 7 * produceA + 6 * produceB
Profit + deficit_profit >= 200
! Meet or exceed production goal for product B
produceB + deficit_productB >= 40
! Utilize wiring department:
! Products A and B require 2 and 3 hours of wiring, 120 hours are available
2 * produceA + 3 * produceB - surfeit_wiring + deficit_wiring = 120
! Utilize assembly department:
! Products A and B require 6 and 5 hours of assembly, 300 hours are available
6 * produceA + 5 * produceB - surfeit_assembly + deficit_assembly = 300

! Objective configuration
Goals:=[deficit_profit, deficit_productB, surfeit_wiring + deficit_wiring,
surfeit_assembly + deficit_assembly]
(!  Cfg:= [objconfig("priority=4 abstol=0 reltol=0"),
objconfig("priority=3 abstol=0 reltol=0"),
objconfig("priority=2 abstol=0 reltol=0"),
objconfig("priority=1 abstol=0 reltol=0")] !)
! Same as:
forall(i in 1..4) Cfg+=[objconfig(5-i,1,0,0)]

! Uncomment this line to try out the effect of inversing priority order:
! forall(i in 1..4) Cfg(i).priority:=i

! setparam("XPRS_VERBOSE", true)

! Minimize deviations, in priority order
minimize(Goals,Cfg)

! **** Solution reporting
declarations
SolStat,SolvStat: array(integer) of string    ! Status messages
end-declarations

SolvStat:: ([XPRS_SOLVESTATUS_UNSTARTED, XPRS_SOLVESTATUS_STOPPED,
XPRS_SOLVESTATUS_FAILED, XPRS_SOLVESTATUS_COMPLETED])
["The solve has not been started.", "Optimization has been interrupted.",
"Optimization has run into a nonrecoverable problem and failed.",
"Search completed."]

SolStat:: ([XPRS_SOLSTATUS_NOTFOUND, XPRS_SOLSTATUS_OPTIMAL,
XPRS_SOLSTATUS_FEASIBLE, XPRS_SOLSTATUS_INFEASIBLE, XPRS_SOLSTATUS_UNBOUNDED])
["No solution available.", "An optimal solution has been found.",
"A solution that is not proven optimal is found.",
"No solution exists.", "The problem is unbounded, if feasible."]

writeln("Problem solve status: ", SolvStat(getparam("XPRS_SOLVESTATUS")),
" Solution status: ", SolStat(getparam("XPRS_SOLSTATUS")),
" Objectives solved: ", getparam("XPRS_SOLVEDOBJS"))
if getparam("XPRS_SOLVESTATUS")=XPRS_SOLVESTATUS_COMPLETED and
getparam("XPRS_SOLSTATUS")=XPRS_SOLSTATUS_OPTIMAL and
getparam("XPRS_SOLVEDOBJS")=4 then
writeln('Production plan:')
writeln('Product A: ', produceA.sol, ' units')
writeln('Product B: ', produceB.sol, ' units')
writeln('Profit: $', Profit.sol) if deficit_profit.sol > 0: writeln('Profit goal missed by$', deficit_profit.sol)
if deficit_profit.sol > 0:
writeln('Profit goal missed by \$', deficit_profit.sol)
if deficit_productB.sol > 0:
writeln('Contractual goal for product B missed by ', deficit_productB.sol, ' units')
if surfeit_wiring.sol > 0:
writeln('Unused wiring department hours: ', surfeit_wiring.sol)
if deficit_wiring.sol > 0:
writeln('Wiring department overtime: ', deficit_wiring.sol)
if surfeit_assembly.sol > 0:
writeln('Unused assembly department hours: ', surfeit_assembly.sol)
if deficit_assembly.sol > 0:
writeln('Assembly department overtime: ', deficit_assembly.sol)
else
writeln('Problem could not be solved')
end-if
end-model