(!*********************************************************************
Mosel Example Problems
======================
file dynbigm2.mos
`````````````````
Production planning problem
-- Formulation using indicator constraints in place of BigM values --
Example discussed in section 14.1.2.1 of
J. Kallrath: Business Optimization Using Mathematical Programming -
An Introduction with Case Studies and Solutions in Various Algebraic
Modeling Languages. 2nd edition, Springer Nature, Cham, 2021
author: S. Heipcke, Jan. 2020
(c) Copyright 2020 Fair Isaac Corporation
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*********************************************************************!)
model dynbigm2
uses "mmxprs"
declarations
PRODS: range ! Set of products
Y: array(PRODS) of real ! Sales prices in $/ton
C: array(PRODS) of real ! Machine capacities in tons/day
P: array(PRODS) of integer ! Required personnel
N: array(PRODS,PRODS) of real ! BigM values
Pmax: integer ! Max. available personnel
D: real ! Total demand per day
DELTA: real ! Max. difference between production amounts
x: array(PRODS) of mpvar ! Amount of product produced on a day
delta: array(PRODS) of mpvar ! Whether product is produced on a day
end-declarations
C::(1..7)[100,80,90,60,100,110,100]
P::(1..7)[11,6,6,5,5,4,1]
D:=120
DELTA:=20
Pmax:=19
forall(i in PRODS) Y(i):=1+i
! Initial BigM values
! forall(i1,i2 in PRODS | i2 <> i1) N(i1,i2):= maxlist(M(i1),M(i2))-DELTA
Cmax:= max(i in PRODS) C(i)
forall(i1,i2 in PRODS | i2 <> i1) N(i1,i2):= Cmax
! Satisfy the total demand per day
sum(i in PRODS) x(i) = D
! Production is only possible if product has been selected
forall(i in PRODS) indicator(-1, delta(i), x(i) <= 0)
forall(i in PRODS) delta(i) is_binary
! Amounts produced for selected products should not differ by more than DELTA tons
forall(i1,i2 in PRODS | i2 <> i1) do
! abs(x(i1)-x(i2)) <= DELTA + N(i1,i2)*(2-delta(i1)-delta(i2))
x(i1) -x(i2) <= DELTA + N(i1,i2)*(2-delta(i1)-delta(i2))
x(i2) -x(i1) <= DELTA + N(i1,i2)*(2-delta(i1)-delta(i2))
end-do
! Limit on available personnel (knapsack constraint)
sum(i in PRODS) P(i)*delta(i) <= Pmax
! Objective: total sales price
TotYield:= sum(i in PRODS) Y(i)*x(i)
! Solve the problem
setparam("XPRS_VERBOSE", true)
maximize(TotYield)
writeln("Solution: Yield=", getobjval)
writeln(getparam("XPRS_SIMPLEXITER"), " iterations, ", getparam("XPRS_NODES"), " nodes")
end-model