Overview of Mosel examples for 'Business Optimization' book
Description
List of FICO Xpress Mosel implementations of examples discussed in the book
'J. Kallrath: Business Optimization Using Mathematical Programming -
An Introduction with Case Studies and Solutions in Various Algebraic
Modeling Languages' (2nd edition, Springer, Cham, 2021, DOI 10.1007/978-3-030-73237-0).
List of provided model files
(Examples marked with * are newly introduced in the 2nd edition,
all other models have been converted from the mp-model versions
that were provided with the 1st edition of the book in 1997.)
| Filename | Description | Section |
| absval.mos | Modeling absolute value terms (linearization) | 6.5 |
* | absval2.mos, absval2a.mos | Modeling absolute value as general constraints | 6.5 |
| bench101.mos | Parkbench production planning problem (solution to Exercise 10.1) | 10.9 |
| bench102.mos | Parkbench production planning problem, MIP problem (solution to Exercise 10.2) | 10.9 |
| blend, blend_graph | Ore blending problem | 2.7.1 |
* | boat.mos | Boat renting problem (solution for Exercise 3.3) | 1.4.1, 3.7 |
* | boat2.mos | Multi-period Boat renting problem | 1.6 |
| boatdual.mos | Dual of the Boat renting problem (solution for Exercise 3.3) | 3.7 |
| brewery.mos | Brewery production planning (data files: brewery.xlsx, brewdata.dat) | 8.3 |
| burgap.mos | Generalized assignment problem (solution for Exercise 7.3) | 7.10 |
| burglar | Small knapsack problem | 7.1.1 |
| buscrew.mos | Bus crew scheduling | 7.8.4 |
| calves.mos | Calves and pigs problem | 3.3.1 |
| carton.mos | Carton production scheduling problem (data file: carton.dat) | 10.3 |
* | ch-2tri.mos | Minimal perimeter convex hull for two triangles | 10.3 |
* | contract.mos, contract_graph | Contract allocation problem with semi-continuous variables | 10.2.1 |
| couples.mos | Feasibility puzzle problem (solution for Exercise 6.5) | 6.11 |
| dea.mos | Data envelopment analysis (solution for Exercise 5.2) | 5.3 |
| dual.mos | Dual problem for a small LP (solution for Exercise 3.1b) | 3.5.1 |
* | dynbigm.mos | Dynamic computation of big-M coefficients for production planning | 14.1.2.1 |
* | dynbigm2.mos | Production planning problem formulation using indicator constraints | 14.1.2.1 |
* | ea_smpld.mos | Evolutionary algorithm for supply management | 14.1.3.3 |
| euro.mos | Choosing investment projects (solution for Exercise 7.5) | 7.10 |
| flowshop.mos, flowshop_graph | Flowshop scheduling problem (solution for Exercise 7.7) | 7.10 |
* | fracprog.mos | Fractional programming example | 11.1 |
| gap.mos | Generalized assignment problem (solution for Exercise 7.2) | 7.10 |
* | goalprog.mos | Lexicographic Goal Programming | 5.4.3 |
* | lagrel.mos | Lagrange relaxation applied to the GAP | 14.1.3.3 |
| lim1.mos, coco | Multi-period, multi-site production planning, LP model (solution for Exercise 5.1) | 5.3 |
| lim2.mos, coco_fixbv | Multi-period, multi-site production planning, MIP model (solution for Exercise 6.7) | 6.11 |
* | manufact.mos | Production scheduling problem with SOS formulation (solution for Exercise 6.9) | 6.11 |
| multk.mos | Multi-knapsack problem (solution for Exercise 7.4) | 7.10 |
| network.mos | Network flow problem (solution for Exercise 4.3) | 4.7 |
| network2.mos | Generic formulation of network flow problem (Exercise 4.3) | 4.7 |
* | newsvendor.mos | Newsvendor problem: 2-stage stochastic programming | 11.3.2.1 |
| npv.mos | Net present value problem (solution for Exercise 6.8) | 6.11 |
* | optgrid.mos, optgrid2.mos | Optimal breakpoints for piecewise linear approximation | 14.2.3 |
* | portfolio.mos | Multi-stage stochastic portfolio investment model | 11.3.2.5 |
| primal.mos | Primal problem for a small LP (solution for Exercise 3.1a) | 3.7 |
| prodx.mos | Simple production planning example | 2.5.2 |
| projschd.mos, projplan_graph | Project scheduling case study | 10.2.3 |
| quadrat.mos | Linearized quadratic programming example | 11.4 |
* | quadrat2.mos | Quadratic programming example solved as NLP | 11.4 |
| set.mos | Set covering problem (solution for Exercise 7.6) | 7.10 |
| simple1.mos | Simple LP problem (solution for Exercise 2.2) | 2.13 |
| simple2.mos | Simple LP problem (solution for Exercise 2.3) | 2.13 |
| slab.mos | Lifting slabs (solution for Exercise 6.6) | 6.11 |
| sludge.mos | Sludge production planning example illustrating recursion | 11.2.1 |
* | sludge2.mos | Recursion example solved as NLP | 11.2.1 |
* | teams.mos | (solution for Exercise 6.4) | 6.11 |
| trim1.mos | Trimloss problem LP formulation (solution for Exercise 4.1) | 4.1.1 |
| trim2.mos | Trimloss problem MIP formulation (solution for Exercise 4.2) | 4.1.2 |
* | trimminlp.mos | Trimloss problem formulated as a MINLP problem | 13.3 |
* | trimminlp2.mos | Alternative NLP solver choice for trimloss problem | 13.3 |
| tsp.mos | Traveling salesman problem (solution for Exercise 7.1) | 7.10 |
* | vrp, vrp_graph | Vehicle routing - heating oil delivery problem | 7.2.3 |
* | woods.mos | (solution for Exercise 2.1) | 2.13 |
| yldmgmt.mos | Yield management, financial modeling | 8.4.2 |
Source Files
By clicking on a file name, a preview is opened at the bottom of this page. Data Files
gap.mos
(!*********************************************************************
Mosel Example Problems
======================
file gap.mos
````````````
Generalised assignment problem (GAP)
Example solution to exercise 7.2 in section 7.10 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, June 2018
(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 'gap'
uses "mmxprs"
declarations
RC=1..3 ! Set of containers
RI=1..8 ! Set of items
C: array(RC,RI) of real ! Cost of delivery on items
W: array(RC,RI) of real ! Weights of items
B: array(RC) of real ! Size of containers
x: array(RC,RI) of mpvar ! Allocate items to containers
end-declarations
C::[27,12,12,16,24,31,41,13,
14,5,37,9,36,25,1,34,
34,34,20,9,19,19,3,34]
W::[21,13,9,5,7,15,5,24,
20,8,18,25,6,6,9,6,
16,16,18,24,11,11,16,18]
B::[26,25,34]
! Objective: minimise total cost
Obj:= sum(i in RC,j in RI) C(i,j)*x(i,j)
! Container capacity is limited
forall(i in RC) Lim(i):=sum(j in RI) W(i,j)*x(i,j)<= B(i)
! Each item must be assigned
forall(j in RI) Conv(j):=sum(i in RC) x(i,j)=1
forall(i in RC,j in RI) x(i,j) is_binary
! Solve the problem
minimise(Obj)
writeln("Solution: ", getobjval)
forall(i in RC)
writeln(" Container ", i, ": ", union(j in RI | x(i,j).sol=1) {j},
" Unused capacity: ", Lim(i).slack)
end-model
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