Ground transport
Description
| Problem name and type, features | Difficulty | Related examples |
| E‑1 | Car rental: Transport problem | *** | transport_graph.mos |
|---|
| data preprocessing, set operations, sqrt and ^2, if-then-elif |
| E‑2 | Choosing the mode of transport: Minimum cost flow | ** | mincostflow_graph.mos |
|---|
| formulation with extra nodes for modes of transport; encoding of arcs, finalize, union of sets, nodes labeled with strings |
| E‑3 | Depot location: Facility location problem | *** | facilityloc_graph.mos |
|---|
| modeling flows as fractions, definition of model cuts |
| E‑4 | Heating oil delivery: Vehicle routing problem (VRP) | **** | vrp_graph.mos |
|---|
| elimination of inadmissible subtours, cuts; selection with `|', definition of model cuts |
| E‑5 | Combining different modes of transport | *** | |
|---|
| modeling implications, weak and strong formulation of bounding constraints; triple indices |
| E‑6 | Fleet planning for vans | *** | |
|---|
| maxlist, minlist, max, min |
Further explanation of this example:
'Applications of optimization with Xpress-MP', Chapter 10: Ground transport
Source Files
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Data Files
e5combine.mos
(!******************************************************
Mosel Example Problems
======================
file e5combine.mos
``````````````````
Combining different modes of transport
A large load needs to be transported through 5 cities via
3 possible transportation modes. Transportation type can
be changed in any of the three intermediate cities. How
should this load be transported so that the total cost of
transportation and changing modes is minimized?
This problem introduces triple indices for the variable
'change' since this is the change from mode m to mode n
for leg l.
(c) 2008-2022 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)
model "E-5 Combined transport"
uses "mmxprs"
declarations
NL = 4
LEGS = 1..NL ! Legs of the transport
MODES: set of string ! Modes of transport
CTRANS: array(MODES,LEGS) of integer ! Transport cost
CCHG: array(MODES,MODES) of integer ! Cost of changing mode of transport
end-declarations
initializations from 'e5combine.dat'
CTRANS CCHG
end-initializations
declarations
use: array(MODES,LEGS) of mpvar ! 1 if a mode is used, 0 otherwise
change: array(MODES,MODES,1..NL-1) of mpvar ! 1 if change from mode m to n
! at end of leg, 0 otherwise
end-declarations
! Objective: total cost
Cost:= sum(m in MODES, l in LEGS) CTRANS(m,l)*use(m,l) +
sum(m,n in MODES,l in 1..NL-1) CCHG(m,n)*change(m,n,l)
! One mode of transport per leg
forall(l in LEGS) sum(m in MODES) use(m,l) = 1
! Change or maintain mode of transport between every pair of legs
forall(l in 1..NL-1) sum(m,n in MODES) change(m,n,l) = 1
! Relation between modes used and changes
forall(m,n in MODES,l in 1..NL-1) use(m,l) + use(n,l+1) >= 2*change(m,n,l)
forall(m in MODES, l in LEGS) use(m,l) is_binary
forall(m,n in MODES,l in 1..NL-1) change(m,n,l) is_binary
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ", getobjval)
forall(l in LEGS) do
write(" ",l, "-", l+1,": ")
forall(m in MODES | getsol(use(m,l))>0) do
write(m)
break
end-do
end-do
writeln
end-model
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