Ground transport
Description
| Problem name and type, features | Difficulty |
| E‑1 | Car rental: Transport problem | *** |
|---|
| data preprocessing, set operations, sqrt and ^2, if-then-elif |
| E‑2 | Choosing the mode of transport: Minimum cost flow | ** |
|---|
| 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 | *** |
|---|
| modeling flows as fractions, definition of model cuts |
| E‑4 | Heating oil delivery: Vehicle routing problem (VRP) | **** |
|---|
| 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
Data Files
e6vanrent.mos
(!******************************************************
Mosel Example Problems
======================
file e6vanrent.mos
``````````````````
Fleet planning for van rental
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "E-6 Van rental"
uses "mmxprs"
declarations
NM = 6
MONTHS = 1..NM ! Months
CONTR = 3..5 ! Contract types
REQ: array(MONTHS) of integer ! Monthly requirements
COST: array(CONTR) of integer ! Cost of contract types
NINIT: integer ! Vans rented at beginning of plan
rent: array(CONTR,MONTHS) of mpvar ! New rentals every month
end-declarations
initializations from 'e6vanrent.dat'
REQ COST NINIT
end-initializations
! Objective: total cost
Cost:= sum(c in CONTR, m in MONTHS) COST(c)*rent(c,m)
! Fulfill the monthly requirements
forall(m in MONTHS)
if(m<=2, NINIT, 0) +
sum(c in CONTR, n in maxlist(1,m-c+1)..minlist(m,NM-c+1)) rent(c,n) >=
REQ(m)
! Solve the problem
minimize(Cost)
! Solution printing
declarations
NAMES: array(MONTHS) of string
end-declarations
initializations from 'e6vanrent.dat'
NAMES
end-initializations
writeln("Total cost: ", getobjval)
write("new rents ")
forall(m in MONTHS) write(NAMES(m), " ")
writeln
forall(c in CONTR) do
write(c, " months ")
forall(m in MONTHS) write(strfmt(getsol(rent(c,m)),5))
writeln
end-do
write("Total ")
forall(m in MONTHS) write(strfmt(getsol(if(m<=2, NINIT, 0) +
sum(c in CONTR, n in maxlist(1,m-c+1)..minlist(m,NM-c+1)) rent(c,n)), 5))
writeln
end-model
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