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Local authorities and public services

Description
Problem name and type, featuresDifficultyRelated examples
J‑1 Water conveyance / water supply management: Maximum flow problem ** j1water_graph.mos, g1rely.mos
encoding of arcs, selection with `|', record data structure
J‑2 CCTV surveillance: Maximum vertex cover problem ** j2bigbro_graph.mos, g6transmit.mos, d5cutsh.mos
encoding of network, exists
J‑3 Rigging elections: Partitioning problem **** j3elect_graph.mos, partitioning_graph.mos
algorithm for data preprocessing; file inclusion, 3 nested/recursive procedures, working with sets, if-then, forall-do, exists, finalize
J‑4 Gritting roads: Directed Chinese postman problem **** j4grit_graph.mos
algorithm for finding Eulerian path/graph for printing; encoding of arcs, dynamic array, exists, 2 functions implementing Eulerian circuit algorithm, round, getsize, break, while-do, if-then-else, list handling
J‑5 Location of income tax offices: p-median problem ****
modeling an implication, all-pairs shortest path algorithm (Floyd-Warshall); dynamic array, exists, procedure for shortest path algorithm, forall-do, if-then, selection with `|'
J‑6 Efficiency of hospitals: Data Envelopment Analysis (DEA) ***
description of DEA method; loop over problem solving with complete re-definition of problem every time, naming and declaring constraints


Further explanation of this example: 'Applications of optimization with Xpress-MP', Chapter 15: Local authorities and public services

mosel_app_10.zip[download all files]

Source Files
By clicking on a file name, a preview is opened at the bottom of this page.
j1water.mos[download]
j1water2.mos[download]
j1water_graph.mos[download]
j2bigbro.mos[download]
j2bigbro_graph.mos[download]
j3elect.mos[download]
j3elect_calc.mos[download]
j3elect_calc2.mos[download]
j3elect_graph.mos[download]
j4grit.mos[download]
j4grit2.mos[download]
j4grit_graph.mos[download]
j5tax.mos[download]
j6hospit.mos[download]

Data Files
j1water.dat[download]
j1water2.dat[download]
j2bigbro.dat[download]
j3elect.dat[download]
j3elect2.dat[download]
j4grit.dat[download]
j5tax.dat[download]
j6hospit.dat[download]




j1water.mos

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

   file j1water.mos
   ````````````````
   Water conveyance/water supply management

   A water transport network is provided. Nodes correspond
   to cities, reservoirs, and pumping stations. Arcs
   correspond to pipes. Capacities for each reservoir,
   demand for each city, and capacities for the pipe
   connections are given. How much water should flow through
   each pipe to maximize the flow in the network?

   A network transformation is presented to introduce fictitious
   source and sink nodes. A LP model based on the transport
   network representation is presented.

   (c) 2008 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002
*******************************************************!)

model "J-1 Water supply"
 uses "mmxprs"

 declarations
  ARCS: range                       ! Set of arcs
  NODES=1..12
  
  PIPE: array(ARCS,1..2) of integer ! Definition of arcs (= pipes)
  CAP: array(ARCS) of integer       ! Capacity of arcs
  SOURCE,SINK: integer              ! Number of source and sink nodes
 end-declarations

 initializations from 'j1water.dat'
  PIPE CAP SOURCE SINK
 end-initializations

 declarations
  flow: array(ARCS) of mpvar       ! Flow on arcs
 end-declarations

! Objective: total flow
 TotalFlow:= sum(a in ARCS | PIPE(a,2)=SINK) flow(a)

! Flow balances in nodes
 forall(n in NODES | n<>SOURCE and n<>SINK) 
  sum(a in ARCS | PIPE(a,1)=n) flow(a) = sum(a in ARCS | PIPE(a,2)=n) flow(a)

! Capacity limits
 forall(a in ARCS) flow(a) <= CAP(a)

! Solve the problem
 maximize(TotalFlow)
 
! Solution printing
 writeln("Total flow: ", getobjval)
 forall(a in ARCS) writeln(PIPE(a,1), " -> ", PIPE(a,2), ": ", getsol(flow(a)))
 
end-model
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