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Scheduling problems

Description
Problem name and type, featuresDifficultyRelated examples
B‑1 Construction of a stadium: Project scheduling (Method of Potentials) *** projplan_graph.mos
2 problems; selection with `|', sparse/dense format, naming and redefining constraints, subroutine: procedure for solution printing, forward declaration, array of set
B‑2 Flow shop scheduling **** flowshop_graph.mos
alternative formulation using SOS1
B‑3 Job shop scheduling *** jobshop_graph.mos
formulating disjunctions (BigM); dynamic array, range, exists, forall-do,array of set, array of list
B‑4 Sequencing jobs on a bottleneck machine: Single machine scheduling *** sequencing_graph.mos
3 different objectives; subroutine: procedure for solution printing, localsetparam, if-then
B‑5 Paint production: Asymmetric Traveling Salesman Problem (TSP) ***
solution printing, repeat-until, cast to integer, selection with `|', round
B‑6 Assembly line balancing ** linebal_graph.mos
encoding of arcs, range


Further explanation of this example: 'Applications of optimization with Xpress-MP', Chapter 7: Scheduling problems

mosel_app_2.zip[download all files]

Source Files
By clicking on a file name, a preview is opened at the bottom of this page.
b1stadium.mos[download]
b1stadium2.mos[download]
b2flowshop.mos[download]
b3jobshop.mos[download]
b3jobshop2.mos[download]
b3jobshop3.mos[download]
b4seq.mos[download]
b5paint.mos[download]
b6linebal.mos[download]

Data Files
b1stadium.dat[download]
b1stadium2.dat[download]
b2flowshop.dat[download]
b3jobshop.dat[download]
b3jobshop2.dat[download]
b3jobshop3.dat[download]
b4seq.dat[download]
b5paint.dat[download]
b6linebal.dat[download]




b3jobshop.mos

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

   file b3jobshop.mos
   ``````````````````
   Job shop production planning.

   Three types of wallpaper pass through three machines in
   different orders depending on the design. Processing times
   differ based on surface and design. What order should the
   paper be scheduled so that the production is completed as soon
   as possible.

   Let 'JOBS' represent a printing job for one paper. In total,
   there are 8 jobs (2 for paper 1, 3 for paper 2, 3 for paper 3).
   Conjunctive constraints represent the precedence between jobs.
   Disjunctive constraints show that a machine can only have one
   job at a time. Note this problem introduces dynamic arrays and
   a range index. 'range' indicates an unknown index set that
   are consecutive integers. Dynamic arrays are used here for
   arrays with very few entries defined or of a priori unknown size. 

   (c) 2008-2022 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002, rev. Nov. 2017
*******************************************************!)

model "B-3 Job shop"
 uses "mmxprs"
 
 declarations                          
  JOBS=1..8                           ! Set of jobs (operations)

  DUR: array(JOBS) of integer         ! Durations of jobs on machines
  ARC: dynamic array(JOBS,JOBS) of integer   ! Precedence graph
  DISJ: dynamic array(JOBS,JOBS) of integer  ! Disjunctions between jobs
 
  start: array(JOBS) of mpvar         ! Start times of jobs
  finish: mpvar                       ! Schedule completion time
  y: dynamic array(range) of mpvar    ! Disjunction variables
 end-declarations

 initializations from 'b3jobshop.dat'
  DUR ARC DISJ
 end-initializations
 
 BIGM:= sum(j in JOBS) DUR(j)         ! Some (sufficiently) large value

! Precedence constraints
 forall(j in JOBS) finish >= start(j)+DUR(j) 
 forall(i,j in JOBS | exists(ARC(i,j)) ) start(i)+DUR(i) <= start(j)

! Disjunctions
 d:=1
 forall(i,j in JOBS | i<j and exists(DISJ(i,j)) ) do
  create(y(d))
  y(d) is_binary
  start(i)+DUR(i) <= start(j)+BIGM*y(d)
  start(j)+DUR(j) <= start(i)+BIGM*(1-y(d))
  d+=1
 end-do

! Bound on latest completion time
 finish <= BIGM

! Solve the problem: minimize latest completion time
 minimize(finish)

! Solution printing
 writeln("Total completion time: ", getobjval)
 forall(j in JOBS)
  writeln(j, ": ", getsol(start(j)), "-", getsol(start(j))+DUR(j))

end-model
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