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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]




b5paint.mos

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

   file b5paint.mos
   ````````````````
   Planning of paint production

   5 batches of paint needs produced each week. The blender
   needs cleaned between each batch. Blending and cleaning
   times vary by color and paint type. What is the order of the 
   batches so that all 5 are completed in the quickest time?

   A new loop type ('repeat-until') is introduced to enumerate
   the batches in scheduled order. The function 'integer' 
   is used to transform the solution variables from real so 
   that the value is truncated and is displayed as an integer.
   
   (c) 2008-2022 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)

model "B-5 Paint production"
 uses "mmxprs", "mmsystem"

 declarations   
  NJ = 5                             ! Number of paint batches (=jobs)
  JOBS=1..NJ

  DUR: array(JOBS) of integer        ! Durations of jobs
  CLEAN: array(JOBS,JOBS) of integer ! Cleaning times between jobs

  succ: array(JOBS,JOBS) of mpvar    ! =1 if batch i is followed by batch j,
                                     ! =0 otherwise
  y: array(JOBS) of mpvar            ! Variables for excluding subtours
 end-declarations

 initializations from 'b5paint.dat'
  DUR CLEAN 
 end-initializations
 
! Objective: minimize the duration of a production cycle
 CycleTime:= sum(i,j in JOBS | i<>j) (DUR(i)+CLEAN(i,j))*succ(i,j)

! One successor and one predecessor per batch
 forall(i in JOBS) sum(j in JOBS | i<>j) succ(i,j) = 1
 forall(j in JOBS) sum(i in JOBS | i<>j) succ(i,j) = 1

! Exclude subtours
 forall(i in JOBS, j in 2..NJ | i<>j) y(j) >= y(i) + 1 - NJ * (1 - succ(i,j))

 forall(i,j in JOBS | i<>j) succ(i,j) is_binary
                                         
! Solve the problem
 minimize(CycleTime)
 
! Solution printing
 writeln("Minimum cycle time: ", getobjval)
 writeln("Sequence of batches:\nBatch Duration Cleaning")
 first:=1 
 repeat
  second:= round(sum(j in JOBS | first<>j) j*getsol(succ(first,j)) )
  writeln(formattext("  %g%8g%9g", first, DUR(first), CLEAN(first,second)))
  first:=second
 until (second=1)   

end-model
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