Planning problems
Description
| Problem name and type, features | Difficulty | Related examples |
| C‑1 | Planning the production of bicycles: Production planning (single product) | *** | |
|---|
| modeling inventory balance; inline if, forall-do |
| C‑2 | Production of drinking glasses: Multi-item production planning | ** | prodplan_graph.mos |
|---|
| modeling stock balance constraints; inline if, index value 0 |
| C‑3 | Material requirement planning: Material requirement planning (MRP) | ** | |
|---|
| working with index (sub)sets, dynamic initialization, automatic finalization, as |
| C‑4 | Planning the production of electronic components: Multi-item production planning | ** | c2glass.mos |
|---|
| modeling stock balance constraints; inline if |
| C‑5 | Planning the production of fiberglass: Production planning with time-dependent production cost | *** | transship_graph.mos |
|---|
| representation of multi-period production as flow; encoding of arcs, exists, create, isodd, getlast, inline if |
| C‑6 | Assignment of production batches to machines: Generalized assignment problem | * | assignment_graph.mos |
|---|
Further explanation of this example:
'Applications of optimization with Xpress-MP', Chapter 8: Production planning
Source Files
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Data Files
c6assign.mos
(!******************************************************
Mosel Example Problems
======================
file c6assign.mos
`````````````````
Machine assignment for production batches
10 batches must be produced in the upcoming period. There
are 5 machines that can produce any given batch. However,
processing time and cost depends on machine assignment.
Each machine has a max production capacity. Determine the
batch to machine assignment that minimizes the total cost
of production.
This is a generalized assignment problem and is a very
compact mathematical model. Each batch must be assigned
to only one machine and each machine must produce no more
than its specified capacity.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "C-6 Machine assignment"
uses "mmxprs"
declarations
MACH = 1..5 ! Set of machines
PRODS = 1..10 ! Set of production batches
CAP: array(MACH) of integer ! Machine capacities
DUR: array(MACH,PRODS) of integer ! Production durations
COST: array(MACH,PRODS) of integer ! Production costs
use: array(MACH,PRODS) of mpvar ! 1 if machine assigned to batch,
! 0 otherwise
end-declarations
initializations from 'c6assign.dat'
DUR CAP COST
end-initializations
! Objective: total production cost
Cost:= sum(m in MACH, p in PRODS) COST(m,p)*use(m,p)
! Assign a single machine to every batch
forall(p in PRODS) sum(m in MACH) use(m,p) = 1
! Limits on machine capacities
forall(m in MACH) sum(p in PRODS) DUR(m,p)*use(m,p) <= CAP(m)
forall(m in MACH, p in PRODS) use(m,p) is_binary
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ",getobjval)
forall(m in MACH) do
write("Machine ", m, ": ")
forall(p in PRODS)
if (getsol(use(m,p))=1) then
write(p, " ")
end-if
writeln(" (total duration: ", getsol(sum(p in PRODS) DUR(m,p)*use(m,p)), ")")
end-do
end-model
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