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
By clicking on a file name, a preview is opened at the bottom of this page.
Data Files
c4compo.mos
(!******************************************************
Mosel Example Problems
======================
file c4compo.mos
````````````````
Planning the production of electronic components
A company produces cards with microchips and electronic
badges. They also produce the components for these. The
company would like to meet the forecasted demand while
minimizing the cost associated to production, storage,
and product changes.
This is a simple planning problem with an addition of
one new cost type (product changes). A balance constraint
is necessary to define the products stored from one period
to the next.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002
*******************************************************!)
model "C-4 Electronic components"
uses "mmxprs"
declarations
NT = 6 ! Number of time periods (months)
MONTHS = 1..NT
PRODS = 1..4 ! Set of components
DEM: array(PRODS,MONTHS) of integer ! Demand of components per month
CPROD: array(PRODS) of integer ! Production costs
CSTOCK: array(PRODS) of real ! Storage costs
CADD,CRED: real ! Cost of additional/reduced prod.
ISTOCK,FSTOCK: array(PRODS) of integer ! Initial and final stock levels
produce: array(PRODS,MONTHS) of mpvar ! Quantities produced per month
store: array(PRODS,MONTHS) of mpvar ! Stock levels at end of every month
reduce: array(MONTHS) of mpvar ! Reduction of production per month
add: array(MONTHS) of mpvar ! Increase of production per month
end-declarations
initializations from 'c4compo.dat'
DEM CPROD CSTOCK CADD CRED ISTOCK FSTOCK
end-initializations
! Objective: total cost of production, storage, and change of prod. level
Cost:= sum(p in PRODS, t in MONTHS) (CPROD(p)*produce(p,t) +
CSTOCK(p)*store(p,t)) +
sum(t in 2..NT) (CRED*reduce(t) + CADD*add(t))
! Stock balance constraints (satisfy demands)
forall(p in PRODS, t in MONTHS)
store(p,t) = if(t>1, store(p,t-1), ISTOCK(p)) + produce(p,t) - DEM(p,t)
! Changes to the level of production
forall(t in 2..NT)
sum(p in PRODS) (produce(p,t) - produce(p,t-1)) = add(t) - reduce(t)
! Guarantee final stock levels
forall(p in PRODS) store(p,NT) >= FSTOCK(p)
! Solve the problem
minimize(Cost)
! Solution printing
declarations
PNAME: array(PRODS) of string ! Product names
end-declarations
initializations from 'c4compo.dat'
PNAME
end-initializations
writeln("Total cost: ",getobjval)
write(strfmt("Month",13))
forall(t in MONTHS) write(strfmt(t,5))
forall(p in PRODS) do
write("\n", PNAME(p), ": Prod. ")
forall(t in MONTHS) write(strfmt(getsol(produce(p,t)),5))
write("\n", strfmt("Store ",14))
forall(t in MONTHS) write(strfmt("("+store(p,t).sol+")",5))
end-do
write("\nTotal ")
forall(t in MONTHS) write(strfmt(sum(p in PRODS) produce(p,t).sol,5))
writeln
end-model
|
