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
c5fiber.mos
(!******************************************************
Mosel Example Problems
======================
file c5fiber.mos
````````````````
Planning the production of fiberglass
The next 6 weeks of fiberglass production needs to be
planned. Capacity is limited and varies by week. Production
and storage costs also change over time. Determine
the plan that minimizes total cost of production and
storage while meeting demand for the time period.
This problem introduces a transshipment flow formulation.
The demand and capacity data are represented as node weights
and are combined into a single array 'WEIGHT'. 'ARC' defines
the cost of flow between nodes. Note that since the array of
variables 'flow' is dynamic, it must be created after the data is
read and only for node combinations where 'ARC' exists. Two new
functions are introduced here: 'isodd' determines if an integer
value is odd or even and 'getlast' returns the last entry of a
range or a list.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002, rev. Nov. 2017
*******************************************************!)
model "C-5 Fiberglass"
uses "mmxprs"
declarations
NODES: range ! Production and demand nodes
! odd numbers: production capacities
! even numbers: demands
ARC: dynamic array(NODES,NODES) of real ! Cost of flow on arcs
WEIGHT: array(NODES) of integer ! Node weights (capacities/demand)
flow: dynamic array(NODES,NODES) of mpvar ! Flow on arcs
end-declarations
initializations from 'c5fiber.dat'
ARC WEIGHT
end-initializations
forall(m,n in NODES | exists(ARC(m,n))) create(flow(m,n))
! Objective: total cost of production and storage
Cost:= sum(m,n in NODES | exists(ARC(m,n))) ARC(m,n)*flow(m,n)
! Satisfy demands (flow balance constraints)
forall(n in NODES | isodd(n)=FALSE)
if(n>2, flow(n-2,n), 0) + flow(n-1,n) =
if(n<getlast(NODES), flow(n,n+2), 0) + WEIGHT(n)
! Production capacities
forall(n in NODES | isodd(n)) flow(n,n+1) <= WEIGHT(n)
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ",getobjval)
write("Week")
forall(t in 1..integer(getlast(NODES)/2)) write(strfmt(t,5))
write("\nProd.")
forall(n in NODES | isodd(n))
write(strfmt(getsol(sum(m in NODES) flow(n,m)),5))
write("\nStock")
forall(n in NODES | not(isodd(n)))
write(strfmt(getsol(sum(m in NODES) flow(n,m)),5))
writeln
end-model
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