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
c3toy.mos
(!******************************************************
Mosel Example Problems
======================
file c3toy.mos
``````````````
Planning the production of toy lorrys
A company produces two types of large toy lorry (trucks).
Each toy has 13 components. A subset of items can be assembled
by the company or subcontracted. Given the demand is the
same for both toys, how much should the company buy or
subcontract to meet demand and minimize cost?
Index sets are not fixed and are instead initialized from
the data file when reading the array data. The index sets of dense
arrays are automatically finalized by Mosel. As a consequence,
the arrays of decision variables 'produce' and 'buy' that are
declared in the same declarations block and are first accessed after
data has been initialized (when their index sets are known and
have been finalized) will be created automatically without any
need for an explicit call of the function 'create'.
(c) 2008 Fair Isaac Corporation
author: S. Heipcke, Mar. 2002, re. Mar. 2022
*******************************************************!)
model "C-3 Toy production"
uses "mmxprs", "mmsystem"
declarations
ITEMS: set of string ! Set of all products
FINAL: set of string ! Set of final products
ASMBL: set of string ! Set of assembled products
PREPROD: set of string ! Set of preproducts
CAP: array(ASMBL) of integer ! Capacity of assembly lines
DEM: array(FINAL) of integer ! Demand of lorrys
CPROD: array(ASMBL) of real ! Assembly costs
CBUY: array(ITEMS) of real ! Purchase costs
REQ: array(ASMBL,PREPROD) of integer ! Items req. for assembling a product
produce: array(ASMBL) of mpvar ! Quantity of items produced
buy: array(PREPROD) of mpvar ! Quantity of items bought
end-declarations
initializations from 'c3toy.dat'
DEM CBUY REQ
[CPROD, CAP] as 'ASSEMBLY'
end-initializations
! Objective: total costs
Cost:= sum(p in PREPROD) CBUY(p)*buy(p) +
sum(p in ASMBL) CPROD(p)*produce(p)
! Satisfy demands
forall(p in FINAL) produce(p) >= DEM(p)
! Assembly balance
forall(p in PREPROD) buy(p) + if(p in ASMBL, produce(p), 0) >=
sum(q in ASMBL) REQ(q,p)*produce(q)
! Limits on assembly capacity
forall(p in ASMBL) produce(p) <= CAP(p)
forall(p in PREPROD) buy(p) is_integer
forall(p in ASMBL) produce(p) is_integer
! Solve the problem
minimize(Cost)
! Solution printing
writeln("Total cost: ",getobjval)
writeln("Buy:")
forall(p in PREPROD)
writeln(formattext(" %-18s: %5g", p, getsol(buy(p))))
writeln("Produce:")
forall(p in ASMBL)
writeln(formattext(" %-18s: %5g", p, getsol(produce(p))))
end-model
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