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Multi-period, multi-site production planning Description The company Coco has two plants that can produce two types
of cocoa powder. The plant capacities are limited.
It is possible to store raw materials and finished product
from one time period to the next. Raw material prices,
sales revenues, and the maximum amount that may be sold
depend on the time period. Raw material storage capacity
is limited.
Storing product between time periods incurs storage costs.
Some product is held in stock at the beginning of the
planning period.
The objective function of maximizing the total profit is
to maximize the sales revenues, minus the cost of production,
buying raw material, and storing finished products and raw
material.
Source Files By clicking on a file name, a preview is opened at the bottom of this page.
Data Files prodplan_graph.mos
(!*******************************************************
Mosel Example Problems
======================
file prodplan.mos
`````````````````
TYPE: Multi-period multi-item production planning
DIFFICULTY: 2
FEATURES: LP or MIP problem, formulation of resource constraints and
material balance constraints, formatted solution printing
DESCRIPTION: The company Coco has two plants that can produce two types
of cocoa powder. The plant capacities are limited.
It is possible to store raw materials and finished product
from one time period to the next. Raw material prices,
sales revenues, and the maximum amount that may be sold
depend on the time period. Raw material storage capacity
is limited.
Storing product between time periods incurs storage costs.
Some product is held in stock at the beginning of the
planning period.
The objective function of maximizing the total profit is
to maximize the sales revenues, minus the cost of production,
buying raw material, and storing finished products and raw
material.
FURTHER INFO: `Applications of optimization with Xpress-MP teaching
material', Section 2.5 `Development of a model'.
Similar problems:
`Applications of optimization with Xpress-MP',
Section 8.2 `Production of drinking glasses',
Section 8.4 `Planning the production of electronic components'
(c) 2008 Fair Isaac Corporation
authors: Y. Colombani & S. Heipcke, 2001, rev. Sep. 2017
*******************************************************!)
model "Coco3"
uses "mmxprs", "mmsvg", "mmsystem"
parameters
PHASE=3
(!
PHASE = 3: Multi-period parameterised model; factories always open (LP)
PHASE = 4: Factories may open/closed freely; when closed save 20000 per month (MIP)
PHASE = 5: Once closed always closed; larger saving (MIP)
!)
end-parameters
declarations
NPROD = 2
NFACT = 2
NRAW = 3
NT = 4
PRODS = 1..NPROD ! Range of products (p)
FACT = 1..NFACT ! factories (f)
RAW = 1..NRAW ! raw materials (r)
TIME = 1..NT ! time periods (t)
REV: array(PRODS,TIME) of real ! Unit selling price of products
CMAKE: array(PRODS,FACT) of real ! Unit cost to make product p
! at factory f
CBUY: array(RAW,TIME) of real ! Unit cost to buy raw materials
COPEN: array(FACT) of real ! Fixed cost of factory f being
! open for one period
REQ: array(PRODS,RAW) of real ! Requirement by unit of product p
! for raw material r
MXSELL: array(PRODS,TIME) of real ! Max. amount of p that can be sold
MXMAKE: array(FACT) of real ! Max. amount factory f can make
! over all products
IPSTOCK: array(PRODS,FACT) of real ! Initial product stock levels
IRSTOCK: array(RAW,FACT) of real ! Initial raw material stock levels
CPSTOCK = 2.0 ! Unit cost to store any product p
CRSTOCK = 1.0 ! Unit cost to store any raw mat. r
MXRSTOCK = 300 ! Raw material storage capacity
make: array(PRODS,FACT,TIME) of mpvar ! Amount of products made at factories
sell: array(PRODS,FACT,TIME) of mpvar ! Amount of product sold from factories
buy: array(RAW,FACT,TIME) of mpvar ! Amount of raw material bought
pstock: array(PRODS,FACT,1..NT+1) of mpvar ! Product stock levels at start
! of period t
rstock: array(RAW,FACT,1..NT+1) of mpvar ! Raw material stock levels
! at start of period t
openm: array(FACT,TIME) of mpvar ! 1 if factory f is open in
! period t, else 0
end-declarations
initializations from 'prodplan.dat'
CMAKE REQ MXMAKE REV as "REVT" CBUY as "CBUYT" MXSELL as "MXSELLT"
IPSTOCK IRSTOCK COPEN
end-initializations
! Objective: maximize total profit
MaxProfit:=
sum(p in PRODS,f in FACT,t in TIME) REV(p,t) * sell(p,f,t) - ! revenue
sum(p in PRODS,f in FACT,t in TIME) CMAKE(p,f) * make(p,f,t) - ! prod. cost
sum(r in RAW,f in FACT,t in TIME) CBUY(r,t) * buy(r,f,t) - ! raw mat.
sum(p in PRODS,f in FACT,t in 2..NT+1) CPSTOCK * pstock(p,f,t) - ! p storage
sum(r in RAW,f in FACT,t in 2..NT+1) CRSTOCK * rstock(r,f,t) ! r storage
! Factory fixed cost
if PHASE=4 then
MaxProfit -= sum(f in FACT,t in TIME) (COPEN(f)-20000)*openm(f,t)
elif PHASE=5 then
MaxProfit -= sum(f in FACT,t in TIME) COPEN(f)* openm(f,t)
end-if
! Product stock balance
forall(p in PRODS,f in FACT,t in TIME)
ProdBal(p,f,t):= pstock(p,f,t+1) = pstock(p,f,t) + make(p,f,t) - sell(p,f,t)
! Raw material stock balance
forall(r in RAW,f in FACT,t in TIME)
RawBal(r,f,t):=
rstock(r,f,t+1) =
rstock(r,f,t) + buy(r,f,t) - sum(p in PRODS) REQ(p,r)*make(p,f,t)
! Capacity limit at factories
forall(f in FACT,t in TIME)
Capacity(f,t):= sum(p in PRODS) make(p,f,t) <= MXMAKE(f)*openm(f,t)
! Limit on the amount of prod. p to be sold
forall(p in PRODS,t in TIME)
Demand(p,t):= sum(f in FACT) sell(p,f,t) <= MXSELL(p,t)
! Raw material stock limit
forall(f in FACT,t in 2..NT+1)
RawStock(f,t):= sum(r in RAW) rstock(r,f,t) <= MXRSTOCK
! Once closed, always closed
if PHASE=5 then
forall(f in FACT,t in 1..NT-1) Closed(f,t):= openm(f,t+1) <= openm(f,t)
end-if
! Initial product and raw material stock levels
forall(p in PRODS,f in FACT) pstock(p,f,1) = IPSTOCK(p,f)
forall(r in RAW,f in FACT) rstock(r,f,1) = IRSTOCK(r,f)
if PHASE>=4 then
forall(f in FACT,t in TIME) openm(f,t) is_binary ! MIP model
else
forall(f in FACT,t in TIME) openm(f,t) = 1 ! LP model
end-if
! Solve the problem
maximize(MaxProfit)
! Solution printing
hline:=60*"-"
writeln("Total profit: ", getobjval)
writeln(hline)
write("Period ")
forall(t in TIME) write(strfmt(t,-13))
writeln("\n", hline)
writeln("Production and finished product stocks\n",
getsize("Production and finished product stocks")*"=")
forall(f in FACT) do
writeln("Factory ", f, ":")
forall(p in PRODS) do
write(" ", p, ": ")
forall(t in TIME) write(strfmt(getsol(make(p,f,t)),6,1), "(",
strfmt(getsol(pstock(p,f,t+1)),5,1), ")")
writeln
end-do
end-do
writeln(hline)
writeln("Raw material bought and stored\n",
getsize("Raw material bought and stored")*"=")
forall(f in FACT) do
writeln("Factory ", f, ":")
forall(r in RAW) do
write(" ", r, ": ")
forall(t in TIME) write(strfmt(getsol(buy(r,f,t)),6,1), "(",
strfmt(getsol(rstock(r,f,t+1)),5,1), ")")
writeln
end-do
end-do
writeln(hline)
writeln("Sales\n",getsize("Sales")*"=")
forall(f in FACT) do
writeln("Factory ", f, ":")
forall(p in PRODS) do
write(" ", p, ": ")
forall(t in TIME) write(strfmt(getsol(sell(p,f,t)),4),9*" ")
writeln
end-do
end-do
writeln(hline)
! Solution drawing
declarations
cum,cumr: array(TIME) of real
end-declarations
FAC:=5
forall(f in FACT,p in PRODS) do
svgaddgroup("F"+f+"_"+p, "Fact "+f+", prod"+p)
svgsetstyle(SVG_FILL,SVG_CURRENT)
forall(t in TIME) do
svgaddrectangle(t*FAC*2,cum(t), 3,(getsol(make(p,f,t)))/FAC)
cum(t)+=(getsol(make(p,f,t)))/FAC
end-do
end-do
(!
forall(f in FACT,r in RAW) do
svgaddgroup("F"+f+"_R"+r, "Fact "+f+", raw mat"+r)
svgsetstyle(SVG_FILL,SVG_CURRENT)
forall(t in TIME) do
svgaddrectangle(t*FAC*2+2,cumr(t), 2(getsol(buy(r,f,t)))/FAC)
cumr(t)+=(getsol(buy(r,f,t)))/FAC
end-do
end-do
!)
svgsetgraphviewbox(0,0,NT*FAC*2+5, 10+1/FAC*max(t in TIME)sum(f in FACT,p in PRODS)getsol(make(p,f,t)))
svgsetgraphscale(FAC)
svgsetgraphlabels("Time", "Production quantities")
svgsave("prodplan.svg")
svgrefresh
svgwaitclose("Close browser window to terminate model execution.", 1)
end-model
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