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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.
- problem formulation alterntives selected via a runtime parameter
- if-then, if-then-else, if-then-elif statements
Further explanation of this example:
'Xpress teaching material', Section 2.5 'Development of a model'.
Similar problems:
'Applications of optimization with Xpress-MP',
Section 8.2 'Production of drinking glasses' (c2glass.mos),
Section 8.4 'Planning the production of electronic components' (c4compo.mos)
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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