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Dantzig-Wolfe decomposition: combining sequential and parallel solving Description Dantzig-Wolfe decomposition is a method for solving large
LP problems. The model implementation shows the following
features:
- iterative sequence of concurrent solving of a set of subproblems
- data exchange between several models via shared memory and memory pipe
- coordination of several models via events
Further explanation of this example:
Xpress Whitepaper 'Multiple models and parallel
solving with Mosel', Section 'Dantzig-Wolfe decomposition:
sequential and parallel solving'.
Source Files
Data Files coco3.mos (!******************************************************* Mosel Example Problems ====================== file coco3.mos `````````````` Coco Problem, mid-term model. (c) 2008 Fair Isaac Corporation author: S. Heipcke, r2001, ev. Apr. 2005 *******************************************************!) model "Coco3" uses "mmxprs" parameters DATAFILE = "coco2.dat" end-parameters declarations NPROD, NFACT, NRAW, NT: integer end-declarations initializations from DATAFILE NPROD NFACT NRAW NT end-initializations declarations 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 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: real ! Unit cost to store any product p CRSTOCK: real ! Unit cost to store any raw mat. r MXRSTOCK: real ! 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 end-declarations initializations from DATAFILE REV CMAKE CBUY REQ MXSELL MXMAKE IPSTOCK IRSTOCK MXRSTOCK CPSTOCK CRSTOCK end-initializations ! Product stock balance forall(p in PRODS,f in FACT,t in TIME) PBal(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) RBal(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) MxMake(f,t):= sum(p in PRODS) make(p,f,t) <= MXMAKE(f) ! Limit on the amount of prod. p to be sold forall(p in PRODS,t in TIME) sum(f in FACT) sell(p,f,t) <= MXSELL(p,t) ! Raw material stock limit forall(f in FACT,t in 2..NT+1) MxRStock(f,t):= sum(r in RAW) rstock(r,f,t) <= MXRSTOCK ! 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) ! Objective: maximize total profit Profit:= 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 ! Solve the problem maximize(Profit) ! Solution printing writeln("Total profit: ", getobjval) writeln("Finished products:") 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("Raw material:") 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("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)) writeln end-do end-do end-model | |||||||||||||||||||||||||||

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