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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
- 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 cocoSubFd.mos (!******************************************************* Mosel Example Problems ====================== file cocoSubFd.mos `````````````````` Coco Problem, single factory subproblem. -- Distributed computing version -- *** Not intended to be run standalone - run from cocoMd.mos *** (c) 2010 Fair Isaac Corporation author: S. Heipcke, May 2010 *******************************************************!) model "Coco Subproblem (factory based decomp.)" uses "mmxprs", "mmjobs" parameters Factory = 0 TOL = 0.00001 DATAFILE = "coco3.dat" RMT = "rmt:" ! Files are on (remote) root node end-parameters forward procedure process_solution declarations PHASE_0=2 ! Event codes sent to submodels PHASE_1=3 PHASE_2=4 PHASE_3=5 EVENT_SOLVED=6 ! Event codes sent by submodels EVENT_FAILED=7 EVENT_READY=8 NPROD, NFACT, NRAW, NT: integer end-declarations send(EVENT_READY,0) ! Model is ready (= running) initializations from RMT+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,TIME) of mpvar ! Amount of products made at factory sell: array(PRODS,TIME) of mpvar ! Amount of product sold from factory buy: array(RAW,TIME) of mpvar ! Amount of raw material bought pstock: array(PRODS,1..NT+1) of mpvar ! Product stock levels at start ! of period t rstock: array(RAW,1..NT+1) of mpvar ! Raw material stock levels ! at start of period t sol_make: array(PRODS,TIME) of real ! Amount of products made sol_sell: array(PRODS,TIME) of real ! Amount of product sold sol_buy: array(RAW,TIME) of real ! Amount of raw mat. bought sol_pstock: array(PRODS,1..NT+1) of real ! Product stock levels sol_rstock: array(RAW,1..NT+1) of real ! Raw mat. stock levels Profit: linctr ! Profit of proposal Price_sell: array(PRODS,TIME) of real ! Dual price on sales limits end-declarations initializations from RMT+DATAFILE REV CMAKE CBUY REQ MXSELL MXMAKE IPSTOCK IRSTOCK MXRSTOCK CPSTOCK CRSTOCK end-initializations ! Product stock balance forall(p in PRODS,t in TIME) PBal(p,t):= pstock(p,t+1) = pstock(p,t) + make(p,t) - sell(p,t) ! Raw material stock balance forall(r in RAW,t in TIME) RBal(r,t):= rstock(r,t+1) = rstock(r,t) + buy(r,t) - sum(p in PRODS) REQ(p,r)*make(p,t) ! Capacity limit at factories forall(t in TIME) MxMake(t):= sum(p in PRODS) make(p,t) <= MXMAKE(Factory) ! Limit on the amount of prod. p to be sold forall(p in PRODS,t in TIME) sell(p,t) <= MXSELL(p,t) ! Raw material stock limit forall(t in 2..NT+1) MxRStock(t):= sum(r in RAW) rstock(r,t) <= MXRSTOCK ! Initial product and raw material stock levels forall(p in PRODS) pstock(p,1) = IPSTOCK(p,Factory) forall(r in RAW) rstock(r,1) = IRSTOCK(r,Factory) ! Total profit Profit:= sum(p in PRODS,t in TIME) REV(p,t) * sell(p,t) - ! revenue sum(p in PRODS,t in TIME) CMAKE(p,Factory) * make(p,t) - ! prod. cost sum(r in RAW,t in TIME) CBUY(r,t) * buy(r,t) - ! raw mat. sum(p in PRODS,t in 2..NT+1) CPSTOCK * pstock(p,t) - ! p storage sum(r in RAW,t in 2..NT+1) CRSTOCK * rstock(r,t) ! r storage ! (Re)solve this model until it is stopped by event "PHASE_3" repeat wait ev:= getnextevent Phase:= getclass(ev) if Phase=PHASE_3 then ! Stop the execution of this model break end-if Price_convex:= getvalue(ev) ! Get new pricing data if Phase<>PHASE_0 then initializations from "bin:" + RMT+ "Price_sell.dat" Price_sell end-initializations end-if ! (Re)solve this model if Phase=PHASE_0 then maximize(Profit) elif Phase=PHASE_1 then maximize(sum(p in PRODS,t in TIME) Price_sell(p,t)*sell(p,t) + Price_convex) else ! PHASE 2 maximize( Profit - sum(p in PRODS,t in TIME) Price_sell(p,t)*sell(p,t) - Price_convex) end-if writeln("Factory ", Factory, " - Obj: ", getobjval, " Profit: ", getsol(Profit), " Price_sell: ", getsol(sum(p in PRODS,t in TIME) Price_sell(p,t)*sell(p,t) ), " Price_convex: ", Price_convex) fflush if getobjval > TOL then ! Solution found: send values to master process_solution elif getobjval <= TOL then ! Problem is infeasible (Phase 0/1) or send(EVENT_FAILED,0) ! no improved solution found (Phase 2) else send(EVENT_READY,0) end-if until false !----------------------------------------------------------- ! Process solution data procedure process_solution forall(p in PRODS,t in TIME) do sol_make(p,t):= getsol(make(p,t)) sol_sell(p,t):= getsol(sell(p,t)) end-do forall(r in RAW,t in TIME) sol_buy(r,t):= getsol(buy(r,t)) forall(p in PRODS,t in 1..NT+1) sol_pstock(p,t):= getsol(pstock(p,t)) forall(r in RAW,t in 1..NT+1) sol_rstock(r,t):= getsol(rstock(r,t)) Prop_cost:= getsol(Profit) initializations to "bin:" + RMT + "sol_"+Factory+".dat" sol_make sol_sell sol_buy sol_pstock sol_rstock Prop_cost end-initializations send(EVENT_SOLVED,0) end-procedure end-model | |||||||||||||||||||

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