INTRODUCTION INTRODUCTION. Moisès Graells Semi-continuous processes

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1 INTRODUCTION Mosès Graells Barcelona / Catalona / Span Unverstat Poltècnca de Catalunya CEPIMA, PSE research group Emertus Prof. Lus Puganer IECR Specal Issue INTRODUCTION Sem-contnuous processes Elsabet Capón-García, Sergo Ferrer-Nadal, Mosès Graells, and Lus Puganer. An Extended Formulaton for the Flexble Short- Term Schedulng of Multproduct Semcontnuous Plants. Ind. Eng. Chem. Res. 2009, 48, A TSP-based MILP Model for Medum-Term Plannng of Sngle-Stage Contnuous Multproduct Plants. Songsong Lu, Jose M. Pnto, and Lazaros G. Papageorgou. Ind. Eng. Chem. Res. 2008, 47, PRODUCTION PLANNING OF CHEMICAL PROCESSES 3. Mosès Graells Chemcal Engneerng Department Unverstat Poltècnca de Catalunya moses.graells@upc.edu ASSIGNMENT PROBLEMS (LP) THE TRANSPORT PROBLEM STANDARD CASES A sub-class of network problems A commodty can be produced n dfferent locatons (factory) needs to be shpped to dfferent dstrbuton centers (markets) The transportaton problem Mosès Graells.UPC. 1

2 THE TRANSPORT PROBLEM Gven: the shppng costs ( c ) the capacty of each producton center ( a ) the demand at each dstrbuton center ( b ) Determne the optmum shppng plan What does t mean? PROBLEM FORMULATION LINEAR PROGRAM (LP) mn Z = s. t. c x x a x b x 0, TOOLS: The spreadsheet TOOLS: The GAMS package PROBLEM FORMULATION PROBLEM FORMULATION mn Z = s. t. x 0, c x x a x b SETS I cannng plants / SEATTLE, SAN-DIEGO / J markets / NEW-YORK, CHICAGO, TOPEKA / ; PARAMETERS A(I) capacty of plant n cases / SEATTLE 350 SAN-DIEGO 600 / B(J) demand at market n cases / NEW-YORK 325 CHICAGO 300 TOPEKA 275 / ; TABLE D(I,J) dstance n thousands of mles NEW-YORK CHICAGO TOPEKA SEATTLE SAN-DIEGO ; SCALAR F freght n dollars per case per thousand mles /90/ ; PARAMETER C(I,J) transport cost n thousands of dollars per case ; C(I,J) = F * D(I,J) / 1000 ; VARIABLES X(I,J) shpment quanttes n cases Z total transportaton costs n thousands of dollars ; POSITIVE VARIABLE X ; EQUATIONS COST defne obectve functon SUPPLY(I) observe supply lmt at plant DEMAND(J) satsfy demand at market ; COST.. Z =E= SUM((I,J), C(I,J)*X(I,J)) ; SUPPLY(I).. SUM(J, X(I,J)) =L= A(I) ; DEMAND(J).. SUM(I, X(I,J)) =G= B(J) ; MODEL TRANSPORT /ALL/ ; SOLVE TRANSPORT USING LP MINIMIZING Z ; SETS I cannng plants / SEATTLE, SAN-DIEGO / J markets / NEW-YORK, CHICAGO, TOPEKA / ; PARAMETERS A(I) capacty of plant n cases / SEATTLE 350 SAN-DIEGO 600 / B(J) demand at market n cases / NEW-YORK 325 CHICAGO 300 TOPEKA 275 / ; TABLE D(I,J) dstance n thousands of mles NEW-YORK CHICAGO TOPEKA SEATTLE SAN-DIEGO ; SCALAR F freght n dollars per case per thousand mles /90/ ; PARAMETER C(I,J) transport cost n thousands of dollars per case ; C(I,J) = F * D(I,J) / 1000 ; VARIABLES X(I,J) shpment quanttes n cases Z total transportaton costs n thousands of dollars ; POSITIVE VARIABLE X ; EQUATIONS COST defne obectve functon SUPPLY(I) observe supply lmt at plant DEMAND(J) satsfy demand at market ; COST.. Z =E= SUM((I,J), C(I,J)*X(I,J)) ; SUPPLY(I).. SUM(J, X(I,J)) =L= A(I) ; DEMAND(J).. SUM(I, X(I,J)) =G= B(J) ; MODEL TRANSPORT /ALL/ ; SOLVE TRANSPORT USING LP MINIMIZING Z ; SOLVER ( MINOS, CONOPT, CPLEX...) Mosès Graells.UPC. 2

3 INTERFACE & SOLVER ALGEBRAIC MODELING LANGUAGE J x a Abstracton, pen and paper EQ1(I).. SUM(J,X(I,J)) =L= A(I,J) X(1,1)+X(1,2)+X(1,3)... A(1) X(2,1)+X(2,2)+X(2,3)... A(2) X(3,1)+X(3,2)+X(3,3)... A(3) X(4,1)+X(4,2)+X(4,3)... A(4) Input fle GAMS Output fle SOLVER ( MINOS, CONOPT, CPLEX...) AIMMS AMPL APMontor ASCEND GAMS OptmJ Algebrac Modelng Languages (AML) are hgh-level computer programmng languages for descrbng and solvng hgh complexty problems for large scale mathematcal computaton. An AML does not solve those problems drectly; nstead, t calls approprate external algorthms to obtan a soluton. General_Algebrac_Modelng_System EXERCISE COMPARING TOOLS... Use both tools for the same case study Download GAMS.EXE Download TRNSPORT.GMS Compare them: Lst advantages and drawbacks... Is there a clearly better tool? EXCEL xxx GAMS xxx To be flled and dscussed tomorrow MODELING SOFTWARE Why GAMS? Conceved for: Math programmng LP, NLP Dscrete optmzaton MILP, MINLP Reference for: Computer Aded Process Engneerng (CAPE) feld AIChE Journal Computers & Chemcal Engneerng Industral Engneerng and Chemstry Research... MATERIALS AVAILABLE Mosès Graells.UPC. 3

4 OTHER TOOLS... (sutes) OTHER TOOLS... (sutes) MATLAB? LINEAR PROGRAMMING Powerful matrx algebra Poor syntax for complex problems MATLAB? By Mchael C. Ferrs ( Madson-Wsconsn ) Mchael C. Ferrs, Olv L. Mangasaran and Stephen J. Wrght. Lnear Programmng wth MATLAB. MPS-SIAM Seres on Optmzaton, MATGAMS Interface GAMS / Matlab Download t from: matlab/deprecated.html MATLAB? thread/ BACK TO EXCEL MIXED INTEGER NON-LINEAR PROGRAMMING Better look for another tool (TOMLAB) Mosès Graells.UPC. 4

5 Exercse: You ve got the model (a pcture of t! ) Wrte down a problem statement Implement t n EXCEL Fnd the problem soluton Ten mnutes 600 s (SI) Obectve functon to be mnmzed: Makespan, total tme, penalty functons? Constrants: Forcng the same completon tme? Dverse problem formulatons dependng on what you want THE MAKESPAN OBJECTIVE Rsky functons: MIN MAX ABS INT etc. Example: Solver_test.xls The mproved EXCEL Solver Frontlne / Global optmzaton? NLP Solver wth mult-start Evolutonary Solver Model assumptons: Only the assgnment problem s addressed All the lnes are equally weghted (same cost) There are no set-up or cleanng tasks Ths could be consdered by addng more lnear terms Model assumptons: No sequencng problems are consdered There are no sequence dependent change-over tmes or costs Ths has to be consdered by usng another language If there s not It t s prevous Otherwse More varable types and functons wll be needed x N In case or x { 0,1} x R Mosès Graells.UPC. 5

6 WHAT HAVE WE LEARNT? Learn from the standards (Transport) Adapt to your partcular problems (Lnes) Use the avalable tools EXCEL: Allows nce smulaton approach ( + Solver ) GAMS: Allows compact and powerful formulatons Be careful! EXERCICE Sem-contnuous lnes: Why not usng GAMS? semcontnuous_lnes.gms Interfacng GAMS & EXCEL Examples n GDX.zp QUANTITATIVE EXTENSION EXTENDING THE MODEL Includng set-ups, change-over tmes From LP to MILP Mosès Graells.UPC. 6

7 INCLUDING SET-UPS INCLUDING SET-UPS MINLP MILP Bg-M reformulaton CHANGEOVERS CHANGEOVERS Sequence-dependent (IP) Travellng Salesman Problem (TSP) Mller-Tucker-Zemln (MTZ) formulaton Sub-tour excluson CHANGEOVERS CONCLUSIONS The perfect tool does not exst Optmze Smulate Usng Excel Solver (Evolutonary) Valdate Vsualze Mosès Graells.UPC. 7

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