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A Fuzzy Linear Programming Approach for Aggregate Production Planning

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Supply Chain Management Under Fuzziness

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 313))

Abstract

Aggregate Production Planning (APP) is considered as an important stage in production systems, since it links operations with strategies and plays a key role in enterprise resource planning and organizational integration. An effective APP should not only provide the minimization of production and inventory costs, but also increase the level of service available to the customers. When maintaining APP, some of cost and demand parameters cannot be frequently determined as crisp values. Fuzzy logic is utilized in many engineering applications so as to handle imprecise data. This chapter provides a mathematical programming framework for aggregate production planning problem under imprecise data environment. After providing background information about APP problem, together with fuzzy linear programming, the fuzzy linear programming model of APP is solved on an illustrative example for different α-cut values.

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Author information

Authors and Affiliations

  1. Department of Transport, Technical University of Denmark, P.O. Zip 2800Kgs, Lyngby, Copenhagen, Denmark

    Cagatay Iris

  2. Department of Industrial Engineering, Istanbul Technical University, P.O. Box 34367, Istanbul, Turkey

    Emre Cevikcan

Authors
  1. Cagatay Iris
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  2. Emre Cevikcan
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Corresponding author

Correspondence to Emre Cevikcan .

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Istanbul Technical University, İstanbul, Turkey

    Cengiz Kahraman

  2. Department of Industrial Engineering, Istanbul Technical University, İstanbul, Turkey

    Başar Öztayşi

Appendix: LINGO code of given Aggregate Production Planning Model

Appendix: LINGO code of given Aggregate Production Planning Model

  • MODEL:

    • SETS:

    • months/1..6/:P,W,O,H,F,I,B,WD,D,pc,hc,oc,fc,ic,bc;

    • ENDSETS

  • min = @sum(months(t):pc(t)*P(t) + 8*WD(t)*W(t)*6 + oc(t)*O(t) + hc(t)*H(t) + fc(t)*F(t) + ic(t)*I(t) + bc(t)*B(t));

    • @for(months(t)| t#GT#1: P(t) + I(t − 1) + B(t) − I(t) − B(t − 1) = D(t););

    • P(1) + I0 + B(1) − I(1) − B0 = D(1);

    • @for(months(t)| t#GT#1: W(t) − W(t − 1) − H(t) + F(t) = 0;);

    • W(1) − W0 − H(1) + F(1) = 0;

    • @for(months(t): 90*P(t) − 8*WD(t)*W(t) − O(t) < 0;);

    • @for(months(t):O(t) <= 0.25*W(t)*WD(t)*8;);

    • B(6) = 0;

    • @for(months(t): @GIN(H));

    • @for(months(t): @GIN(F));

    • @for(months(t): @GIN(W));

    • @for(months(t): @GIN(P));

    • DATA:

    • D = 100,100,150,200,150,100;

    • WD = 15,15,18,18,15,15;

    • pc = 7, 8, 8, 8, 7, 8;

    • oc = 22.5,22.5,27,27,22.5,22.5;

    • hc = 1000,1000,1000,1000,1000,1000;

    • fc = 1500,750,1250,1000,1500,950;

    • ic = 3, 4, 4, 4, 3, 2;

    • bc = 20,25,25,25,20,15;

    • I0 = 3;

    • B0 = 0;

    • W0 = 0;

    • ENDDATA

  • END

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Iris, C., Cevikcan, E. (2014). A Fuzzy Linear Programming Approach for Aggregate Production Planning. In: Kahraman, C., Öztayşi, B. (eds) Supply Chain Management Under Fuzziness. Studies in Fuzziness and Soft Computing, vol 313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53939-8_15

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  • DOI: https://doi.org/10.1007/978-3-642-53939-8_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53938-1

  • Online ISBN: 978-3-642-53939-8

  • eBook Packages: EngineeringEngineering (R0)

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