A Fuzzy Linear Programming Approach for Aggregate Production Planning

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.

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

Corresponding author

Correspondence to Emre Cevikcan .

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

• 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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