ENGINEERING JOURNAL CHIANG MAI UNIVERSITY

Volume 25, No. 03, Month DECEMBER, Year 2018, Pages 151 - 166

Benders decomposition combining with a special purpose method for production/inventory planning having uncertain demand under production constrains

Aphisak Wittayapraphakorn and Peerayuth Charnsethikul

Abstract Download PDF

This article aims to present how to apply Benders Decomposition to the problem of production planning having uncertain demand within a finite horizon under production constrains that the application is divided into 2 methods called “Single Step Bender” and “Bi Step Bender”. According to the experimental results comparing with the result of Integer programming, it is found that both methods can cause the quality results not being different from the result performed by Integer programming with the statistic significant level 0.05. For this experiment, Bender 1 Step leads to the different result from lower bound with the average value 0.0475% , but Bender 2 Step and Integer programming have the average value 0.0495% and 0.0556% respectively. In part of processing time, if it is not a big problem, Bender 2 Step will use time lower than Bender 1 Step. On the other hand, if it is a big problem, Bender 1 Step will use time lower than Bender 2 Step. Moreover, Integer programming cannot provide the answer in case of too big problem.

Keywords

Stochastic linear programming, Production planning under the uncertain demand, Large-scale linear programming problems, Benders Decomposition.

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