A branch‐and‐price approach for the stochastic generalized assignment problem

Abstract

In this article, we address a stochastic generalized assignment machine scheduling problem in which the processing times of jobs are assumed to be random variables. We develop a branch‐and‐price (B&P) approach for solving this problem wherein the pricing problem is separable with respect to each machine, and has the structure of a multidimensional knapsack problem. In addition, we explore two other extensions of this method—one that utilizes a dual‐stabilization technique and another that incorporates an advanced‐start procedure to obtain an initial feasible solution. We compare the performance of these methods with that of the branch‐and‐cut (B&C) method within CPLEX. Our results show that all B&P‐based approaches perform better than the B&C method, with the best performance obtained for the B&P procedure that includes both the extensions aforementioned. We also utilize a Monte Carlo method within the B&P scheme, which affords the use of a small subset of scenarios at a time to estimate the “true” optimal objective function value. Our experimental investigation reveals that this approach readily yields solutions lying within 5% of optimality, while providing more than a 10‐fold savings in CPU times in comparison with the best of the other proposed B&P procedures. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 131–143, 2014

Stokastik Darboğaz Çok Kaynaklı Genelleştirilmiş Atama Problemi

“…Sarin vd. [8], çalışmalarında GAP problemini ele almışlardır. Kaynak tüketiminin stokastik olduğu durum için bir dal fiyat algoritması önermişlerdir.…”

“…Kısıt (7), senaryo bazında kapasite kısıtıdır. Kısıt (8), her senaryo için enbüyük ajan yükünü belirlemektedir. Kısıt (9), 𝑍 𝑤 karar değişkenine ait işaret kısıtıdır.…”