حل مدل انتخاب تامین کننده چند محصولی با تقاضای تصادفی همراه با سطح خدمات و محدودیت های بودجه با استفاده از الگوریتم ژنتیک

This study presents a stochastic demand multi-product supplier selection model with service level and budget constraints using Genetic Algorithm. Recently, much attention has been given to stochastic demand due to uncertainty in the real world. Conflicting objectives also exist between profit, service level and resource utilization. In this study, the relationship between the expected profit and the number of trials as well as between the expected profit and the combination of mutation and crossover rates are investigated to identify better parameter values to efficiently run the Genetic Algorithm. Pareto optimal solutions and return on investment are analyzed to provide decision makers with the alternative options of achieving the proper budget and service level. The results show that the optimal value for the return on investment and the expected profit are obtained with a certain budget and service level constraint.

Both Genetic Algorithms (GAs) and Supply Chain Management (SCM) are relatively new research areas that capture the interest of many researchers due to their significant contributions. A GA is a promising search technique which based on the mechanics of natural selection and natural genetics. Holland (1975) and his team applied their understanding of the adaptive processes of natural systems to design software for creating artificial systems that retained the robustness of natural systems. During the last decade, GA has been commonly used to solve complex-structured global optimization problems with many variables. Khouja, Michalewicz, and Wilmot (1998) studied the application of GA for solving lot-sizing problems. Poulos, Rigartos, Tzafestas, and Koukos (2001) derived a Pareto-optimal GA for warehouse optimization. Aytug, Khouja, and Vergara (2003) made a review of using GA to solve production and operations management problems. Altiparmak, Gen, Lin, and Paksoy (2006) used a GA approach to optimize supply chain networks with various constraints and constant demand. Liao and Rittscher (2007) developed a multi-objective supplier selection model under normal distribution demand and lead time. Ha and Krishnan (2008) used a hybrid approach to supplier selection and order allocation for the maintenance of a competitive supply chain. Demirtas and Ustun (2008) used an analytic network process and a mixed integer linear programming for supplier selection decisions. In supply chain, the importance of a single order problem has been increasing due to the shortening life cycle of products for the recent years. Hadley and Whitin (1963) derived a constrained multi-item problem in a single period. Khouja (1995) developed a newsboy model in which multiple discounts are used to sell excess inventory. Khouja and Mehrez (1996) extended Khouja’s model (1995) to consider multi-items. Lau and Lau (1996) derived a capacitated multi-product single period inventory model. In this study, a supplier selection for a single buyer with multi-product and stochastic demand in a single period considering service level and budget constraints is developed using GA. This paper is organized as follows: a mathematical model with various constraints is derived in Section 2. The GA solution procedure is illustrated in Section 3. A numerical example and sensitivity analysis are carried out in Sections 4 and 5. Finally, concluding remarks are given in Section 6.

To maximize the expected profit subject to budget or/and service level constraints, we develop a single buyer, stochastic demand, multi-product supplier selection model using GA. The relationship between the expected profit and budget as well as between the return on investment/expected profit and service level are presented in the study. It has been illustrated that the optimal expected profit and the return on investment can be derived for a specific budget and service level. However, the optimal return on investment and the optimal expected profit do not occur at the same service level. The study provides managerial insights for decision makers to maximize their expected profit through the budget and service level control. Further research can be done to investigate the correlations between the return on investment and the expected profit.