الگوریتم ژنتیک تنظیم شده با پارامتر برای مدل مقدار تولید اقتصادی چند محصولی با محدودیت فضا، سفارشات تحویلی گسسته و کمبود

In this paper, a multi-product economic production quantity problem with limited warehouse-space is considered in which the orders are delivered discretely in the form of multiple pallets and the shortages are completely backlogged. We show that the model of the problem is a constrained non-linear integer program and propose a genetic algorithm to solve it. Moreover, design of experiments is employed to calibrate the parameters of the algorithm for different problem sizes. At the end, a numerical example is presented to demonstrate the application of the proposed methodology.

The economic production quantity (EPQ) is one of the most applicable models in production and inventory control environments. This model can be considered as an extension to the well-known economic order quantity (EOQ) model that was introduced by Harris [1] in 1913. Regardless of the simplicity of EOQ and EPQ, they are still applied industry-wide today [2]. In spite of wide acceptance, some practitioners and researchers have questioned the practical applications of the EOQ model due to several unrealistic assumptions regarding model input parameters. These parameters are setup costs, holding costs and demand rate. For example Woolsey [3] severely critiqued the use of the EOQ model, arguing that the assumptions (i.e. constant demand, fixed carrying capacity, constant price, unlimited storage capacity, and paying for the price of items as soon as they are received) necessary to justify the use of this model are not met in real world environment. This has motivated many researchers to modify the EOQ model to match real-life situations. Chang et al. [4] developed an EOQ model for deteriorating items, in which the supplier provides a permissible delay to the purchaser if the order quantity is greater than or equal to a predetermined quantity. Li et al. [5] developed EPQ-based models with planned backorders to evaluate the impact of the postponement strategy on a manufacturer in a supply chain. They derived the optimal total average costs per unit time for producing and keeping end-products in a postponement system and a non-postponement system, respectively.

In this paper a multi-product EPQ model with limited warehouse space was presented in which the orders were delivered discretely in the form of multiple pallets. Moreover, it was assumed that the shortages were allowed and were completely backlogged. Under these conditions, the problem was formulated as a non-linear integer-programming model and a parameter-tuned genetic algorithm was proposed to solve it.