یک الگوریتم ساده و بهتر برای حل سیستم کنترل موجودی مدیریت فروشنده برای مدل مقدار سفارشی اقتصادی چند محصولی با محدودیت چندگانه

This research presents an alternative heuristic algorithm to solve the vendor management inventory system with multi-product and multi-constraint based on EOQ with backorders considering two classical backorders costs: linear and fixed. For this type of inventory system, the optimization problem is a nonlinear integer programming (NLIP). Several numerical examples are given to demonstrate that the proposed heuristic algorithm is better than the previous genetic algorithm published based on three aspects: the total cost, the number of evaluations of the total cost function and computational time. Furthermore, the proposed algorithm is simpler and can be implemented by any people.

Almost a century ago, the economic order quantity (EOQ) inventory model without backorders was proposed by Harris (1913). Five years later, the economic production quantity (EPQ) inventory model without backorders was proposed by Taft (1918). Later, Hadley and Whitin (1963) proposed the EOQ/EPQ inventory models with backorders. A complete review of different optimization methods used in inventory field can be seen in Cárdenas-Barrón (2011). Recently, Pasandideh, Niaki, and Nia (2011) presented a genetic algorithm for vendor management inventory system with multi-product, multi-constraint based on EOQ with backorders considering two classical backorders costs: linear and fixed. In the vendor management inventory system both retailer and supplier manage their inventories in a win to win manner. The vendor management inventory has attracted the attention of the researchers and practitioners, e.g. Kwak et al., 2009, Lin et al., 2010 and Arora et al., 2010, just to name a few recently works. We have read the paper with considerable interest. Pasandideh et al. (2011) solved a hard optimization problem thorough a valuable and elegant approach based on genetic algorithms. Genetic algorithms have received an increasing attention from the researchers and practitioners since they give us an alternative to traditional optimization techniques. This approach uses a directed random search to locate very good solutions for complex optimization problems in many different fields of study. The use of genetic algorithms to solve inventory problems has been a common research topic recently. However, in some cases, the genetic algorithms are computationally expensive as Cárdenas-Barrón (2010) stated. We found some interesting points to discuss: (1) the mathematical formulation of the problem has some shortcomings, (2) some of solutions to the test problems are infeasible and (3) there exist better solutions for the test problems.

In this paper, we have presented an alternative heuristic algorithm to solve a vendor management inventory system with multi-product, multi-constraint based on EOQ with backorders considering two classical backorders costs: linear and fixed. The proposed heuristic algorithm always obtains better solutions than the solutions of the genetic algorithm proposed by Pasandideh et al. (2011). Additionally, the heuristic algorithm finds near-optimal solutions due to the fact that they are close to the lower bound. Furthermore, the proposed heuristic algorithm is simple. It does not require tedious computational effort and obtains the solution in a very short time. We conclude that the proposed heuristic algorithm performs very well on the all tested problems. Further research can be performed to get improvements on the proposed heuristic algorithms to obtain better solutions to the NLIP problem.