مشکل تعیین اندازه دسته تولید مشترک اقتصادی برای یک زنجیره تامین سه لایه با تقاضای تصادفی

This paper considers the joint economic lot-sizing problem (JELP) for multi-layer supply chain with multi-retailers and single manufacturer and supplier. The paper extends the work of (Ben-Daya et al., 2013) and relaxes the assumption of deterministic demand and constant holding and ordering costs. The paper proposes modifying four computational intelligent algorithms to solve mixed integer problems and compares their performance for solving the problem at hand. The paper, further, compares between adopting a centralized safety stock policy versus a decentralized policy. Results showed cuckoo search to outperform other tested algorithms and, also, favored adopting a centralized policy.

The unprecedented competitive business environment in the past twenty years has brought supply chain management to the surface as one of the most influential strategies used for enhancing organizational competitiveness (Gunasekaran et al., 2008, Moncayo-Martínez and Zhang, 2013 and Moncayo-Martínez and Zhang, 2011). Organizations are not only seeking an enhanced internal operational efficiency but also coordinating with their customers and suppliers for the efficient management of inventories across the supply chain (Sari et al., 2012). With this regard, all parties are seeking an economic order quantity (EOQ) based-policy that ensures the fulfillment of customers’ demand while minimizing their integrated total cost function (Ben-daya and As’ad, 2009 and Harris, 1913). Such a problem is generally called the joint economic lot-sizing problem (JELS) (Sari et al., 2012). This problem has been the focus of a major stream of articles in the supply chain body of knowledge starting with Goyal (1977) to recent ones such as Ben-Daya et al. (2013). The reader is kindly referred to Ben-Daya et al. (2008), Glock (2012a) for a comprehensive review on the problem. Recent literature shows a noticeable number of articles that aimed to develop mathematical models addressing this class of problems with a primary objective of identifying the optimal coordinated production and shipment policy with a minimum chain-wide total cost (Ben-daya and As’ad, 2009). The vast majority of these models were limited to two layer supply chains with deterministic constant demand and with single-vendor single-buyer (Ben-daya and As’ad, 2009 and Glock, 2012b). Building on the work of Ben-daya and As’ad (2009), an enhanced optimization model of JELS was proposed in Ben-Daya et al. (2013) for a three layers network with a single supplier, a single manufacturer, and multi-retailers. Getting the optimal solution for NLIP models using traditional mathematical methods is difficult even by using specialized software as it will be computationally expensive (Cárdenas-Barrón et al., 2012). Thus, the model was solved by relaxing all integer decision variables to continuous variables to convert the model from non-linear integer programming (NLIP) to a non-linear programming (NP).The authors, then, used algebraic methods to drive a near optimal solution and developed an algorithm to get the integer values for those relaxed decision variables. Some mathematical shortcoming in the model was later corrected in Cárdenas-Barrón et al. (2012) and an algorithm was proposed and proved to find the integer values more efficiently and effectively with respect to CPU time than the algorithm developed in Ben-Daya et al. (2013). To bear a better resemblance to practice, this paper studies the effect of relaxing the assumptions of deterministic demand and the assumption of holding and ordering costs equality among all retailers as was in the former models. Besides solving the new problem using derivative-free method, the paper proposes, implements, and compares four bio-inspired algorithm for solving this problem given its stochastic nature. Following the introduction section, the rest of this paper is organized as follows. Section 2 defines the problem under consideration and the proposed model assumptions. The mathematical model is developed in Section 3 and model analysis methods are provided in Section 4. Numerical analysis are presented in Section 5 and, finally, concluding remarks are given in Section 6.

This paper considered the joint economic lot-sizing problem (JELP) for multi-layer supply chain with multi-retailers and single manufacturer and supplier. A mathematical model that tolerates for stochastic demand and varying holding and ordering costs was proposed as an extension to the work of Ben-Daya et al. (2013). In addition to solving the model using an algebraic solution method as in Ben-Daya et al. (2013), Cárdenas-Barrón et al. (2012), the paper proposed, implemented, and tested the performance of four computational intelligent algorithms, namely: particle swarm optimization (PSO); gravitational search algorithm (GSA); cuckoo search (CS); and charged system search (CSS). Those algorithms were modified to deal with mixed integer variables so that they can solve the problem at hand. The numerical analysis provided showed CS to be the best algorithm in solving the problem followed by CSS. The paper, further, tested the effect of adopting a centralized vs. decentralized safety stock and results came consistent with literature favoring following a centralized policy form the cost perspective.