A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage

The purpose of this paper is to develop a multi-item economic order quantity (EOQ) model with shortage for a single-buyer single-supplier supply chain under green vendor managed inventory (VMI) policy. This model explicitly includes the VMI contractual agreement between the vendor and the buyer such as warehouse capacity and delivery constraints, bounds for each order, and limits on the number of pallets. To create a kind of green supply chain, tax cost of green house gas (GHG) emissions and limitation on total emissions of all items are considered in the model. A hybrid genetic and imperialist competitive algorithm (HGA) is employed to find a near-optimum solution of a nonlinear integer-programming (NIP) with the objective of minimizing the total cost of the supply chain. Since no benchmark is available in mperialist competitive algorithm (ICA) endor managed inventory (VMI) ybrid algorithm reen house gas (GHG) emissions the literature, a genetic algorithm (GA) is developed as well to validate the result obtained. For further validation, the outcomes are also compared to lower bounds that are found using a relaxed model in which all variables are treated continuous. At the end, numerical examples are presented to demonstrate the application of the proposed methodology. Our results proved that the proposed hybrid procedure was able to find better and nearer optimal solutions. © 2015 Published by Elsevier B.V. 39 40 41 42 43 44 45 46 47 48 49 50 51 . Introduction One of the most important problems in companies that utilize endors to provide raw materials, components, and finished prodcts is to determine the order quantity and the points to place rders. Various models in production and inventory control field ave been proposed and devoted to solve this problem in different cenarios. Two of the models that have been employed extensively re the economic order quantity (EOQ) and economic production uantity (EPQ) models (see for example [1,2]). However, these odels are developed based on some assumptions and conditions hat bound their applicability in real-world situations. The EOQ ormula gives an optimal solution when the vendor and buyer Please cite this article in press as: A. Roozbeh Nia, et al., A green vendor managed inventory of multi-item multi-constraint http://dx.doi.org/10.1016/j.asoc.2015.02.004 nventory problems are treated in isolation under the deterministic onditions [3]. ∗ Corresponding author. Tel.: +98 281 3665275; fax: +98 281 3665277. E-mail addresses: [email protected] (A. Roozbeh Nia), [email protected] (M. Hemmati Far), [email protected] (S.T.A. Niaki). ttp://dx.doi.org/10.1016/j.asoc.2015.02.004 568-4946/© 2015 Published by Elsevier B.V. 52 53 54 55 In real business world, sometimes a manufacturer, supplier and markets/retailer would like to make a long-term cooperative relationship as an integrated system to get a tensionless stable source of supply and demand of items as well as reliability to gain optimum profit from each other. Globally, the industrial environment gradually becomes more and more competitive and much effort has been made toward the efficiency and effectiveness. So in this connection, the supply chain (SC) management plays an important role in the present situation [4]. Several programs of collaboration and coordination between SC partners have been successfully implemented in practice. Vendor managed inventory (VMI) is collaborative initiatives that have been theoretically and empirically shown to improve SC efficiency and responsiveness [5]. Under VMI partnership, the vendor (supplier) is responsible for managing inventory levels at the retail store by determining the right timing and size of the orders. In return, the vendor gets a better visibility about the final customer demand. Historically, VMI originated hybrid genetic and imperialist competitive algorithm for EOQ model under shortage, Appl. Soft Comput. J. (2015), in the retail industry to overcome some of the problems regarding the amount of required retail shelf space, the amount of inventory to be kept on hand, inventory obsolescence, and the logistics of returned products [6,7]. The benefits of VMI are well recognized 56 57 58 59