“…The two warehouse inventory modeling problem was introduced by Hartley (1976) and later was developed to include realistic aspects of the inventory system, such as item deterioration (Bhunia and Maiti, 1998;Yang, 2004Yang, , 2006Rong et al, 2008;Hsieh et al, 2008;Lee and Hsu, 2009;Thangam and Uthayakumar, 2010;Liang and Zhou, 2011), and backlogging (Goswami and Chaudhuri, 1992;Bhunia and Maiti, 1998;Zhou, 2003;Yang, 2004Yang, , 2006Rong et al, 2008;Hsieh et al, 2008;Jaggi and Verma, 2008). In addition, other issues such as stock-level dependent demand (Zhou and Yang, 2005;Mondal et al, 2007;Bhunia et al, 2011), item quality (Chung et al, 2009) and trade credit (Thangam and Uthayakumar, 2010;Liang and Zhou, 2011) are incorporated to reflect different cases of the inventory system. Different from the classical models that focus on the inventory level of a single item, Maiti et al (2006) introduced a nonlinear model and applied real-code genetic algorithm to solve a variant of the problem, which involves multi-item inventory levels.…”