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Supply chain management (SCM) (Handfield & Nichols, 1999) has shifted its focus from single-enterprise analysis to multi-enterprise since a single-enterprise mode is facing the challenge of increased competition among enterprises. Different from the single mode, a collaborative supply chain focuses on the coordination of multiple enterprises to integrate their operational activities and decisions. Coordination is perceived as a prerequisite to integrate operations of supply chain entities to achieve common goals and a lack of coordination may result in poor performance of supply chain. Benefits can be accrued from such coordination, such as elimination of excess inventory, low manufacturing costs, increased sales, and improved customer service (Horvath, 2001). A study of the US food industry indicated that poor coordination among supply chain partners was wasting $30 billion annually (Fisher, Raman, & McClelland, 2000). Wal-Mart (Parks, 2001) collaborated with Warner-Lambert to attain mutual benefits. Its lead times were shortened from 21 to 11 days, on-hand inventory was cut by two weeks, orders were more consistent, and sales were increased by 8.5 million dollars.
Supply chain coordination involves multiple aspects, such as logistics, inventory, forecasting, transportation, among which inventory coordination plays a vital role throughout the whole supply chain. A good inventory coordination is able to meet anticipated demands, smooth production requirements, protect against stock-outs and reduce inventory cost. Li (Li & Wang, 2007) reviewed the coordination mechanisms of supply chain in a framework of product/inventory decision structure, and revealed that inventory decision making is mostly driven by the demand downstream. An uncertain demand of customers may cause the bullwhip (Lee, Padmanabhan, & Whang, 1997) effect in the whole supply chain, and as such, it is difficult to coordinate the inventory decision under uncertain demand.
Most of the developed inventory coordination models are based on the restrictive assumption that the demand is a deterministic constant (Banerjee, Kim, & Burton, 2007; Chu & Leon, 2008; Darwish & Odah, 2010; Huang, Huang, & Newman, 2011; Nguyen, Li, Zhang, & Truong, 2014; Ryu, Moon, Oh, & Jung, 2013) or a stochastic variable with a known distribution function (Berling & Marklund, 2013; Kang & Kim, 2010; Kastsian & Mönnigmann, 2011; Seliaman & Ahmad, 2008; Tsou, 2013). However, assuming the demand as a deterministic constant cannot reflect the practical market demand, resulting in an inaccurate inventory coordination scheme; assuming the demand follows a known distribution function makes the model inaccurate when the demand distribution is ambiguous or highly variable, which practitioners frequently encounter in practice. Therefore, there is a need to develop a method to relax the demand assumption to allow a more realistic analysis of the inventory coordination. In this paper, we propose a Monte Carlo simulation model of inventory coordination to mimic the inventory changing procedure of a supply chain with uncertain demand. This model is able to model uncertain demand with an arbitrary distribution function. Moreover, a PSO is combined with the simulation model to find a good quality collaborate scheme. In order to improve search efficiency, fitness inheritance techniques are embedded into the PSO to make it converge quickly.
The contributions of this paper include: (1) a Monte Carlo simulation model of inventory coordination is proposed; and (2) fitness inheritance techniques are introduced into the inventory coordination to reduce the computational effort of Monte Carlo simulation. To the best of our knowledge, there have been no studies using a fitness inheritance PSO to solve such problem.