سیستم موجودی با توزیع کننده واحد و خرده فروشان چندگانه: سناریوهای عملیاتی و مقایسه عملکرد

We consider a single-distributor multi-retailer inventory system in six operating scenarios for a finite horizon. Five scenarios are in decentralized control and the other one is in centralized control. Approximate dynamic programming (ADP) procedures are developed to obtain system performances for scenarios in decentralized control, and a stochastic dynamic programming approach is applied to the scenario in centralized control. The efficiency and effectiveness of ADP procedures are demonstrated by numerical results. Taking the system performance in centralized control as a benchmark, system performances in decentralized control are investigated and compared for different operating scenarios. The results provide useful insights in system planning and operations.

With advance of information technology, various levels of information sharing emerge in supply chains. The cooperation between Wal-Mart and Procter & Gamble is a successful case (Mason-Jones and Towill, 1997). More and more world class enterprises, e.g., Dell and Cisco, share information with their suppliers to enhance supply chain competitive edge (Zhou and Benton, 2007). Further studies upon impact of supply chain integration in practice can be found in Doyle and Snyder (1999), Vickery et al. (2003), Narasimhan and Jayaram (2007) and Zhou and Benton (2007). Researchers have paid much attention to the value of information sharing. Lee et al. (2000) discuss a single-distributor single-retailer system in decentralized control, in which the demand process is correlated over time and the distributor accesses retailer's information to refine the forecast of demand. Cachon and Fisher (2000), Cachon (2001), Zhao and Xie (2002), Abdul-Jalbar et al. (2009), and Lee and Jeong (2010) address a decentralized control scenario for system consisting of single supplier and multiple retailers. On the other hand, operating scenarios where participators in a supply chain coordinate and collaborate through contracts are extensively investigated (Chen et al., 2001, Cachon, 2003, Wang et al., 2004 and Bernstein and Federgruen, 2005). Investigation through game approaches can be referred to Esmaeili and Zeephongsekul (2010). There exist various ways of information sharing in supply chains. We categorize all information sharing instances in single-distributor multi-retailer systems into the following six different operating scenarios, in which the first five scenarios are in decentralized control. All-independent (AI, for short). There is no information sharing among participators except the information transmission between the distributor and the retailers via ordering. All participators of the supply chain make their decisions based on local information independently. For such scenario, installation-stock policies are discussed by Svoronos and Zipkin (1988) and Axsäter (1998). Distributor-access-retailers (DAR). The distributor is allowed to access full or partial information of retailers, e.g., inventory level and ordering policy, but not a retailer can access the distributor's information. A real case of scenario DAR is that Wal-Mart opens its information to main suppliers (e.g., Procter & Gamble) and the whole system benefits from the sharing ( Mason-Jones and Towill, 1997). The impact of such unilateral information sharing is widely discussed in the literature in terms of demand estimation and forecasting ( Lee et al., 2000, Armony and Plambeck, 2005 and Byrne and Heavey, 2006), echelon-stock policies or position-based policies ( Axsäter and Rosling, 1993 and Axsäter et al., 2008) and other issues ( Lau et al., 2004). Retailers-access-distributor (RAD). In contrast to the situation in scenario DAR, every retailer is allowed to access the distributor's information whereas the distributor cannot access retailers’. Such scenario exists in many third-party logistic systems where the information of the common warehouse is announced to all retailers. This scenario can be observed in B2B e-commerce as well, where all retailers can access the distributor's information via its web site. In a rationing game environment, a retailer accesses distributor's information, estimates available stock at the distributor, and may over-order to hedge against potential shortage in supply. Such inflation can cause information distortion and may low performance of the supply chain. Lee et al. (1997) state that the inflation in a rationing game environment may result in the so-called bullwhip effect and can incur enormous cost increasing. Two-way-access (TWA). The information sharing is bilateral in this scenario. The distributor is allowed to access retailers’ information, and every retailer is also allowed to access the distributor's. This scenario is a combination of scenarios DAR and RAD. As in scenario RAD, retailers may also over-order in a rationing game environment. The distributor faces distorted information from retailers. Two-way information sharing is a significant mechanism for Cisco to enhance supply chain planning, JIT production, and delivery practices ( Zhou and Benton, 2007). All-access (AA). Information is shared systemwide, i.e., all participators of the supply chain can access any other's information. The previous scenarios DAR, RAD and TWA concern vertical information sharing in supply chain, and such scenario AA takes horizontal information sharing into consideration. The incentive of horizontal information sharing in supply chain has been well discussed in the literatures, e.g., Gal-Or (1985), Li (2002), and an empirical examination in motor vehicle industry is presented by Doyle and Snyder (1999). In such scenario, with fully shared information, whether the participators operate selfishly or not may result in different performances of the supply chain. In a cooperating environment, an idea on supply chain coordination is to allow everyone to make decisions based on the information from everyone else, and many enterprise and cross-enterprise systems have been developed under this idea ( Davenport and Brooks, 2004). Centralized-control (CC). A “super-manager” makes centralized decisions instead of decentralized ones. Such scenario has been well discussed ( Chen and Zheng, 1997 and Kim et al., 2005), and it can be applied when the distributor and all retailers belong to the same enterprise. It can also be adopted under special configurations, e.g., vendor-managed inventory (VMI) ( Choi et al., 2004 and Bernstein et al., 2006). Performances comparison is an important issue for supply chain integration and information sharing. However, it is the lack of knowledge on impact of various operating scenarios on supply chain performance. Only a few works can be found in the literature, in which operating policies are pre-specified. Lau et al. (2004) study a three-stage supply chain, in which each participator adopts a (R, Q) policy to control its inventory and may share information with its immediate upstream partner. Disney et al. (2008) examine impact of different coordination strategies on system performance of a two-echelon supply chain, where each echelon implements a generalized order-up-to policy. In this paper, a single-distributor multi-retailer system is considered for a finite horizon. For generality, we do not pre-specify policies for inventory management. System performances are compared in terms of system costs for different operating scenarios. We adopt approximate dynamic programming (ADP, see Powell, 2007) to obtain system costs in the first five scenarios in decentralized control, while a stochastic dynamic programming procedure is implemented for the scenario in centralized control. According to operations of many actual systems, we consider that both inventory levels and ordering histories can be accessed as shared information, and assume that the distributor and retailers make decisions simultaneously. Recently, Qiu et al. (2007) apply a reinforcement learning approach to investigate business service modes on distribution systems which are similar as the scenarios in our paper but with different operating mechanisms and for infinite horizon. Other related works include Qiu and Zhao (2006), Zhao and Qiu (2007), and Qiu et al. (2008). Our motivations are: (1) propose models for all different scenarios; (2) develop an ADP approach to obtain system performances; (3) provide numerical experiments to compare system performances in different scenarios. Some results can provide managerial insights into actual logistics systems.

The contemporary information technology enables managers of inventory systems to establish various operating mechanisms with different levels of information sharing. The managers concern performances of different operating scenarios. System cost is one of the most important performance measures. In this paper, we develop ADP algorithms to solve single-distributor multi-retailer systems that are intractable by dynamic programming, and compare the system costs under six different operating scenarios. In all six scenarios, the centralized control performs the best. However, the participators of a supply chain are usually not under manipulation by a super-manager. One reason is that the participators commonly do not belong to the same enterprise and they always behave on their own interests. Another reason is that the management cost for centralized control may be relatively high. Hence, the managers sometimes have to choose an alternative decentralized control scenario. Numerical results show that system cost in scenario DAR is no more than 50% higher than that in centralized control in most cases, and this scenario is distinctly better than any other scenarios in decentralized control. Actually, the case of Wal-Mart and Procter & Gamble demonstrates the benefit of this scenario (Mason-Jones and Towill, 1997). It only requests accesses for the distributor to obtain the information of retailers, hence is feasible for being implemented. If we aim to lower system cost with a limited budget, scenario DAR is a preferred operating scenario in consideration. As indicated in the figures, in a strong rationing game environment, system with higher levels of information sharing may not perform better than in scenario AI. This is because, if the supply chain participators are competing with each other, the rationing game among selfish retailers yields significant information distortion, by which more leftover goods at retailers and higher shortage at the distributor occur. It makes sense to design mechanisms to regular competitions and induce coordinations in supply chains. One possible way is to develop a suitable allocation rule, because we find that batch-size allocation rule yields lower inflation of order quantities than proportional allocation rule. Other regulations may include contract and incentive mechanism for coordination, etc.