کنترل موجودی در زنجیره تامین: روش های جایگزین برای مشکل "تعیین اندازه دسته تولید" دو مرحله ای بودن

The principal challenge of inventory control in supply chains is that the interacting autonomous enterprises have to plan their production and logistics under information asymmetry, driven by different, often conflicting objectives. In this paper, four different computational approaches are investigated to cope with this challenge: decomposition, integration, coordination, and bilevel programming. The four approaches are applied to solving the same two-stage economic lot-sizing problem, and compared in computational experiments. The prerequisites of the approaches are analyzed, and it is shown that the profits realized and the costs incurred at the different parties largely depend on the solution approach applied. This research also resulted in a novel coordination mechanism, as well as a new algorithm for the bilevel optimization approach to the investigated lot-sizing problem. A specific goal of this study is to highlight the so far less recognized application potential of the coordination and the bilevel optimization approaches for controlling inventories in a supply chain.

The principal challenge of inventory control in supply chains is that the autonomous enterprises have to plan their production and logistics under information asymmetry, driven by different, often conflicting objectives. Moreover, the individual enterprises typically make decisions that affect the entire supply chain, and for this purpose they also exploit private information that is inaccessible to the other parties. This paper investigates four different approaches to cope with this challenge. According to the classical decomposition approach, each party optimizes its own production and logistic decisions without explicitly considering the consequences on the supply chain level. The integrated approach optimizes the overall performance of the supply chain by centralized planning, however, this requires a tight integration of the parties. By lifting the latter requirement, the coordinated approach seeks for mechanisms that motivate the autonomous enterprises to cooperate in finding mutually beneficial plans by negotiation and benefit sharing. Finally, the bilevel approach enables an individual party, in possession of sufficient information about its partners, to optimize its production taking into account the actions that it can expect from the partners. The goal of this study is to provide a clear-cut comparison of the above fundamental approaches by applying them to a common problem model. The main modeling, computational, and managerial implications are investigated with a focus on the prerequisites of each approach, such as the availability of information, the contractual requirements, or the assumptions on the type of cooperation. Furthermore, the potential gains for the different parties of adopting a given approach are examined, and the resulting solutions, profits and costs are compared. To the best of our knowledge, this is the first study that provides a self-contained comparison of these approaches, applied to the same inventory control problem in different settings. A specific goal of the paper is to highlight the benefits of the two less recognized approaches, coordination and bilevel optimization, for the different parties in the supply chain. A new coordination mechanism (Section 5) and a new algorithm for solving the bilevel version of the investigated lot-sizing problem (Section 6) are also presented. The investigated problem corresponds to an uncapacitated economic lot-sizing problem in a two-echelon supply chain. In a dyadic situation where a buyer–supplier chain meets external demand, this problem involves both the production related decisions of the supplier, as well as the logistic decisions of the buyer. Although for the sake of analytical clarity some simplifying assumptions have to be taken, the basic problem has direct application relevance. Primarily, a retailer may assume the role of the buyer, connecting exogenous market demand and the service of the supplier. Further on, a similar buyer–supplier relationship may hold between multiple divisions of a large enterprise. For a review of inventory control problems, both as faced by a single decision maker and in a supply chain, the reader is referred to Axsäter (2006). The potential gain by integrated versus decentralized decision making in supply chains is investigated in Perakis and Roels (2007), where the difference of the induced costs is defined as the price of anarchy. The coordination of supply chains consisting of autonomous enterprises is studied in detail in Albrecht (2010), while a comprehensive taxonomic survey of coordinated buyer–vendor models in a deterministic, time invariant setting is provided in Sarmah et al. (2006). The fundamental ideas of bilevel programming are presented in Dempe (2002), and the application of this approach to the management of multidivisional organizations is studied by Bard (1983). Further, more specific references are provided later in 3, 4, 5 and 6, each of which investigate one of the four possible computational approaches to the studied lot-sizing problem.

This paper investigated four different computational approaches to solving the same lot-sizing problem in a supply chain consisting of two parties. The comparison focused on how each of the approaches handles the aspects of autonomy, information asymmetry, and conflicting objectives. Moreover, to compare the incurred profits and costs for the different parties, algorithms have been implemented for solving the analyzed problem according to each of the four approaches. This also required the development of a new coordination mechanism for the coordinated approach, as well as a new exact algorithm for the bilevel approach. Certain findings of this study are relevant beyond the scope of the specific lot-sizing problem as well. Especially, it has been demonstrated that for a given inventory control problem, the profits incurred for the different parties extraordinarily depend on the applied solution approach: e.g., the buyer could increase its profit by ca. 34% on average, if in the possession of sufficient information, it switched from a decomposition strategy to bilevel optimization. Also, it has been emphasized that such novel approaches as coordination or bilevel optimization are applicable to lot-sizing problems, and they can provide additional benefits for the parties in the supply chain. In particular, the applicability of the classical integrated approach is limited to cases where the business objectives of the parties are completely aligned and they are ready to share all relevant data with each other. In case of autonomous parties with disparate objectives, a coordination approach may bring comparable savings, if the dynamics of the chain (both in terms of stable network design and non-critical response times) allow for appropriate contracts and communication mechanisms. On the other hand, an individual party, having access to sufficiently precise data about its upstream partners, may optimize its own production or logistics by implementing a bilevel optimization approach.