سیستم تولید - موجودی یکپارچه در زنجیره تامین چندمرحله ای چند شرکتی

We first generalize a number of integrated models with/without lot streaming and with/without complete backorders under the integer–multiplier coordination mechanism, and then individually derive the optimal solution to the three- and four-stage model, using algebraic methods of complete squares and perfect squares. We subsequently deduce optimal expressions for some well-known models. For our model, we check that the optimal solution, which is algebraically derived, is a global one. We present three numerical examples for illustrative purposes. We finally suggest some future research work involving extension or modification of the generalized model.

Increasing attention has been given to management of multi-stage multi-firm supply chains in recent years. This is due to rising competition, shorter life cycles of products, quick changes in today’s business environment and severity of green issues. Integrated deteriorating production-inventory models incorporating the factor of environmental consciousness can be found in Yu et al., 2008, Chung and Wee, 2008 and Wee and Chung, 2009. Integration of a (green) supply chain is now crucial to successful international business operations since an integrated approach improves global systems’ performance and cost effectiveness. Besides integrating operations of all members in a supply chain, improvement of the traditional method of solving inventory problems is also necessary. Without using derivatives, Grubbström (1995) first derived optimal expressions for the classical EOQ (economic order quantity) model using the unity decomposition method, which is an algebraic approach. Adopting this method, Grubbström and Erdem, 1999 and Cárdenas-Barrón, 2001 derived optimal expressions for EOQ and EPQ (economic production quantity) models with complete backorders. In this paper, a generalized model for a three- or four-stage multi-firm integrated production-inventory system is solved, using the methods of complete squares and perfect squares proposed in Leung, 2008a and Leung, 2008b, which are simple algebraic methods; ordinary readers unfamiliar with differential calculus can also easily understand how to derive optimal expressions of decision variables and the objective function.

Notice that most work in this paper echoes the last two future research endeavors recommended in Section 7 of Leung (2009). The main contribution of the paper to the literature is threefold: First, we extend Leung (2009) model by including Assumption (9). Secondly, we establish the n -stage (n=3,4,…)(n=3,4,…) model, which is more pragmatic than that of Ben-Daya and Al-Nassar (2008), by including Assumptions (5), (6), (7), (8) and (9). Also, we provide an optimal solution procedure much more simplified that that in Ben-Daya and Al-Nassar (2008, p. 102), developed using the methods of complete squares and perfect squares. Users can easily understand and apply this model. We also illustrate the procedure with three numerical examples. Thirdly, we deduce and solve three additional special models: Yang and Wee, 2002 and Wu and Ouyang, 2003 or Wee and Chung, 2007 and Chung and Wee, 2007. Two ready extensions of our model that warrant future research endeavors in this field are: First, following the evolution of three- and four-stage multi-firm supply chains shown in Sections 3 and 4, we can readily formulate and algebraically analyze the integrated model of a five- or higher-stage multi-firm supply chain. Secondly, using complete and perfect squares, we can solve the integrated model of a n-stage multi-firm supply chain either for an equal cycle time, or an integer multiplier at each stage with a fixed ratio partial backordering allowed for some/all downstream firms (or retailers), with or without lot streaming.