An Augmented Lagrangian Approach for Distributed Supply Chain Planning for Multiple Companies

An integrated strategy for a production planning and warehouse layout problem: Modeling and solution approaches

“…The Lagrangian decomposition and coordination method is one of the widely used approaches for capacitated lot-sizing problem (Buschkühl et al, 2010), integrated optimization of production scheduling and distribution planning (Nishi et al, 2007), supply chain coordination (Nishi et al, 2008), multi-product newsvendor problem with supply discount (Zhang, 2010), and so on. The key idea of this method is to relax the coupling constraints through Lagrangian multipliers and to decompose the original problem into some simple subproblems.…”

A game theoretic model for coordination of single manufacturer and multiple suppliers with quality variations under uncertain demands

“…Supply chain has received much attention with regard to broad activities such as production planning, scheduling, transportation, and distributions (Nishi, Konishi, & Hasebe, 2005;Nishi, Shinozaki, & Konishi, 2008;Tominaga, Nishi, & Konishi, 2008). Many researchers have investigated global supply chain planning from different perspectives, such as inventory planning, transportation network, or risk management (Goh, Lim, & Meng, 2007;Golini & Kalchschmidt, 2011;Meixell & Gargeya, 2005;Scholz-Reiter, Frazzon, & Makuschewitz, 2010).…”

Analysis of quantity discounts for multi-period production planning for single supplier and retailer under uncertain demands

“…Moreover, Stackelberg equilibrium is obtained by using the multi-period model of the supplier of (20), (21), (22), (4) and (5) and the retailer of (22), (4) and (5).…”

“…The production and distribution planning with different organizations should be coordinated to optimize the global supply chains [5]. However, it is well-known that the equilibrium solution for decentralized decision making is inferior to the solution of centralized problem.…”