A coordination mechanism for capacitated lot-sizing in non-hierarchical n-tier supply chains

Abstract

In the context of an n-tier supply chain, a coalition of agents is considered that has to jointly solve a distributed multi-level capacitated lot-sizing problem in order to minimize the agents joint total costs. Due to asymmetric information between the agents, e.g., with respect to setup costs, inventory holding costs or available machine capacities, this problem cannot be solved by a single, central decision maker. Therefore, this paper introduces a coordination mechanism to enable collaborative planning by taking asymmetric information into account. Furthermore, the coordination mechanism is able to deal with non-hierarchical assignment of items to agents within a mutual bill of material. To evaluate the coordination mechanism, test instances for the classical multi-level capacitated lot sizing problem are extended. A computational study shows that the coordination mechanism works well for instances without setup times. That is, for these instances solution quality for the distributed case deviates on average by less than five percent from best-known solutions in the non-distributed case.

Collaborative Distributed Planning with Asymmetric Information. A Technological Driver for Sustainable Development

“…Another alternative to speed up searches among alternatives is to use metaheuristics or mathematical decomposition tools as coordination mechanisms. Metaheuristic coordination mechanisms can use the ant colony [43], simulated annealing [22,[44][45][46][47], neighbourhood search [48], genetic algorithms [49] or immune systems [50]. They all allow searches for better coordination according to preestablished rules, but do not guarantee optimality or knowing the assumed gap.…”

Coordination mechanisms with mathematical programming models for decentralized decision-making: a literature review

“…Another alternative of a coordinating mechanism has been meta-heuristics, such as ant colony or pheromone (Silva et al, 2009) or Simulated Annealing (Buer et al, 2015;Dudek et al, 2007;Eslikizi et al, 2015;Ziebuhr et al, 2013Ziebuhr et al, , 2015 or variable neighbourhood search (Reiss et al, 2014) that allow to seek a better coordination according to pre-established rules but without guarantees of being optimal.…”

“…This limitation usually occurs in the automotive industry where the structure of the product is known throughout the suppliers. These works also stand out for their uncapacitated models except one (Reiss et al, 2014). However, all of them have limited possible alternative solutions that have to be evaluated.…”