Design and operation of a two-level supply chain for production-time-dependent products using Lagrangian relaxation

• We consider a design and operation problem of a two-level supply chain.
• The problem considers several types of production-time-dependent products.
• We develop a heuristic algorithm based on Lagrangian relaxation.
• The algorithm gives good solutions within an acceptable time.

We consider a design and operation problem of a two-level supply chain of a poultry company. The supply chain consists of a number of (candidate) suppliers and one manufacturing plant. Each supplier, if established or opened, produces semi-finished products and delivers them to the manufacturing plant that produces finished products to satisfy dynamic demand. In each supplier, production times of different types of semi-finished products are different, but production of those semi-finished products should be started at the same time if they are in the same process batch, although they may be completed at different times. The problem considered in this paper is to determine whether to establish suppliers among candidates at the beginning of the planning horizon for operation during the planning horizon and to determine production plans of the suppliers with the objective of minimizing the sum of transportation costs and production costs as well as establishment cost of the suppliers. We present a mixed integer programming model, and develop a heuristic algorithm based on Lagrangian relaxation. Performance of the algorithm is evaluated through a series of computational experiments on randomly generated instances based on data from a poultry company in Korea and results are reported.