Supply chain

Business

Total cost

Procurement

Benders' decomposition

Mathematics

Operations research

Biology

Mathematical optimization

Stochastic programming

Engineering

Visual arts

Marketing

Paleontology

Joint (building)

Management

Economics

Architectural engineering

Microeconomics

Holding cost

Geometry

Constraint (computer-aided design)

Sizing

Context (archaeology)

Computer science

International Journal of Systems Science Operations & Logistics

Joint Economic Lot-sizing Problems (JELPs) have received a great deal of attention in recent years because they are the bedrock of pushing forward the frontiers of knowledge in supply chain (SC). JELP can manage efficiently SC through promoting cooperation among the levels of the SC. In this paper, we deal with JELP in the context of the integrated four-level SC in order to minimise the total inventory cost. The model is multi-product and considers raw material replenishment. Real stochastic constraints, including space limitation, procurement cost, ordering, and joint economic lot-size limitations can make the model more applicable for real-world SCs. The objectives are both to determine the joint economic lot-sizing policy and the optimum period length such that the total inventory cost of the SC is minimised, while the stochastic constraints are satisfied. Mathematical formulation of the problem is stochastic, MINLP, large scale and hard to solve. In this regard, we utilised Generalised Benders Decomposition (GBD) in order to minimise the MINLP model of research. The results of numerical examples and sensitivity analysis illustrate that proposed method has satisfactory performance in optimum solution, number of taken iterations, the dual infeasibility, constraint violation, and the complementarity.

Joint Economic Lot-sizing in Multi-product Multi-level Integrated Supply Chains: Generalized Benders Decomposition