A new hybrid algorithm of scatter search and Nelder–Mead algorithms to optimize joint economic lot sizing problem

• It introduces a new hybrid algorithm of Nelder–Mead and scatter search algorithms.
• The new algorithm is able to find global optimal solution of constrained problems.
• It considers joint economic lot sizing problem with price-sensitive demand.
• It models lot sizing problem for three shipment policies that were not modeled yet.
• It develops solution procedures based on the new algorithm to solve the models.

This paper introduces a hybrid algorithm of Nelder–Mead and scatter search algorithms called SSNM. Numerical results for some known test problems with varying dimensions from 2 to 100 variables prove its great performance for a bounded or constrained problem. This paper also has a considerable contribution to the joint economic lot sizing (JELS) problem literature. This problem is considered for a two-stage supply chain with price-sensitive demand for geometric, geometric-then-equal size and optimal shipment policies. Solution procedures are also developed which use the SSNM algorithm in their steps. These models and solution procedures are novel in the JELS literature.