Supply chain network design with direct and indirect production costs: Hybrid gradient and local search based heuristics

Many works in the area of Supply Chain Network Design (SCND) have integrated production costs as one lumped cost. However, production costs embody indirect (overhead) and direct costs. This work brings a model that integrates these two production costs along with inventory and transportation costs. In particular, the work looks at the tradeoff between the shortening of the production duration (Pd) and the consequent increase in direct production costs. The work implicitly incorporates direct production costs that are the result of applying additional production resources to shorten Pd. Integrating both costs results in a nonlinear mathematical model. The overall objective function also includes binary variables to govern the selection of production plants resulting in a nonlinear mixed integer mathematical model. In this work, we prove the convexity of the objective function and we introduce a combination of a gradient and a local search heuristic to solve the resulting model. For practical implications, the paper presents four different scenarios to cover a wide range of supply chain settings. Principally, our results demonstrate promising benefits of reduced overall production costs, reduced production lead time, freed-up production capacity, and improved supply chain throughput.