A hybrid genetic algorithm based heuristic for an integrated supply chain problem

• Present a new formulation that simultaneously considers facility location and inventory management problems.
• The new formulation does not increase the complexity of the two problems individually.
• Demonstrate the benefit of the integrated modeling approach.
• Develop a GA that is capable of solving large scale of the problem in acceptable computational time.

Supply chain management is becoming an essential component of efficient decision-making for companies, as they are increasingly implementing optimization strategies in order to improve their business performance. In this paper we develop a capacitated multi-echelon joint location-inventory model, according to which a single product is distributed from a manufacturer to retailers through a set of warehouses, the locations of which are to be determined by the model. Each retailer is assigned exactly one warehouse, while each warehouse can serve multiple retailers. The model decides where to locate warehouses, assigns retailers to the warehouses and decides the times between orders at the warehouses and the retailers, so as to minimize the cost of operating the supply chain. Notably, the model considers capacity constraints for each warehouse, ensuring that the reorder quantity is below the capacity limit. We develop a genetic algorithm (GA) based heuristic to solve the problem and the GA is validated on small size problems by comparing its solution to the optimal solution obtained by the General Algebraic Modeling System (GAMS). We focus our attention on specifically customizing the GA and thus an experimental analysis is carried out to find the optimal parameter setting for the GA as well as to obtain insights on the effect of the various GA parameters. Finally, a sensitivity analysis is conducted to show the effect of the capacity constraints.