Integrating packaging and supply chain decisions: Selection of economic handling unit quantities

In this work, a new framework is developed for selecting the packaging parameters that optimize end-to-end supply chain costs assuming a fixed supply chain network for one period of deterministic demand for a single product shipping to multiple customers. The Handling Unit Quantities represent the type and size of the nested handling units such as containers, pallets, cases and sub-cartons. The approach seeks the optimal or Economic Handling Unit Quantities (EHUQ) that fully define the choice of container type and loading configuration, pallet and case quantities, warehouse pick profiles, as well as the prediction of end-to-end supply chain costs. The problem is formulated as a non-convex Mixed Integer Non Linear Programming (MINLP) problem, and transformed into a Quadratically Constrained Quadratic Program (QCQP). It considers a 3-echelon supply chain of factories, warehouses and customers. The model optimizes the total supply chain costs of manufacturing, packaging consumables, in- and out-bound transportation, warehouse receiving, picking and packing costs. The formulation requires integer variables to model the packaging choices, binary variables to capture transportation choices, non-linear inverse bi- and tri-linear terms, and discontinuous step functions which are required to model warehouse picking costs. A power law relationship is used for customer demand to generate test problems that replicate the complexity of real world problems. With a small amount of information, the cost, operational performance and environmental impact for supply chain options under evaluation may be predicted. Because of the size and complexity of the problem, a heuristic method was developed to provide solutions quickly.