Integrated multiproduct batch production and truck shipment scheduling under different shipping policies

The classical economic lot-scheduling problem (ELSP) involves the batch sizing and scheduling of multiple products in a single facility under deterministic conditions over an infinite planning horizon. It is assumed that the products are delivered to customers at continuous rates. In today's supply chains, however, often employing complex delivery networks, the finished goods are usually transported in discrete lots to succeeding stages along the distribution process, in order to take advantage of economies of scale in transportation. In this paper, we formulate mathematical models that attempt to integrate the production lot scheduling problem with outbound shipment decisions. The optimization objective is to minimize the total relevant costs of a manufacturer, which distributes a set of products to multiple retailers. In making the production/distribution decisions, the common cycle approach is employed to solve the ELSP, for simplicity. Two different shipping scenarios, i.e. periodic full truckload (TL) peddling shipments and less than truckload (LTL) direct shipping, are integrated with and linked to the multiproduct batching decisions. We consider these two shipment policies for both coordinated and uncoordinated scenarios. The resulting mixed-integer, non-linear programming models (MINLPs) are solved by the BONMIN solver. Finally, a set of numerical examples illustrate and evaluate the relative efficacies of these policies.