The existence of positive and negative externalities ought to be considered in a productivity analysis in order to obtain unbiased measures of efficiency. In this research we present an additive style, data envelopment analysis model that considers the production of both negative and positive externalities and permits a limited increase in input utilisation where relevant. The directional economic environmental distance (DEED) function is a unified approach based on a linear program that evaluates the relative inefficiency of the units under examination with respect to a unique reference technology. We discuss the impact of disposability assumptions in depth and demonstrate how different versions of the DEED model improve on models presented in the literature to date.
In this paper we propose a framework for shift-level container scheduling and resource allocation decisions at a cross-dock facility. The Multi-Mode Resource-Constrained Cross-Dock Scheduling Problem (MRCDSP) approach minimizes material flow and schedules inbound and outbound containers to dock-doors such that the total processing time is minimized subject to the resource constraints at the cross-dock. While container scheduling and resource allocation problems at cross-dock facilities have been studied previously in isolation, our work is the first to consider a complete view of cross-dock operations providing optimal container to dock-door allocation, and a makespan minimizing schedule of containers to the cross-dock. We present a comprehensive framework that includes identification of container clusters to reduce the problem size, a container-to-dock-door assignment algorithm, and a container clusters scheduling model that is solvable for practically sized problems. In a comparative numeric study based on data simulating a cross-dock facility, our approach is shown to outperform current practice, reducing the average time required for processing a set of containers by 37% and reducing the weighted-distance material traveled within the cross-dock by 45%.