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Air cargo management

This project was developed by Sabine Limbourg (HEC-ULg, QuantOM), Michaël Schyns (HEC-ULg, QuantOM) and Gilbert Laporte (HEC Montréal, CIRRELT).The details are provided in their paper "Automatic Aircraft Cargo Loading", Journal of the Operational Society, DOI 10.1057/jors.2011.134 .

Links: Air cargo mgt & team - W&B problem - Our solution & video - Download - Additional information

What is load planning for cargo aircraft?

An aircraft being loadedHow to optimally load a set of shipments of different types, contours and shapes in an aircraft? What is the optimal location of each of these packages in the aircraft? On any given day, this question is considered tens of thousands of times worldwide. This problem is of crucial importance to airline companies for at least two reasons. First, aircraft loading is subject to strict safety constraints. Indeed, the stress imposed on the structure of an improperly loaded aircraft can result in the destruction of valuable equipment and ultimately in the loss of lives. Second, improper loading decreases the efficiency of an aircraft with respect to its altitude, manoeuvrability, rate of climb, and speed. At the opposite, an optimal load should yield a lesser fuel consumption and, consequently, lead to a decrease in costs and environmental impact. A shift of less than one meter of the centre of gravity (CG) can lead to a reduction of several tons of fuel for each long-range flight and therefore substantial financial savings.

Shipment and aircraft

The shipment to load, known before the planning starts, is defined by a set of ULDs. A ULD is an assembly of components consisting of a container or of a pallet covered with a net, whose purpose is to provide standardized size units for individual pieces of baggage or cargo, and to allow for rapid loading and unloading. This standardized system is used by all the main handlers and for the most usually operated cargo aircrafts (Airbus, Boeing, Lockheed, McDonnell-Douglas...).


Goal and constraints

The solution should be such that the centre of gravity (CG) of the loaded plane should be as close as possible to a recommended position determined by safety and fuel economy considerations. In addition, the loading should be concentrated or "packed" around this central position. This is particularly important when the aircraft is not fully loaded. This double goal implies an increase in aircraft efficiency and a decrease in fuel consumption. We propose an original approach for handling this feature, based on the moment of inertia. In addition to these basic constraints, a feasible solution must also satisfy other requirements:

Combined weight limits
  • Each position can only accept some specific types of ULDs, depending on their contour, type and weight;
  • The plane must be balanced longitudinally and transversally;
  • The total weight concentrated at each inch of the aircraft length and for each deck must be less than given thresholds (combined weight constraints);
  • The cumulative weight at each inch from the front up to the middle of the plane must also be less than another threshold function (cumulative forward constraint);
  • A two-level threshold is also applied to the aft part (cumulative aft constraints).
  • Hazardous products cannot be located in some positions or close to some other products;

Because of the weight and CG constraints the loading problem is sometimes called the weight and balance problem.

Day to day approach

The aircraft cargo loading problem is normally solved by loadmasters who use interactive graphical tools with drag and drop capabilities. This means the loadmaster can generate several potential solutions whose quality is assessed by a set of indicators. This works well in practice but is time consuming. For example, an experienced loadmaster can load 40 ULDs on a Boeing 747 in about 15 minutes. The solution typically satisfies the basic constraint but may be suboptimal. Load planning is often executed at the last possible moment before the plane departure, which means that fine tuning is not always a practical option. This is particularly true for express delivery companies such as FedEx, TNT and DHL whose business model relies on timely operations.

We have developed a fully automatic software to quickly compute optimal solutions. This software can handle all constraints of the problem and tests carry out on a set of real instances show that feasible and optimal solutions can be reached within a few seconds only. Our solutions were compared to those obtained by an experienced loadmaster and shown to be at least as good, and often better, in every respect. Details are provided in the solution approach page.

New improved version

Virginie Lurkin and Michaël Schyns are still working on this problem and try to integrate new requests from the industry. They have developed a new model that extends the previous work to the case of multiple legs trips. Due to the Pickup and Delivery operations that can occur at intermediate airports, it is simultaneously a weight and balance problem and a sequencing problem. The new objective is to minimize two types of costs: the costs associated with the fuel consumption and the costs associated with the unloading and loading operations.
Beside, the software computes several indicators requested by the authorities.
This research was presented at the AGIFORS meeting in August 2013 and won the price of the best technical presentation (about this talk).

Links: Air cargo mgt & team - W&B problem - Our solution & video - Download - Additional information

  HEC-Management School - University of Liège