Management presentation

PRESENTATION ON: AUTOMATIC AIR CARGO

LOAD PLANNING

Submitted to: Dr. Sunil Agrawal

SUBMITTED BY :

ECE Group 5

Akshay Vyas -2010014

Amit Choubey -2010018

Navneet Chaudhary -2010120

Rakesh Raj -2010145

Rishi Jain -2010153

Rohit Singh -2010157

Shubham Tiwari -2010187

MANAGERIAL DOMAIN

OPERATIONS MANAGEMENT –

The goal of operations management is to ensure that the organization is able to keep costs to a minimum and obtain revenue in excess of costs through careful planning and control of operations.

Agenda

• Problem statement

• Importance of optimal loading planning

• Mathematical model

• Constraints

• Objective function

• Conclusion

• Software used for load planning

• Future Scope

• References

PROBLEM STATEMENT

The problem of loading as much freight as possible in an aircraft while balancing the load in order to minimize fuel consumption and to satisfy stability and safety requirements.

AERODYNAMICS DON’T CHANGE ; AIRCRAFT LOAD PLANNING DOES

Law of physics and aerodynamics that apply to aviation don’t change. However, other components of flying, such as size, weight, distance flown and speed continually evolve. Therefore, preparation for a flight must adhere to strict aircraft and flight limits.

Aircraft must be loaded so structural limits are not exceeded. It must be loaded correctly so it maintains its balance from takeoff through landing and unloading.

Consideration must be given to each component being added to aircraft. This includes the additional weight and distribution of fuel, cargo, bags and passengers.

For every action there is an equal and opposite reaction. As the pressure over the wing decreases, the pressure below it increases — resulting in lift.

WHY IT IS CRUCIAL?

Firstly, 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.

Secondly, improper loading decreases the efficiency of an aircraft with respect to its altitude, maneuverability, rate of climb, and speed. An inappropriate load could even prevent the flight from being safely completed. An optimal load should yield a lesser fuel consumption and lead to a decrease in costs and environmental impact.

IMPORTANCE OF OPTIMAL LOADING PLANNING

AIRLINES 2010 (MILLIONS) 2009(MILLIONS) 

FED EX EXPRESS 15,743 15,939

UPS AIRLINES 10,194 10,566

CATHAY PACIFIC 9,587 9,109

KOREAN AIR 9,542 8,974

EMIRATES 7,913 8,132

LUFTHASANA 7,423 7,674

SINGAPORE AIRLINES CARGO 7,001 7,118

CHINA AIRLINES 6,410 5,411

CARGOLUX 5,166 -

EVA AIR 4,901 -

Scheduled Total (International + domestic) freight tonne-kilometres flown

FLEET SIZE OF DIFFERENT CARGO AIRLINES

AIRLINES FLEET SIZE

FED EX EXPRESS 688 

UPS AIRLINES 214

CATHAY PACIFIC 75

KOREAN AIR 50

EMIRATES 24

LUFTHASANA 24

SINGAPORE AIRLINES CARGO 19

CHINA AIRLINES 18

CARGOLUX 18

EVA AIR 16

FUEL SAVINGS The primary importance of exact load planning for an airline is legality

and safety. However, efficiency of loading and unloading the aircraft are also very important to an airline’s ground operations. With today’s price of fuel, the savings that can be provided through proper load planning is extremely important to an airline’s operational costs.

Successful airlines carefully calculate passenger, cargo and fuel weights to provide the most effective load plans which can reduce fuel burn enroute. These airlines try to create the optimal aircraft center-of-gravity balance to meet these goals as well as save fuel.

CENTER OF GRAVITY

The center-of-gravity (CG) is the point at which an aircraft would balance if it were possible to suspend it at that point. It is the mass center of the aircraft, or the theoretical point at which the entire weight of the aircraft is assumed to be concentrated. Its distance from the reference datum is determined by dividing the total moment by the total weight of the aircraft.

The center-of-gravity point affects the stability of the aircraft.

To ensure the aircraft is safe to fly, the center-of-gravity must fall within specified limits established by the manufacturer.

Illustration of the build-up of weight associated with the operations of an aircraft.

ACCIDENTS DUE TO IMPROPER LOADING

MODEL FORMULATION

We are concerned with positioning the center of gravity only along the longitudinal (fore and aft) axis of the aircraft, as the problem of balancing the load from side to side is commonly considered of marginal importance.

In accordance with international regulations, when it comes to computing the location of the center of gravity, we proceed as if every container of a given compartment were positioned at the geometric center of that compartment. We aim at allocating each given container to one compartment (or to the ground, when not loaded). We next set the notation.

VARIABLES USED IN MODELING

NCont = Number of containers on the ground,

NComp = Number of compartments,

NHold = Number of holds,

HK = (subset of {1,2,,..,Ncomp}) are the compartments in hold k (k = 1.2,. . . ,NHOLD),

Mi = Mass of container i (i = 1,2,. . ., NCONT),

MA = Mass of the aircraft (before loading),

MMax = Maximal mass of freight that can be loaded,

KMMax= maximal mass of freight that can be loaded in hold k (k = 1.2,. . . , NHOLD),

XA= (longitudinal) position of the center of gravity of the aircraft before loading,

Xj= (longitudinal) position of the geometric center

of compartment j (j = 1,2,. . ., NCOMP),

xTarget= ideal (longitudinal) position of the center of gravity of the aircraft after loading,

XStab= maximal (longitudinal) position of the center of gravity of the aircraft after loading in order to satisfy stability requirements.

XTarget and XStab are given by a load-and-balance software provided by the aircraft manufacturer.

Further data given as input include the following:

1) the dimensions and weight of each of the NCont

given containers;

2) all the possible locations of the containers in the cargo holds.

3) a given subset I of the container list that the user wishes to be loaded (containers that cannot be left on the ground e.g. perishable goods) will determine the freight constraints (7) in what follows.

4) a list of couples (i, k) for any given container i that the user wants to be in a specific compartment k (for eg: near a door to be landed at a stopover, or for toxic material containers to be away from the foodstuff container hold, etc.).

OPTIMIZATION VARIABLES (UNKNOWNS)

The decision variables are binary: xij ε {O, 1} is 1 if container i is to be placed in compartment j , and 0 otherwise (i = 1,2,. . . , Ncont ; j = 1,2,. . . . NComp ).

OUTPUT The purpose of the method is producing a list

of containers to be loaded in each compartment, plus a list of containers that are to be left on the ground.

Further Notation

Two critical quantities, which both depend upon the vector x of decision variables xij defined above

1. Total mass loaded:

----------------------------(1)

Mi = Mass of container i (i = 1,2,. . ., NCONT),

2. Center of gravity of the aircraft after loading

-----------------------------(2)

XA= (longitudinal) position of the center of gravity of the aircraft before loading,

Xj= (longitudinal) position of the geometric center

CONSTRAINTS

1) Aircraft Constraints:

Stability requirements:

CG(x)XStab ----------------------------(3)

2) Mass capacity constraints (overall and for each hold):

M(x) Mmax- ----------------------------------

(4) -------------------(5)

XStab= maximal (longitudinal) position of the center of gravity of the aircraft after loading in order to satisfy stability requirements.

KMMax= maximal mass of freight that can be loaded inhold k (k = 1.2,. . . , NHOLD)

MATHEMATICAL CONSTRAINTS

Each container must be loaded at most once. By the binary definition of the xij this can equivalently simply be written as

----------------------------(6)

CONTAINER CONSTRAINTS

If a subset I of the container list is required to be loaded:

----------------------(7)

For any given container i required to be in a specific compartment k:

------------------------------(8)(and therefore, by (6), Xij = 0, for all j ≠k).

OBJECTIVE OF THE OPTIMIZATION PROBLEMWe are faced with two contradictory objectives

• Maximizing M(x)

• CG(x) as far aft as possible (but not behind the limit imposed by stability requirements,(Constrain (3)).

How to Achieve???????????????

One way to proceed, with an optimization approach, would be to consider the (longitudinal) position of the center of gravity of the aircraft as the objective function to be maximized, subject to the constraint of loading at least some pre-specified mass of freight.

The problem with this approach is twofold• Firstly, the total freight mass loaded is not optimized.

• Secondly, the objective function CG(x) is a nonlinear function of the optimization variables Xijs.

REMARK:-

The difficulty of solving an integer nonlinear programming problem is incomparably higher than that of solving an integer linear programming problem.

However, in the case if we assumes that the complete given list of containers must be loaded, the numerator of (2) is then a constant, and CG(x) is therefore linear. This is a rather strong assumption for practical problems. This indeed means that one chooses which containers are to be loaded, and assumes that the containers chosen do fit in the aircraft.

We propose maximizing the mass loaded, given by (1), subject to the constraints (3)-(8), plus the following additional constraints:-

CENTERING CONSTRAINT

1) Keeping the center of gravity within a reasonable distance from the ideal position:

----------------------------(9)

where ε is some positive allowable displacement of the center of gravity of the aircraft from its ideal position. The value of ε is set by the airliner in sucha way as to account for uncertainties in the geometricand weight data.

The previous constraint can equivalently be written as

i.e., it can be expressed as two linear (inequality)

constraints.

--------------------(10)

All of the above constraints, (3)-(8), (10), and the objective function (l), are linear.Thus, the resulting mathematical formulation will be an integer linear programming problem.

The purpose of the next section is therefore to demonstrate how the volume capacity constraints can be modeled so as to fit within the integer linear programming formulation.

MODELING VOLUME CAPACITY CONSTRAINTSThe way we model the volume capacity constraints is specific to each type of aircraft and to the different types of containers one has to load.

In our case we take an exampleWe consider here a special instance: the Airbus A340-300 together with five different types of containers.In practice, these volume capacity constraints are to be generated a priori once and for all, for each type of aircraft owned by the airliner.

DIFFERENT TYPES OF CONTAINERS CONSIDERED

Type Description Space Required

1. Half size60.4 x 61.5 inchesMax IATA contour E, G

1 small place

2. Half size60.4 x 61.5 inchesMax IATA contour C, H

2 small places

3. Full size60.4 x 125 inchesMax IATA contour F

2 small places

4. Full size88 x 125 inchesMax UTA contour F

1 large place

5. Full size96 x 125 inchesMax IATA contour F

1 large place

TABLE II: ARRANGEMENT OF CONTAINERS IN A340- 300 HOLDS

We partition the five types of containers into three categories, according to the space one container occupies in a hold. We note that containers of types 2 and 3 require twice as much space in the hold as one container of type 1.There are many ways of combining small and large places within a given compartment. It is convenient to define, for each compartment sj( j = 1,2 ,..., NComp , is the number of small places occupied in compartment j , and lj, is the number of large places occupied in compartment j . Since for each container i (i = 1,2,. .., NCont ) , we are given its type as input:

Ti (ε {1,2,3,4,5}) type of container i,

we have, in terms of the optimization variables Xij s :

In what follows, for each compartment, we initially model the volume capacity constraints with logical constraints.

--------------(l1)

------------------------(l2)

COMPARTMENT 1

Inspection of Table 2 reveals that one can load in compartment 1 any combination of containers requiring up to a total of 6 small places and 0 large place. One can alternatively fit containers requiring up to a total of 2 small places and 1 large place in compartment 1. A third alternative is: 0 small place and 2 large places.

These possible arrangements cannot be modeled through a single set of inequalities involving linearly the integer optimization variables X ij s. We could consider here, separately, the three alternatives 1, = O,1, or 2.

We choose to consider separately the following two alternatives:

l1≤1 and l2 =2

(remember that by the binary definition of the Xij s the ljs and the sj s are bounded to be nonnegative and integer valued. The above enumeration of combinations of small and large places for loading compartment 1 can equivalently then simply be represented bys1 +4 l1 ≤ 6 if l1 ≤ 1 -----------------------------(l3)

s1 = 0 if l1 = 2 ----------------------------(l4)

how the two alternatives (l3) and (l4) can be expressed so as to fit within an integer linear programming formulation

Constraints (13) and (14) can equivalently be rewritten as the two alternatives

(s1 +4 l1 ≤ 6 and l1 ≤ 1 )(s1 = 0 and l1 = 2)

Let us now introduce an extra binary variable Y1,1 having value zero when the first alternative holds and value one corresponding to the second alternative.

-------------------(l5)

we introduced five “big enough’’ constants B1,i . Each B1,i constant is to be set in such a way that the corresponding inequality is always satisfied for any feasible solution to our problem as soon as the coefficient of B1,i is one.

Consider, for instance, the first inequality. Since s1 +4 l1 can clearly never be above 14, it suffices to set B1,1= 8. Hence, when Y1,1 = 1, the first constraint is not restrictive (since always satisfied), only the last three constraints are relevant. Similarly, it sufficesfor instance to set B1,2 =1,B1,3 =6, B1,4 =2.

Similarly, for compartment 2

Introduce extra binary variables Y2,i

ε{O, l} where i = 1, 2, 3, which monitor which of the three alternatives is relevant.

So the equations formed are as follows

Similar analysis can be done for compartment 3 and 4.

OVERALL FORMULATION

To summarize, here is the overall integer linear programming formulation of the aircraft container loading problem:

maximize M(x), given by (1)

subject to (3),(4),(5),(6).(7),(8),(10),(15),(19).

CONCLUSION

We considered, in this paper, the aircraft container loading problem, more specifically the problem of choosing which containers should be loaded on the aircraft, and how they should be distributed among the different compartments, in order to improve fuel consumption while optimizing freight income, subject to structural and safety constraints.

We can use any off the shelf integer linear programming software to solve the above equations.

Further, one could consider implementing a procedure which automatically chooses which solution is the best among the ones proposed in terms of operationalcost, knowing the income expected per loaded ton of freight, the impact in terms of fuel saving for each centimeter of displacement of the center of gravity ona specific aircraft, and the current cost of fuel.

There are two automated systems available to an airload planner. They are the Automated Air Load Planning System (AALPS) and the Computer-Aided Load Manifesting System (CALM).

AALPS

AALPS is an Army-fielded automated airload planning system that supports deliberate planning and execution phases of air movement as well as force design and analysis.

CALM

CALM is an Air Force-fielded automated system used to load plan C-130, C-141, C-5, and KC-10 aircraft. The system uses interactive graphics to help the load planner produce and complete cargo manifests.

SOFTWARE EXAMPLE

FUTURE SCOPE• A System can be designed that can carry more container as well as

could also use fuel and put CG(x) as far aft as possible simultaneously.

• Enhance the profitability through control of yield and revenue.

• Improve service levels through proactive monitoring and alerts.

• Further work could also consider exploiting systems within our optimization approach in order to allow more flexibility, thereby improving results (the potential of the sole use of fuel transfer systems is indeed limited as the aircraft approaches its destination and less fuel is available to transfer).

• Simultaneously optimization of ULD filling can help to carry more freight.

1. Journal of the Operational Research Society,

S Limbourg, M Schyns and G Laporte

Automatic aircraft cargo load planning.

2.IEEE Marcel Mongeau, Christian Bes

Optimization of Aircraft Container Loading

3. Wikipedia

4.B.Mahadevan,OPERATIONS MANAGEMENT

THANK

YOU