Variable Cost Index
 

Does anyone here have experience of using a variable cost index (CI) for the purposes of optimising their operation?

If so, how are you, as pilots, informed of the CI?

Is it on your NAV LOG?

Do you know how the calculations are performed? i.e., the contributing cost-benefits analysis?

Is your SOP to then endeavour to fly as close as possible (circumstances permitting) to the FMC computed OPT ALT's? Even if it isn't an actual SOP, is it a taught consideration?

Is it appreciated that if one always uses a constant CI, all you are doing is using the CI to achieve a particular schedule of CLB, CRZ and DES speeds?

All comments appreciated.


:ok:

We (a red coloured Australian carrier) operate NG 737's and use a CI that is airframe and route specific.

The aircraft are from different leasing companies, which means different maintenance costs, and we have a number of different engine/airframe/winglet configurations.

We cruise quite slowly, often below 20 when our competitor is cruising at around 120.

The CI is shown on the flight plan and our SOP is to fly as close to optimum/flight planned level all things considered. If you load extra fuel/pax/freight of course you may not be able to make the planned level, in which case you adjust accordingly.

We also have a published list of CI's and also routes where tankering is to be considered, subject to the usual considerations.

I personally don't believe that this removes the ability for a captain to cruise as required to achieve the objective - ie he/she can cruise faster/slower/lower if necessary - as long as they have a sound operational reason.

At my airline, CI is chosen rather arbitrarily so that the average cruise speed fits what the dispatcher (or marketing) wants. CI is designated on the flight dispatch release.

Here's a couple of articles for MD80 ops

http://www.espania.com/aspa/bibliot/md-06.htm

http://www.espania.com/aspa/bibliot/md-13.htm

At my airline (It's not really mine, I just work for them),

Sector specific Cost Index (CI) is used.

Advice to pilots is by company bulletin (through Flight Operations Web page), periodically updated as maintenance / variable overhead / fuel prices vary.

It's not on the Nav Log, or Computer generated Flight Plan (CFP). The CFP uses CI=150 which is MUCH higher than actual CIs used. We love that, we inevitabely 'make' fuel on each sector. Typical CI is in the range 85 to 88, although the 'full' CI=150 is standard on some sectors due to schedule / connection problems. Also, beyond a particular threshold, the CI is bumped up to 150 if late on schedule. Minimum CI=50 (wait for this to change as fuel prices rise further).

The calculation is performed in the traditional Cost Index calculation technique. As speeds increase, flight times, and therefore airframe / maintenance cost decreases. As speeds increase above Maximum Range Cruise, fuel cost increases. Where the decreasing airframe cost crosses the increasing fuel cost on a graph, lies the optimum Cost speed for the sector.

SOPs are to fly the published sector-specific CI, except as mentioned above (schedule etc.).

Everyone in our outfit knows that a fixed CI does lead to the same old set of speeds from day to day. CI=150 was used regularly as standard until a year or so ago, everyone knew the speeds from memory, and are aware in the 'new era' that these speeds now vary somewhat.

SR71, I guess that with a call-sign like yours, your personal CI is 999.

cost index
 

At my last airline cost indices were published seasonally and varied from destination to destination, but never more than a few units (ie between 18 and 30).

At present airline we use one standard cost index of 28. We tried 20 at one stage but all got fed up with the descent speed of 266kts, so have reverted to 28 which gices a rather handy descent speed of 280kts.

Amazingly unscientific considering the price of fuel!

We tested a number of cost index values on specific routes, decided that there wasnt much of a difference between small values, so selected the constant value of 100 for all routes. Goal is to make life easier for crews whilst still saving fuel.

If we had applied the formula correctly for outbound flights, CI values would be around 400. So combined with a fuel tankering policy, the idea is to save cheap outbound fuel to avoid buying foreign fuel.

Mutt.

At our company (OS) we use variable CIs for every single flight. They are printed on the OFP and our flight planning software considers up to time information for its calculation, including a second CI value, if fuel eco is positive and thrutankage could be applied.

The "optimum delay" function of the software calculates a number of combinations regarding routings, altitude, CIs, connecting pax and so on, considering also different ATC fees, AWY restrictions and of course current WX. But additional costs due to different crew salary combinations (old capt & old F/O or young capt & old F/O or ....) and posibly crew overtime are not taken into account for the time being (but will be in the future).

As fuel prices are generally very high right now and especially at our homebase Vienna, we (Fokker 70) usually have quite low CIs, such as 11 or 14.

As all of our CIs are calculated upon preflight assumptions, a second system - the flight priorities - was introduced for inflight manipulation of cruise system if becoming necessary (Pri 1: always fly high speed, Pri 2: if late adjust speed/CI to be right on time, Pri 3: if late adjust speed/CI to be max 10 min behind, Pri 4: stick to CI even with delay greater 10 min). The flight priorities are published by our network management every half year.

CI - some info you may find useful
 

Just to say this might help as to background. And try Airbus Flight Operations Support & Line Assistance - download Getting to Grips with CI, Issue 2 - May1998. It is written a bit in franglais so you have to read it once or twice. But this summary might help kick off a better start than Airbus's intro.

The cost index (CI) approach to flight optimisation is to balance time-related (CT) operating costs ($/hr; $/min) against fuel-related (CF) operating costs ($/100lb; $/kg).
In other words CI = CT /CF .

Rearrange the expressions: [($/hr) / ($/100lb)] = 100lb/hr
[($/min) / ($/kg)] = kg/min

These expressions in 100lb/hr or kg/min represent alternative views of the cost index. Note that 100lb/hr = 0.756kg/min and 1kg/min = 132.3lb/hr.

To remove time dependence from these foregoing expressions it is only necessary to divide cost index by speed:

[(100lb/hr)x(hr/nm)] = 100lb/nm

The right hand side of this last expression can be recognised as the inverse of the specific range (SR), that is the distance travelled in nautical miles per 100lb of fuel. Alternative units also widely used are nm/1000lb, nm/100kg and nm/1000kg.

It is therefore possible to write a specific cost function per nautical mile, T, as follows:

T = (1/SR) + (CI/V)

Generally speaking V is expressed in terms of Mach Number modified by windspeed component


V = (aM + VC) where a is the local speed of sound, M is Mach Number of course and VC is the usual wind component speed normally written with c as a subscript, negative for headwind, positive for tailwind.

Thus the specific cost function T can be written in coherent units as


T = (1/SR) + (CI/(aM + VC))

Two important conclusions can be drawn from this. That for a given sector distance the minimum cost is achieved by combining fuel related costs (1/SR) and time related costs (CI/(aM + VC)) in the correct proportion. And for a given cost index Mach Number variations can compensate for actual fluctuations in windspeed.


With time related costs the faster the aircraft can be flown, the better but the faster it flies the more the fuel burn increases. There must be a point at which each counterbalances the other and this is known as ECON speed. This is calculated within the Flight Management System Computer and generally speaking is given the range 0-999 or 0-99 depending on the style (vendor) chosen.

Remember that CI = CT /CF . If CI is small and tends to zero then relatively speaking time-related costs ($/hr; $/min) are small and fuel-related costs ($/100lb; $/kg) are large. Think of it as time being long with little fuel burnt. This equates to minimum fuel consumption and maximum range. Conversely if CI is large and tends to 999 (99) it is the time-related costs that loom relatively large and fuel-related costs that are relatively small. Think of it as time being short and a lot of fuel burnt which equates to minimum time at maximum speed. There is a restriction applied however by the Maximum Mach Operating Number inasmuch as MMAX = (MMO – 0.02) but the CI value is the tool through which trip fuel is traded against trip time.