5.1.1 Input Data and Assumptions
For simplicity, all 50 sea containers that are to be airlifted directly back to Canada are assumed to have the same dimension, weight and priority. The one-way flight distance for this airlift is assumed to be 12000 km.
The CF expects to have access to up to six airframes for this move: two each of CC-177, AN-124 and IL-76. Within the area of operations, the CF will be restricted to at most one take-off and one-landing per day at the airport of embarkation. With one-way flight times of approximately 15 hours, which necessitate a crew rest period, and also allowing for loading and unloading time, it is assumed that a single round trip will take five days. Based on this information, the anticipated airlift usage schedule is up to two chalks per week for each type of aircraft (that is, one flight per week per unique airframe).
Table 3 shows values assumed for various aircraft planning factors (cargo bay dimensions, MPLs, speed, and operating/hire cost). Additionally, the inter-item distances for loading of aircraft are set to be 0.5m for end-to-end distance, and 0.25m for side-to-side distance. The currency exchange rate from Canadian to American dollars is assumed to fluctuate between 0.95 and 1.05.
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Table 3: Direct airlift aircraft planning factors.
5.1.2 Simulation Results and Options Analysis
With zero, one or two chalks per week for each of three types of aircraft and three priority levels, there are 78 possible unique ordered combinations (triples, double and singletons) of airlift assets.
These range from a single chalk per week of one aircraft type, to two chalks per week for all three aircraft types. One thousand replications were run, generating 1000 cost and time estimates for each of the 78 airlift asset combinations.
Some cost and time estimates generated were invalid, due to the movement being incomplete.
This occurs when the MPL values generated for each aircraft under consideration are too low to permit all items on the movement load list to be moved; that is, one or more items are too heavy to be carried by any of the aircraft. Such observations were removed prior to conducting any analyses.
The aim of the options analysis is to determine combination(s) of aircraft that minimizes the time and cost to move the 50 sea containers from the area of operations back to Canada. Some of the 78 possible ordered combinations of airlift assets can be eliminated from consideration immediately due to the inordinate length of time required. For example, the simulation results indicate that if a single IL-76 chalk per week is used, the move would take 25 weeks to complete.
In order to reduce the number of options to a more manageable number, the following criterion was applied: an option will be considered viable only if the movement was completed in eight weeks or less, at least 50% of the time. Application of this filter to the simulation results yields 38 ordered combinations of CC-177, AN-124 and IL-76 flights. These viable combinations reflect different priority orderings of seven possible pairs and triples of the aircraft types, with one or two chalks per week for each.
A quick means of comparing the timeliness of the airlift options is via a time cumulative frequency plot which indicates the reliability of being able to complete the move within a certain number of weeks. For each of the 38 viable airlift combinations, the frequency with which each time value (in weeks) is observed is tabulated and the cumulative total over time is plotted against
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the observed time values. The priority order within each of the seven pairs/triples of aircraft types did not influence the times to complete the move, reducing the 38 time profiles to a set of seven distinct time frequency curves. The result is shown in Figure 6.
Figure 6: Time cumulative frequency plot for direct airlift options.
As expected the quickest means of completing the move is to use as many flights as possible each week; that is, 2 flights per week for each of the AN-124, CC-177 and IL-76. This particular mixture completes the move within 9 weeks approximately 80% of the time. The other four mixtures involving two AN-124 flights per week attain the 80% reliability mark at 10 weeks.
Three mixture options attain 99% reliability at the 13 week point: 2xAN-124 and 2xCC-177;
2xAN-124, 2xCC-177 and 1xIL-76; and 2xAN-124, 2xCC-177 and 2xIL-76. All seven mixture options complete the move in 17 weeks or less 99% of the time. In all cases, the priority ordering of the aircraft does not influence the time to complete the move.
An examination of the simulation results shows that the remaining 1% of replications, which correspond to time estimates of 25 or 50 weeks, involve moves conducted by AN-124 alone, as the MPLs of the CC-117 and IL-76 aircraft are too low to carry any of the items on the movement load list.
The next consideration is the cost of conducting the move. For each of the 38 viable ordered combinations, the approximate 90th percentile of the cost values corresponding to each observed time is extracted. These values are then plotted against the time to complete the move, producing a cost/time trade-off region graph. Within each of the seven possible pairs/triples of aircraft types, the priority ordering of the aircraft does produce some minor variability in the percentile values for cost, but not enough to allow for practical differentiation between ordered options. In order to simplify displaying the results, the 38 ordered combinations were reduced to the same set of
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seven pairs/triples as see in Figure 6, by averaging the cost percentiles within each set. The resulting cost/time trade-off region graph is shown in Figure 7.
Figure 7: Cost/time trade-off region for direct airlift options.
The least expensive options for conducting the direct airlift to Canada involve the use of one AN-124, two CC-177 and either one or two IL-76 flights per week. As expected, the most expensive option is maximum use of all airlift assets: two flights per week for all three types of aircraft. The extremely high cost values observed at the 25 and 50 week points correspond to instances where only the AN-124 can conduct the move as the MPLs for the other aircraft are too low; recall that these account for no more than 1% of the observed values.
For the purposes of this example, suppose the risk of not completing the move within a desired timeframe is not to exceed 20%. Thus, a minimum reliability level of 80% is required. Table 4 summarizes the time and cost results at the two possible benchmarks: 80% and 99% reliability of completing the move. The first observation that can be made is that when all three types of
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aircraft are being used, the number of IL-76 flights per week (one or two) has no impact on the time and approximate costs associated with attaining the reliability benchmarks.
A closer look at Figure 6 shows that use of two IL-76 flights per week versus only one, results in greater chances of completing the move in the five to eight week range, but makes no discernable difference at the nine week point and beyond. The explanation for this phenomenon is the MPL range of the IL-76. When the IL-76 can carry a sea container, increasing the number of weekly chalks reduces the time to complete the move, condensing the time cumulative frequency plot in the lower week range. However, many of the iterations result in IL-76 MPL values too low to accommodate a single sea container so that only the AN-124 and CC-177 are used, and adding more IL-76 chalks will have no impact. This stretches out the time cumulative frequency plot in the higher week range.
Table 4: Time and cost comparison at benchmark reliability levels.
Weeks 80% reliability 99% reliability
2xAN124, 2xCC177 - $ 37.1M
1xAN124, 2xCC177, 1xIL76 - $35.2M 2xAN124, 2xCC177 - $ 56.2M 1xAN124, 2xCC177, 2xIL76 - $35.2M 2xAN124, 2xCC177, 1xIL76 - $56.2M 13
If a risk level of 20% for not completing the move in the desired timeframe is acceptable, the most cost effective option, at approximately $35.2M and 13 weeks, consists of one AN-124, two CC-177 and either one or two IL-76 flights per week. For an additional expenditure of roughly
$1.9M, four weeks could gained by instead using two AN-124 and two CC-177 flights per week ($37.1M and 9 weeks). In this latter case, there is no gain to be made by adding IL-76 flights to the combination.
If a risk level of 20% is too high, the most cost effective option remains the same as before: one AN-124, two CC-177 and either one or two IL-76 flights per week. The approximate cost is now
$46.9M and the move will take 17 weeks to complete. The time to complete the move can be reduced to 13 weeks by using two AN-124 and two CC-177 flights per week, at a cost of $56.2M;
this is a $9.3M increase over the most cost effective option.