IV. Numerical Experiment
4.4 Sensitivity Analysis
A sensitivity analysis is carried out to find the influential parameters to our objectives.
The parameters we perform in sensitivity analysis are divided into three categories, capacity, time and cost. Capacities parameters include available rented capacities from other carriers (AK), own flights capacities (WA) and own truck capacities (KL); Time parameters include transportation time (T), time spending on re-allocating own trucks (ET), time spending on renting capacities (RT); cost parameters include rent cost(RC) and cost of re-allocating trucks (VC).
In sensitivity analysis, we choose scenario 4 in small network to be the analyzed case. To perform the changes, we present each value as a ratio (𝑌1, 𝑌2) between the new performance value and the original value. The original values are the results of original scenario 4. 𝑌1 and 𝑌2 are defined as follows.
𝑌1 = 𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 1𝑛𝑒𝑤 𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 1𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑌2 = 𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 2𝑛𝑒𝑤
𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 2𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙
Objective 1 is total cargo time value and objective 2 is incremental resilient cost.
1 .Capacity parameters
Call for the resilient strategies in chapter 3.1.1, we mentioned that reserved capacity is one of possible proactive strategies to reduce the disruption impact on transportation. Thus, we analyze the effects of changing capacities parameters in our model including available rented capacities from other carriers (AK), own flights capacities (WA) and own truck capacities (KL) to find how much impact they have.
Figure 4.6, 4.7 and 4.8 depict the variation of Y1and 𝑌2 in AK, WA and WL. We see that the less available rented capacities (AK) the company has, the less cargo time value (Y1) it can reach and less resilient cost (𝑌2) it needs to pay. Because available rented capacities (AK) limits the recovery activities.
In Figure 4.7, when the own flights capacities (WA) becomes smaller, the incremental resilient cost (𝑌2) is increasing and the impact on 𝑌2 is more significant. The reason is that it needs to rent more capacities from others to maintain the cargo time value.
The variation of 𝑌2 in own truck capacities (KL) is similar with own flights capacities (WA) in Figure 4.8. The difference is that KL doesn’t decrease progressively with the less degree. It is close to a linear relationship between resilient cost (𝑌2) and increased own truck capacities (KL).
The fluctuation of 𝑌1 in AK, WA and KL are slight comparing to 𝑌2 so we analyze it in Figure 4.9.
Figure 4.6 Variation of Y1and 𝑌2 in AK -0.2
0.2 0.6 1 1.4
2 1.75 1.5 1.25 1
0.75 0.5 0.25 0.1 ratio
increment multiple
Available capacities (AK)
Y1
Y2
Figure 4.7 Variation of Y1and 𝑌2 in WA
Figure 4.8 Variation of Y1and 𝑌2 in KL
When we compare 𝑌1and 𝑌2 separately (Figure 4.9 and 4.10), we see that 𝑌1 (the ratio of cargo time value) is more sensitive in available rented capacities (AK) and own flights capacities (WA). It means the parameters, AK and WA, have more impact on the cargo time
Y
Own flight capacities (WA)
Y1
Own truck capacities (KL)
Y1 Y2
In Figure 4.10, we find there are two kinds of curves. One is going down and the other is raising. When the own capacities of company including WA and KL decrease, 𝑌2 (the ratio of incremental resilient cost) will increase progressively. But when the rented capacities (AK) decrease, 𝑌2 (the ratio of incremental resilient cost) will decrease. It can be interpreted as following. When the own capacities are few, the company is going to rent more capacities from others. However, when there are few available renting capacities, the company may not recover the cargo flows.
Figure 4.9 Variation of cargo time value in capacity parameters 0.75
0.8 0.85 0.9 0.95 1 1.05 1.1
2 1.75 1.5 1.25 1
0.75 0.5 0.25 0.1
ratio
increment multiple
Y1
(the ratio of cargo time value)
AK WA KL
Figure 4.10 Variation of incremental resilient cost in capacity parameters
2. Time parameters
Figure 4.11, 4.12 and 4.13 illustrate the effects of changing transportation time (T), re-allocation time (ET) and renting time (RT). The changing of transportation time (T) is more significant when the transportation time is larger than twice. 𝑌1 (the ratio of cargo time value) and 𝑌2(the ratio of incremental resilient cost) are declining first and then increase. It can be interpreted that a longer transportation time will force the total cargo time value reducing.
Some of cargos are not delivered on time. Thus, the resilient cost will reduce first. But when the transportation time is over a threshold, it begins to spend a lot of money to prevent the decline of cargo time value and cost is high.
Otherwise, ET and RT have less impact to objective values than T. When renting time (RT) is over 2.75 multiple, 𝑌1 and 𝑌2 decrease.
(the ratio of incremental resilient cost)
AK WA KL
Figure 4.11 Variation of Y1and 𝑌2 in T
Figure 4.12 Variation of Y1and 𝑌2 in ET
0 0.5 1 1.5 2 2.5 3
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
ratio
increment multiple
Transportation time (T)
Y1 Y2
0 0.2 0.4 0.6 0.8 1 1.2
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
ratio
increment multiple
Re-allocation time (ET)
Y1 Y2
Figure 4.13 variation of Y1and 𝑌2 in RT
When we compare 𝑌1and 𝑌2 separately (Figure 4.14), we see that 𝑌1 (the ratio of cargo time value) is declining as transportation time (T) expands generally. Comparing to
transportation time (T), 𝑌1 (the ratio of cargo time value) is less sensitive in time spending on renting capacities (RT) and truck re-allocation (ET). In Figure 4.15, the variation of 𝑌2 in the time parameters is greater when the increment multiple of T is far from 1.
0 0.2 0.4 0.6 0.8 1 1.2
0.25 0.5 0.75 1 1.5 2 2.25 2.5 2.75 3
ratio
increment multiple
Time spending on rent (RT)
Y1 Y2
0.4 0.6 0.8 1 1.2
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
ratio
increment multiple
Y1
(the ratio of cargo time value)
ET RT T
Figure 4.15 variation of incremental resilient cost in time parameters
3. Cost parameters
Obviously, the incremental resilient cost is affected by renting cost. Figure 4.16 and 4.17 demonstrate the results when the renting cost and re-allocation cost change with increment multiple. In Figure 4.16, it shows that 𝑌2 is increasing in RC but 𝑌1 doesn’t change. In Figure 4.17, 𝑌2 is also increasing in VC but 𝑌1 is decreasing slightly when VC is below 0.5 multiple. We can interpret that the renting cost and re-allocation cost directly impact the total incremental resilient cost, which is intuitive. They don’t impact total cargo time value and the choice of recovery activities. The curve of 𝑌2 in RC is linear but it is not linear in VC. This is because there is the fluctuation existing in the balance between two objectives.
0 0.5 1 1.5 2 2.5 3
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
ratio
increment multiple
Y2
(the ratio of incremantal resilient cost)
ET RT T
Figure 4.16 Variation of Y1and 𝑌2 in RC
Figure 4.17 Variation of Y1and 𝑌2 in VC
When we compare 𝑌1and 𝑌2 separately (Figure 4.18 and 4.19), we see that 𝑌1 (the ratio of cargo time value) is no change in RC and a little change in VC. 𝑌2 is increasing as RC and VC increase. We find that incremental resilient cost is more sensitive in renting cost (RC) than in re-allocation cost (VC) because the renting cost is higher than re-allocation cost.
0.2
Cost of re-allocation (VC)
Y1 Y2
Figure 4.18 Variation of cargo time value in cost parameters
Figure 4.19 Variation of incremental resilient cost in time parameters
0.8 0.85 0.9 0.95 1 1.05
0.25 0.5 0.75 1 1.25 1.5 1.75 2
ratio
increment multiple
Y1 (the ratio of cargo time value )
RC
VC
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0.25 0.5 0.75 1 1.25 1.5 1.75 2
ratio
increment multiple
Y2
( the ratio of incremantal resilient cost )
RC VC