In this section, we examine how the variation of the hub coverage radius impacts on the solution of the model. Three hub radii listed in Tab.6-19 are under consideration. The corresponding time windows for tributary network and backbone network are also listed below based on an average highway speed of 90km/h and the time schedule in Tab. 6-3. We also assume direct flight between any potential hubs is less than 5 hours.
Hub coverage radius (km) 225 270 315
Time window for tributary network (hour) 2.5 3 3.5
Table 6-19: Hub coverage radius and corresponding time window for tributary and backbone networks
Hub coverage radius 225 270 315
Hub Nr. 94 69 55
Total cost 68713053 (121.53%) 56540386 49539818 (87.62%)
Total air cost 19639177 (100.43%) 19555555 19303250 (98.71%)
Cost by self-owned aircraft 919735 (57.98%) 1586280 2280160 (143.74%) Cost from air freight market 18719442 (104.17%) 17969275 17023090 (94.73%)
Hub fixed cost 47000000 (136.23%) 34500000 27500000 (79.71%)
Feeder transportation cost 2073876 (83.46%) 2484831 2736568 (110.13%) Volume by self-owned air-
craft (kilo*kilometer) 136427553 (57.59%) 236898338 345386351 (145.80%) Volume by air freight market
(kilo*kilometer) 2674205929 (104.17%) 2567039273 2431870050 (94.73%) Volume by truck (ki-
lo*kilometer) 414775200 (83.46%) 496966110 547313600 (110.13%)
Table 6-20: Scenario planning for variation of hub coverage radius
The solutions under the three scenarios are tabulated in Tab.6-20. Note that the hub location decision is quite sensitive to the controllable factor hub coverage radius. When the hub coverage radius decreases, the number of hubs in the network, the total cost and the transportation cost increase. Although the feeder transportation cost decreases, it cannot compensate the increase of the air cost.
When we go through the traffic volume, we find that the reduction of the hub coverage radius leads to the decrease of volume by truck but the increase of volume by air. However, the average traffic volume on inter- hub links and thus the traffic volume by self-owned aircraft decrease.
A small hub coverage radius means short delivery time if the time window for the air backbone network is fixed. But it also means high total cost that results from the increase of the hub number and air traffic volume. In fact, these two measures of network performance, i.e. delivery time and cost, are conflictive and any gain in one is expected to be accompanied by a loss in the other. For example, with the assumption of a 5-hour time window for the air network the delivery time decreases from 12 hours to 10 hours by 16.67%, when the hub coverage radius decreases from 315km to 225km. However, the reduction of the delivery time leads to a somewhat steady increase of the total cost by 38.7%. If we interpret the delivery time as an indicator of the service quality, we may suggest that a smart company may only allow moderate deterioration of the service quality which leads to steady cost reduction. Otherwise, the mild cost saving cannot compensate the sharp reduction of the revenue.
When we go through all the hub location decisions under the four scenarios, we find that some hubs always stand in optimal solutions. The first kind of these hubs, taking Urumqi as an example, is geographically dis- persed from other potential hubs. Actually, they may be designated as hubs in preprocess procedure. The sec- ond kind is hubs with large origin or destination flow themselves, such as Peking and Shanghai. The third
kind is hubs with location advantage. Although their in-and-out demand volumes are not so large, they locate at the center of node clusters. These hub locations are not sensitive to the other factors so that they can be built with priority if the budget is limited.
However, three concerns must be further considered in real life. First, the model is based on the assumption that hubs are fully inter-connected. Once stopover is allowed, a loose time window for the air network means large transfer opportunities and thus air cost saving. Second, the model assumes that demand nodes are direct- ly connected to “home” hubs. However, pure star-shaped feeder networks seldom appear in reality. When de- mand nodes in the hub regions are connected by several routes rather than by direct service, small hub cover- age radius also means less feeder trucks and thus cost saving of feeder transportation. Third, the service quali- ty of the same day EDS within the hub region is not considered here. Although these three concerns are not included in this dissertation, they must be considered in reality.
6.4.
Summary
This chapter is devoted to empirical study on real-life problem. In Sec.6.1 we illustrate how we collect and modify input data of the models. We illustrate the problems we are faced up with and introduce the methods and mathematical instruments we have used. The purpose of this section is to provide our readers an overview of the project and some guidance to the application of the proposed models and algorithms.
In Sec.6.2 we display the solutions of Ext.1 and Ext.2 by the proposed hybrid GAs under the basic instance. The comparison between them not only suggests some important features of our specific network but also indicates some general conclusions: (1)the cost focus shifts from the tributary networks in pure ground H/S networks to the backbone air network in air-ground H/S networks, which indicates that the planning focus of multimodal EDS networks should also lie in the air network; (2) the concave piecewise linear cost function (that can be easily transformed from the cost selection function in this dissertation) has flow bundling effect; (3) models with concave piecewise linear cost function may automatically present a quasi H/S network alt- hough no such structure is imposed. In this section we also provide a dynamic update strategy of aircraft fleet to guide the implementation of the project. We test the performance of the Improvement technique 5 in Sec.4.2.5 with the project data set. However, its time-saving advantage is not significant in our case probabil- ity due to the short calculation time of the embedded integer programming and the fluctuation of the GAs’ running time.
Sec.6.3 is devoted to scenario planning based on Ext.2. Most of the results in scenario planning suggest that the hub fixed cost in neutral scenario is relatively high so that the model always chooses as few hubs as possi- ble to minimize the total cost. For this reason, the hub location decision is not sensitive under most scenarios, except the hub coverage radius. The hub coverage radius seems to be decisive to the network configuration in our case and must be set with great care. Some general conclusions are obtained or verified: (1) EOS can be obtained in H/S network, which primarily comes from the hub fixed cost and may also from self-owned air- craft; (2) loading factor is a controllable factor for decision-maker to balance costs and the corresponding over- demand risk;(3) the hub coverage radius is a controllable factor to determine the service quality in terms of delivery time according to the cost. However, scenario planning in this section is under some simplifications of the reality which must be considered in real-life cases.