E L MODELO DE R EDESCRIPCIÓN R EPRESENTACIONAL

Virtually the vast majority of HLPs planned at the strategic level are based on the premise that the network is planned from scratch. That is to say, there is no need for planners to consider facilities and other fixed assets, such as vehicles and equipment, in current networks. However, in many real-life cases the planning is based on current networks that may need to be expanded, merged or even shrunk192_{, i.e. modification or reconstruction} of current networks.

This is the pragmatic problem that is faced by many EDS providers. In our case the to-be planned network is partially owned by a relatively large EDS provider in China and is at present supporting its nationwide ex- press delivery business. Besides the resources that the company shares with its partner, a lot of proprietary assets have been invested in the current service network. Specifically, due to capacity bottleneck and market competition, it has built dozens of regional ground hubs, consolidation centers and air gateways consecutively without globally planning the network in the past few years. Built specially for express delivery business, these facilities are invested by Company A alone and not shared by its partner. Moreover, it owns several air- craft exclusively for EDS. We must take these resources into account, when we globally plan the new network.  Current facilities

Current facilities can sometimes be considered in the network planning with conditional facility location prob- lems or facility relocation problems. Conditional facility location problem, whose name is acknowledged in literatures, actually deals with facility expansion problems. It tries to find the best location for p new facilities, when some existing facilities are already located in the area. Customers are assumed to get service from the closest facility whether existing or new, so most probably they are conditional p-center problem or conditional p-median problem193_{. Since they are dependent on the number of existing facilities, q, they are also called the} conditional (p, q)-median/center problems194_{. Facility relocation problem handles with both facility expansion}

191 _{See Kara (1999). Sohn and Park also proved it NP-hard when the hub number is larger than 2. See Sohn/ Park (2000), pp.17-25.} 192 _{See e.g. ReVelle (2007), pp.533-540.}

193 _{See Tamir (2005), p.50.} 194 _{See e.g. Drezner (1995), p.525.}

and phase-out problems. As a matter of fact, it is taken up as a reactive strategy for the organization to adjust itself in time to reality. This problem is also discussed with dynamic location methods195_.

In this dissertation we resort to the “Sunk Cost Theory” to consider current facilities with static models. We regard the value of the facilities that cannot be transferred into the new network or cannot be retrieved by transferring on the market as sunk cost. In the model we only consider extension cost of the potential hub nodes that are currently equipped with consolidation centers or regional ground hubs.

 Current aircraft

Aircraft is another kind of important fixed assets for EDS providers. Compared with truck and van, it incurs much higher purchase price and maintenance cost and has less chance to change hands on the market. Acquisi- tion, possession, mothballing or selling of an aircraft is a relatively long-term decision compared to decision of other ground vehicles and equipment.

As is anticipated, more hubs will be installed in the new network, indicating that more flight routes are neces- sary. Actually, it is unnecessary and also uneconomical to satisfy all the air freight demand by self-owned air- craft due to the small volume on most of the inter-links. Company A intends to continue to adopt a mixed air freight service strategy by out-sourcing and self-owned aircraft with the objective of minimizing the air cost. That means air freight tasks are fulfilled by both self-provided and commercial air services. Therefore, the strategic planning of the EDS network is also faced up with the following issues: how to assign current air- craft in the new air network; is it more economical to purchase new aircraft and what type to choose or stop using current aircraft.

The air service selection decision, basically speaking, aircraft fleet ownership decision, is seldom included in HLPs. However, in perspective of management the decision on whether outsourcing or self-provided service has much longer planning horizon than other tactical decision, such as vehicle routing and scheduling prob- lems. For this reason, we include this decision in our network planning. The rest of this chapter is dedicated to research on air service selection decision and aircraft ownership decision by distinguishing cost functions of different air freight services196_{. In other words, the air cost is no longer as simple as that in the basic model.} We separate different air services with flow-dependent cost functions, including service from self-owned air- craft, normal suppliers on air freight market and contracted suppliers with quantity discount rate. The objec- tive is to minimize the total cost by optimally determining the aircraft fleet ownership (Ext.1) or by making full use of the current self-owned aircraft (Ext.2). Meanwhile, we also investigate if air service selection deci- sions can in turn impact on hub location decisions.

Incorporating flow-dependent air cost functions into HLPs will break the one of the three classical assump- tions197_{, i.e. fixed discount rate on hub arc, which means that the average cost rate of inter-hub links is fixed or}

195 _{For example, Melachrinoudis and Min determined the optimal timing of relocation and phase-out in the planning horizon using a dynamic, multiple}

objective, and mixed-integer programming model. Wang et al. studied a budget constrained location problem in which they simultaneously con- sider opening some new facilities and closing some existing facilities. See Melachrinoudis/Min (2000), pp.1-15; Wang et al. (2003), pp. 2047-2069.

196 _{This method is also applicable to tributary network with ground transportation.} 197 _{For details, please refer to Sec.2.2.5.}

independent on the flow and it is also lower than that on feeder route. In our case, this simple but arbitrary assumption will seriously distort the problem.

For one thing, the travel cost is not always proportional to the flow. It is obvious that the average air cost decreases with the increase of the flow, when we consider link fixed cost. Moreover, contracted air freight suppliers always offer discount to the order that is above the predetermined minimum quantity (or threshold). For another, backbone cost rate is not always lower than feeder cost rate. The classical assumption is con- sistent with the fact that travel cost in ground backbone network is lower than that in feeder network due to the possibility to utilize larger vehicles by bundling parcel streams in backbone transportation198_{. Economies} of scale (EOS) typically result in lower cost rate on backbone links in comparison to that on tributary links. Higher cost in tributary networks may be the reason why nearly all HLRPs include vehicle routing problems (VRPs) for tributary networks rather than for backbone networks. However, the case in air-ground networks for EDS seems to be on the opposite side. Globalization and economic development propel the multimodal transportation systems to offer faster and seamless service. In EDSI, parcels and mails are consolidated for the sake of faster transportation mode rather than only for the sake of lower transportation cost. Backbone transport is more often than not accomplished by air with higher cost rate rather than by more economical lorry. Therefore, the backbone network, a vital factor of the cost and delivery time for the EDS, must be paid more attention.

For these reasons, we put more emphasis on the backbone network and study service selection problem on backbone network rather than on tributary networks.