Problem Description

The resilient strategy in Nair et al. (2010) and Chen & Miller-Hooks (2011) is to recover link capacities from the viewpoint of terminal operator or network manager. But from the transportation carrier standpoint, the express company can’t recover the link capacities, for example repairing the roads or airport runway. Thus, how to enhance the resilience under the limited choices becomes the question that we want to explore. As shown in Figure 3.1(a) (b), the original path flow will be disturbed by disruption. One of possible recovery measures is to amplify the flow on an unrelated link to achieve another state (Figure 3.1 (c)). We think it is suitable for the express companies. Thus, the concept in Figure 3.1 will play important role in our model formulation.

Figure 3.1 One of possible recovery method

(a) the normal operation (b) post-disruption state (c) recovery to another equilibrium

The problem we are handling is a post-event relief problem. We discuss how to re-allocate the current transportation resources and use others resources under several own limitations and the limitation of external environment and then decide the ways of

transportation for shipments after the disruption occurs.

Based on the problem, the mathematical model is formulated to seek a set of optimal actions from resilient strategies during the disruption. We are modeling the reactive resilient strategies in section 3.1.1 including alternative routes, different modes, renting capacities by others into our model. Additionally, we also consider the re-allocating activities to be one of resilient strategies. The resilient strategies here are operational level, which are conducted in the short period. Although the route choice and mode choice problems are applied widely, the focus here is on the complex transportation problem combining with mode choice, route

decision, carrier selection, and cargo selection. We then discuss the design of above selections in our operation model in detail.

1. Mode choice

The intermodal freight transport system in our model involves four modes (trucks , rail, aircrafts, ships) in the movement of cargo between origins and destination.

2. Route decision

In the model we want to choose the best alternative route when the disruption happens. The available routes are determined by the affected infrastructure capacity, for example, the road system and terminals.

3. Carrier selection

As mentioned before, we classify the rental types into contractual partner and non-contractual partner. The advantage of contractual partners is that they can provide more accurate flight so the dispatching and preparing time (renting time) is longer than non-contractual partners. On the contrary, the rental price of contractual partners is higher.

Multi-carrier strategy is the crucial part in our study that differs from the previous literatures.

4. Cargo selection (What kind of freights have higher priority to be transport)

The concept of different time dependent cargo value function is added to our model to reflect the characteristic of express company. From the past literature, we know that Chen & Schonfeld (2010) proposed different kinds of time dependent cargo value function. They stress on the perishable cargo which may have nonlinear time value functions and assume the value of time of cargo decrease over time, for example a

nonconvex piecewise linear function or a nonlinear probabilistic function. Thus, we think the cargo value decreasing over time can present the time-sensitive of express industry.

The time dependent cargo value function in the model can generate the transporting priority of the different cargos. It can make the company earn more business reputation and gain the economic benefit for customers.

In our model, we assume that 𝜇^𝑏 is cargo value function of different order b and each order b includes one type of cargo. The following is the time dependent cargo value function that we allege:

(1) Constant value commodity

The characteristic of this kind of commodities is that the values aren’t easy to change with time, for example personal items and competitive products. We assume the time dependent cargo value function is the constant function of time as following and show in Figure 3.2.

𝜇(𝑡) = 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦

Figure 3.2 Time dependent cargo value function of constant value commodity

Market price is the economic price for which a good or service is offered in the marketplace.

(2) Perishable commodity

The perishable commodity will become spoil with time, for example flowers and seafood. The cargo value of perishable commodity decreases over time which is similar as the theory mentioned by Chen & Schonfeld (2010). We assume the time dependent cargo value function is as following and show in Figure 3.3.

cargo time value 𝜇(𝑡) (dollars)

time period t (days)

𝜇(𝑡) = 1

√2𝜋𝑧𝑒^{−12(𝑣)𝑡 2}

v = the factor which is used to adjust time period z = the factor which is used to adjust time value

When the lifetime of product is shorter, the value of v is smaller. When the market price of products is higher, the value of z is smaller.

Figure 3.3 Time dependent cargo value function of perishable commodity

(3) Short life-cycle commodity

Technologic products, like smartphone and tablet, have the short product life cycles.

The price may come down two to five percentage points every week because new products are going to launch to the market continuously. Certain clothing fashions also have this attribute. The popular style of clothing in each period is easy to be given a discount when time passed by because so many stores start to sell it or the clothing goes out of style. We assume the time dependent cargo value function of this kind of cargo as following and show in Figure 3.4.

𝜇(𝑡) = {𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 , 0 < 𝑡 ≤ 𝑡𝑖𝑚𝑒 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 (1 − 𝑢 )𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 , 𝑡 > 𝑡𝑖𝑚𝑒 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑

u = prices dipped factor cargo time value 𝜇(𝑡) (dollars)

time period t (days)

Figure 3.4 Time dependent cargo value function of short life-cycle commodity

(4) Holiday gift

The cargos which belong to holiday gifts will directly lose total cargo value if the arrival time is not within a specific time period. We assume this kind of cargos have the following time dependent cargo value function in Figure 3.5.

𝜇(𝑡) = {𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 , 0 < 𝑡 ≤ 𝑡𝑖𝑚𝑒 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 0 , 𝑡 > 𝑡𝑖𝑚𝑒 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑

Figure 3.5 Time dependent cargo value function of holiday gift

More valuable cargos will be chosen to transport in the model reflecting on the second objective function. In our model, we assume that the freights with different order numbers have different time dependent cargo value function. It means the value of cargo depends on the order number.

The express company will try to deliver shipments as soon as possible in a best effort according to delivery schedules but it is not liable for any damages or loss caused by delays.

cargo time val e 𝜇(𝑡) (dollars)

time period t (days)

cargo time value 𝜇(𝑡) (dollars)

time period t (days)

Only certain services will provide money-back guarantee for delay in some cases. These shipments account for two to three percent of the total shipments. Although companies don’t have loss with money for most part of delayed shipments, they still need to deliver the shipments as fast as possible to reach the high level of service quality. This way, the business is able to achieve sustainable and successful development. That is also the reason why we consider the time dependent cargo value function in this study. We want shipments to be delivered in the high-valued period and satisfy the customers’ demand as best as company can at same time.

3.2 Model Formulation

The mathematical model will be depicted in this section.