Question

求翻译，数学文章翻译

3. THE LOCATION-ROUTING PROBLEM
The classical facility location problem considers that the deliveries are direct and
independent (see Daskin (10) or Mirchandani and Francis (15)) under the assumption that the delivery is done under Full-Truck-Load (FTL) which means that the truck is filled with supplies for just one customer. However, there are situations in which clients are visited along a specific route. Moreover, most of the deliveries are done under Less-than-Truck-Load (LTL) where the truck contains supplies for different clients who are visited through a route.
In this work, our focus is on situations where the routing problem has to be solved
together with the facility location problem trying to minimize the total cost by selecting a set of facilities and constructing delivery routes with constraints such as
i. Customer demands ii. Vehicle and facility capacities
iii. Number of vehicles iv. Route lengths or route durations (specified time limit)
v. Tour constraint: each vehicle has to start and end at the same facility
The uncapacitated LRP version of the problem, in which there is no facility and
vehicle constraints, was defined by Berger et al. (7) as follows:
Let I be a set of client locations and J be the set of candidate facility locations. We
can define a graph where or the set of nodes and
the set of edges. We can also define k as a feasible route that starts at facility j
visits a subgroup of nodes and returns to facility j and the set of feasible routes for
facility j. The IP formulation for the problem is
Minimize
subject to
where
Cost of fixed facility j
Cost of route k associated with facility j
1 if facility j is selected, 0 otherwise
1 if route k associated with facility j is selected, 0 otherwise
1 if route k associated with facility j visits client i, 0 otherwise
The objective function minimizes both the fixed costs and the routing costs
whenever each client is served by one facility (Constraint 1) and assuring that only routes of selected facilities are selected (Constraint 2). As mentioned in Section 2, Berger et al. (7) solved this problem with a branch and price algorithm which uses Desrosiers et al.
(11) column generation approach (see also Simchi-Levi et al. (20))
In the following section, we will show that the pre-positioning problem can be
addressed with a similar approach but accounting for disruptions both in the links (routes) and the facilities chosen for pre-position items.

Answer 1

3。位置的路由问题
古典设施的选址问题，认为分娩是直接和
独立（见Daskin（10）含姿扮或米尔查达尼和弗朗西斯（15））下的交货卡车负载（FTL），这意味着，这辆卡车是充满用品只有一名顾客下做的假设。然而，有哪些客户端沿特定路线参观的情况。此外，大部分的分娩下低于卡车负载（LTL）卡车包含不同的客户端是通过路由访问用品。
在这项工作中，我们的重点是路由问题是要解决的情况下，
连同设施的选址问题，试图以尽量减少总成本，选择了一套设施，建设与制约，如交付航线
一客户的需求二。车辆和设施的能力
III。车辆IV的数量。路线长册伏度或路线时间（指定期限）
诉之旅约束：每个车辆已开始和结束在同一设施
问题uncapacitated LRP的版本，其中有没有设施和
车辆的限制，是指由Berger等。 （7）如下：
让我是一个客户端的位置和J候选设施位置。我们
可以定义一个图或节点集
边集。我们也可以定义为一个可行的路线，开始在工厂j k
的节点，并返回分组参观设施J和一套可行的路线
设施J.知识产权问题的提法
减少
受
其中
固定设施j的成本
成本与工厂j相关的路线k
1，如果设施j是选择，否则为0
1，如果设施j相关的路线k被选中，否则为0
1，如果设谈灶施j相关的路线k访问客户端的我，否则为0
目标函数最小化的固定费用和成本路由
每当之一设施（1约束）每个客户服务和保证，只有选定的设施路由选择（限制2）。第2节中提到，Berger等。 （7）使用Desrosiers等人的一个分支和价格算法解决这个问题。
（11）列生成的方法（也见Simchi - 列维等人（20））
在下面的章节中，我们将表明，前期定位的问题，可
用类似的方法，但在链路（路由）和前位置的项目选择的设施中断的会计处理。

只能这样了！数学专业英语just so so。

Answer 2

带的问题

经典的设施选址问题,认为直接发货

独立的(见Daskin(10)或Mirchandani和法兰西斯(15)情况下,Full-Truck-Load下完成交货(FTL)这意味着卡车装满手改简供应一个顾客。然而,在一些情况下,客户访问沿某一特定的路线。而且,大部分递毕裤送Less-than-Truck-Load下做的(LTL),为不同的客户提供卡车包含那些参观了通过路线。

在这部作品中,我们歼空的重点是路由问题的情况下,亟待解决

连同设施选址问题试图减少总成本通过选择一套设备交货路线,构建与约束等

我。客户的需求ii。车辆和设备能力

三。四、路线的车辆数目路线长度和时间(指定期限)

v旅游约束:每一个汽车开始和结束在相同的设备

uncapacitated含的版本的问题,其中并无设施

车辆约束规定,柏格丁晓萍。(7)如下:

让我是一组客户位置和J是套候选人设施的地点。我们

哪里可以界定一个图或套节点和吗

集合的边缘。我们还可以定义k作为一个可行的路线,从设施j

访问一个共有节点和返回设施j和设置较为可行的路线

设施j。IP配方的问题所在

减少

受

在

固定设施的成本j

成本相关路线k设施j

如果设备j被选中,0聪明

如果路线k有关设施j被选中,0聪明

如果路线k相关客户,我设施j访问,0聪明

两个目标函数最小化固定成本和路由成本

当每一位客户服务由一个设备(约束1)和确保只有路线选择选定的设施(约束2)。2节所述,柏格丁晓萍。(7)解决这一问题的算法,一根树枝,价格使用Desrosiers丁晓萍。

(11)柱代方法(见也Simchi-Levi丁晓萍。(20)

在接下来的部分里,我们将表明,pre-positioning问题

做一个类似的方法,但都占中断连结(路线)pre-position及其设施使用者选择项目。

Answer 3

哇，鸡肠啊