统计代写|运筹学作业代写operational research代考|Transshipment Problem

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统计代写|运筹学作业代写operational research代考|Transshipment Problem

统计代写|运筹学作业代写operational research代考|Concept of Transshipment Problem

The transshipment problem is an extension of the transportation problem. For the transportation problem, it is assumed that a commodity can only be shipped from an origin to a destination. In many real-life situations, it is also possible to distribute the commodity through the points of origins or through the points of destinations. Sometimes it might be advantageous to distribute a commodity from an origin to an intermediate, or transshipment, point before shipping it to a destination. The transshipment problem allows for these shipments.
The transshipment problem can be described as follows. A manufacturing company has a number of plants, each of which has a limited available capacity, $s_{i}$. After manufacturing, the semifinished products are delivered to the warehouses for final assembly and packaging. Finally, the finished products are shipped to the customers according to their requirements, $d_{j}$. The problem is how to fulfill each customer’s order while not exceeding the capacity of any plant at the minimum cost, $c_{i j \text { – }}$ The problem can be transformed as a conventional transportation model with $(n-b)$ origins and $(n-a)$ destinations, where $n$ is the total number of nodes in the network (i.e., total number of plants, warehouses, and customers), $a$ is the number of node that has supply only (or pure origin), and $b$ is the number of nodes that has demand only (or pure destination). Any node that has both supply and demand is referred to as a transshipment point. The unit transportation costs, $c_{i j}$ are often dependent on the travel distances from node $i$ to node $j$. It is assumed that the cost on a particular route of the network is directly proportional to the amount of products shipped on that route. If there is no route connecting node $i$ and node $j$-or arc $(i, j)$ does not exist-then the cost is considered $\infty$. The cost of delivering 1 unit of product from node $i$ to itself is 0 . By introducing decision variables $x_{i j}$ to represent the amount of product sent from node $i$ to node $j$, the transshipment model can be written as shown in Model 2.3.1.

统计代写|运筹学作业代写operational research代考|Example of Transshipment Problem

The following example, illustrated in Figure $2.12$, shows a transshipment problem. A manufacturing company has two plants. Plant 1 can produce up to 1000 units of products per day, whereas plant 2 can produce as many as 2000 units of products per day. Instead of shipping the products directly to its customers, each product must be distributed to a warehouse first. After assembling and packaging in the warehouses, the products are shipped to the customers. The demand amounts of customer 1 and customer 2 are 1800 and 1200 , respectively. The problem is how to fulfill each customer’s order

while not exceeding the capacity of any plant at the minimum cost, $c_{i \ddot{ }}$. Unit transportation costs, $c_{i j}$, are shown above the arcs (or arrows).

This transshipment model can be converted into a conventional transportation model with five origins (i.e., P1, P2, W3, W4, and C5) and four destinations (i.e., W3, W4, C5, and C6). The supplies of origins and the demands of destinations are computed as follows. For the five origins, each plant (i.e., $P 1$ and P2) will have a supply equal to its original supply, whereas each warehouse and the first customer (i.e., W3, W4, and C5) will have a supply equal to the total available supply. For the four destinations, each warehouse (i.e., W3 and W4) will have a demand equal to the total available supply. The first customer (i.e, C5) will have a demand equal to the summation of its original demand and total available supply, whereas the second customer (i.e., C6) will have a demand equal to its original demand. The reasons for adding the total available supply to the supply and demand at each transshipment point are to ensure that the total amount of products shipped through each transshipment point will not exceed the total available supply and to also balance the transportation model.
Table $2.5$ details this transshipment problem. Decision variables $x_{i j}$ represent the amount of the products delivered from origin $i$ to destination $j$. The demand of each destination, $d_{j}$, and the supply of each origin, $s_{j}$, are shown. The upperright corner of each cell in the tableau represents the unit transportation cost, $c_{i j}$. By introducing decision variables $x_{i j}$ to represent the shipment from origin $i$ to destination $j$, this transshipment problem can be formulated as shown in Model 2.3.2.

统计代写|运筹学作业代写operational research代考| SAS Code for Transshipment Problem

ORTRANS, explained in Section $2.1$ (see also program “sasor_2_3.sas”), is a macro that solves transportation problems, the objective of which is to yield the minimum cost of shipment through a transportation network to destinations. The transshipment problem is an extension of the transportation problem, hence the same macro can be used for this example.

The only difference is that in the transshipment tableau (Table $2.5$ ) some of the costs are set to be $\infty$. Hence in the dataset, we use a large number instead (e.g., $1 \mathrm{E} 10$, which is $10^{10}$ ) because using a large number forces the user to set a variable to 0 . However, such a practice introduces numerical instability, hence we added the code shown next in the program. This constraint explicity fixes the value of the corresponding variables to 0 .
con zero{c in CUSTOMERS, $s$ in SUPPLIERS : cost $[s, c]=1 E 10}$ :
$x[s, c]=0$;
An example data file is seen in Figure 2.13.
Note that the following notations are used in this data file: Cstmer1 (W3), Cstmer2 (W4), Cstmer3 (C5), Cstmer4 (C6), Cstmer5 (P1), and Cstmer6 (P2).
Similar to Section 2.1, two parameters need to be set before calling the \%ortrans macro:
_data: Indicates the name and location of the data file (a text tab delimited file) and contains the cost matrix
_itle: Gives a title in the output of the SAS

统计代写|运筹学作业代写operational research代考|Transshipment Problem


统计代写|运筹学作业代写operational research代考|Concept of Transshipment Problem

转运问题可以描述如下。一家制造公司有许多工厂,每个工厂都有有限的可用产能,s一世. 制造完成后,将半成品运送到仓库进行最终组装和包装。最后,根据客户的要求将成品运送给客户,dj. 问题是如何以最低成本完成每个客户的订单,同时不超过任何工厂的产能,C一世j – 该问题可以转化为传统的交通模型(n−b)起源和(n−一种)目的地,在哪里n是网络中的节点总数(即工厂、仓库和客户的总数),一种是仅具有供应(或纯来源)的节点数,并且b是仅具有需求(或纯目的地)的节点数。任何既有供给又有需求的节点称为转运点。单位运输成本,C一世j通常取决于到节点的行进距离一世到节点j. 假设网络特定路线的成本与该路线上运送的产品数量成正比。如果没有路由连接节点一世和节点j- 或弧(一世,j)不存在-则考虑成本∞. 从节点交付 1 单位产品的成本一世对自身是 0 。通过引入决策变量X一世j表示从节点发送的产品数量一世到节点j, 转运模型可写成模型 2.3.1 所示。

统计代写|运筹学作业代写operational research代考|Example of Transshipment Problem

下面的例子,如图2.12,表示转运问题。一家制造公司有两个工厂。工厂 1 每天最多可以生产 1000 件产品,而工厂 2 每天可以生产多达 2000 件产品。每个产品都必须先分发到仓库,而不是直接将产品运送给客户。在仓库组装和包装后,将产品运送给客户。客户 1 和客户 2 的需求量分别为 1800 和 1200 。问题是如何完成每个客户的订单

在不以最低成本超出任何工厂的产能的同时,C一世¨. 单位运输成本,C一世j, 显示在弧线(或箭头)上方。

这种转运模型可以转换为具有五个起点(即P1、P2、W3、W4 和C5)和四个目的地(即W3、W4、C5 和C6)的常规运输模型。来源地的供给和目的地的需求计算如下。对于五个起源,每个植物(即,磷1和 P2) 的供应量将等于其原始供应量,而每个仓库和第一个客户(即 W3、W4 和 C5)的供应量将等于总可用供应量。对于四个目的地,每个仓库(即 W3 和 W4)的需求量将等于总可用供应量。第一个客户(即 C5)的需求等于其原始需求和总可用供应的总和,而第二个客户(即 C6)的需求等于其原始需求。将可用供应总量添加到每个转运点的供需中的原因是为了确保通过每个转运点运输的产品总量不会超过可用供应总量,同时也是为了平衡运输模式。
桌子2.5详细说明了这个转运问题。决策变量X一世j代表从原产地交付的产品数量一世到目的地j. 每个目的地的需求,dj,以及每个来源的供应,sj, 显示。表格中每个单元格的右上角代表单位运输成本,C一世j. 通过引入决策变量X一世j代表从原产地发货一世到目的地j,这个转运问题可以表述为模型2.3.2。

统计代写|运筹学作业代写operational research代考| SAS Code for Transshipment Problem


唯一的区别是在转运画面(表2.5) 一些成本设定为∞. 因此,在数据集中,我们使用了一个很大的数字(例如,1和10,即1010) 因为使用大数会迫使用户将变量设置为 0 。但是,这种做法会引入数值不稳定,因此我们在程序中添加了接下来显示的代码。此约束明确地将相应变量的值固定为 0 。
客户中的 con zero{c,s在供应商中:成本[s, c]=1 E 10}[s, c]=1 E 10} :
示例数据文件如图 2.13 所示。
请注意,此数据文件中使用了以下符号:Cstmer1 (W3)、Cstmer2 (W4)、Cstmer3 (C5)、Cstmer4 (C6)、Cstmer5 (P1) 和 Cstmer6 (P2)。
与 2.1 节类似,在调用 \%ortrans 宏之前需要设置两个参数: _data
_itle:在输出中给出标题SAS 的

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