首页 >>SC2x-W1-PP6:TemporaryNetworks
SC2x-W1-PP6:TemporaryNetworks
发布来源: 德川家康学艺录 发布时间:2020-07-14
关注德川家康学艺录,置顶公众号

一艺之成,当尽毕生之力

━ ━ ━ ━ ━ ━

Practice Problem 6: Temporary Networks


        When a natural disaster strikes, normal supply chains are disrupted and many vital supplies cannot reach those affected through the normal routes. To handle the first couple of days after the disaster, many specialized Non Governmental Organizations (NGOs) work hard to secure vital supplies such as food, blankets, and medicines, and deliver these to people in the affect areas. To do so, they set up temporary supply networks, which only operate as long as needed.


        Suppose you are working with one such NGO to set up a temporary network to distribute disaster-kits in the aftermath of a hurricane. You have secured kits from your central supply facility that will be flown in regularly. The kits need to be delivered once per week as long as needed to eight (8) temporary shelters, which are located a few hours drive from the airport.


        To simplify the operations, you aim to set up a logistics and distribution center (DC) that controls all distribution. All incoming shipments will be transported from the airport directly to the center by the military, and from the DC you will plan how the kits are delivered to the shelters.


        You are choosing between five (5) locations for the DC. The distances between the five (5) potential locations and the eight (8) shelters are shown in the table below.


        The weekly demand at each shelter has been estimated as follows:        

        The capacity of the DC will be limited to 150,000 kits per week. It costs $100,000 per week to set up and run a DC.

Part 1



        Trucks that can operate on the roads after the hurricane are in short supply, so you want to choose the location of the DC to minimize the transport work (tonkm, or the total kit-miles travelled) in the temporary network. Note that transport work per kit is proportional to distance.

        

        Which of the five locations should the NGO choose to minimize the transport work in the temporary network?

  • DC1

  • DC2

  • DC3

  • DC4

  • DC5


Part 2



        Due to road conditions, the shelters furthest away from the center may suffer from late and unreliable deliveries. As a result you are thinking about opening more than one DC.


        To trade-off the fixed costs with the variable costs, you estimate that each transported mile costs $2 per kit.


        Assuming the military is ok with delivering your supplies to more than one DC, what is the optimal number of DCs?

  • 1

  • 2

  • 3

  • 4

  • 5


Part 3



        You realize that the actual cost of setting up and operating a DC is not perfectly known. What is the optimal number of DCs if the fixed costs are instead $300,000 per week per DC? Assume the same transportation costs as in Part 2.

  • 1

  • 2

  • 3

  • 4

  • 5


Part 4



        When you see the optimal solution from Part 3, you realize that under that solution, much of the demand is more than 2 miles away from a DC. How does the optimal solution change if we require that at least 60% of demand should be less than 2 miles from a DC?

  • The optimal number of DCs increases

  • It is optimal to open DC 2 and DC 5

  • The optimal number of shipments to Shelter 7 increases

  • There are no changes in the optimal design



Answer



Part 1: DC5

        只选一个DC,那么久选距离和需求乘积之和最小的DC即可,算出来为DC5

Part 2: 4

在Excel建立线性规划模型如下:

1.求Total Cost最小值为目标(B28):DC运往各shelter的数量 * 对应的Cost

2.黄色区域是我们要求解的变量:DC运往各shelter的数量以及DC的setup数量

3.限制条件如下:

  1. 需求(第37~39行):DC运往各shelter的数量必须大于当地的需求

  2. 供应能力(第M~O列)

  3. K31~K35只能为0或1(二进制)

  4. Number of DCs必须大于1且小于5

  5. Flow的限制(C42:K46):即如果某DC有发货,则对应的Number of DCs必须等于1.因此某DC到某Shelter的发货量*对应DC的Number of DCs减去某Shelter的总需求量必须≤0.

4.建模如下图,得到DC数量为4(如上图)

Part 3:2

        修改set up DC的cost从100,000到300,000,求解如下:开DC3和DC5。


Part 4:

        在之前的基础上,增加限制条件:即2mile以内的需求要大于60%。操作如下图:

        求解增加一个限制条件(倒数第二个条件):

        求解得:开DC2和DC5。查看选项:

  • 第一个并没有增加DC数量,还是2个;

  • 第二个正确;

  • 第三个Shelter还是18.5(图中四舍五入了显示为19,其实还是18.5)

  • 第四个错误,参照第二个选项。


*点击“ ”进入教材微店

注:本文系本站转载,转载目的在于传递更多信息,并不代表本站赞同其观点和对其真实性负责。如涉及作品内容、版权和其它问题,请与本站联系,我们将在第一时间删除内容!本文版权归原作者所有 内容为作者个人观点 本站只提供参考并不构成任何投资及应用建议。

相关服务

关注我们

关注我们