2016HIMCM B题购物和运输问题数模获奖论文(5篇含代码)

发布于:2022-11-29 ⋅ 阅读:(463) ⋅ 点赞:(0)

Problem B

Problem: Shop and Ship

As online stores start to compete with traditional brick and mortar stores the goal is to combine the benefits of both types of businesses. Brick and mortar stores provide the benefit of seeing the actual items, picking up your purchase right away, and not having to pay for shipping. But, sometimes the store is not convenient to your location, or you do not have time to go shopping. Online stores offer the convenience of shopping from home and the added benefit, in many cases, of no additional sales or other taxes. And, with international shipping, many more items are available to shoppers all over the globe via the Internet. For the purposes of this HiMCM problem, we will use an example from the United States.

Your recreation equipment company currently not selling apparel/clothing has a small brick and mortar store, but conducts most of its business through online sales. Your company’s headquarters and main warehouse is located in New Hampshire (NH), USA. Due to increased demand for your product, you are expanding and your team’s task is to choose locations for the new warehouses. Your initial expansion goal is to service the 48 continental United States (not Alaska-AK or Hawaii-HI or Puerto Rico-PR) with one-day ground shipping with United Parcel Service (UPS).

Part I. Analyze the optimal placement of warehouses to meet the one-day ground shipping requirement. Determine and discuss your criteria as you address the following questions.

1. What is the minimum number of warehouses needed to service the continental United States with one-day ground shipping?
2. Where should the new warehouses be located?

As an example, Figure 1 shows UPS ground shipping from NH.


Figure 1: Ground Transit Times When Shipping From NH (https://www.ups.com/maps/)

Part II. The state of NH has no sales tax, meaning that if you physically buy a product in New Hampshire, you do not have to pay sales tax. Current US federal law requires that companies must collect required sales tax where they have physical locations. Although tax laws in different cities, states, and countries can be complicated, for the purposes of our HiMCM problem, we will assume the following:

*Any online order delivered to a location within a state where a warehouse is located will have that state’s tax added to the order cost.
*Any online order delivered to a location outside a state where a warehouse is located will NOT be taxed.
* Problem Note 1 provides state tax information. For example, DE, MT, NH, and OR do not have state sales tax.
1. Describe and discuss how the warehouse locations you selected in Part I will affect your customer’s tax liability.
2. Analyze and discuss any possible changes to the number of warehouses or locations of those warehouses in order to minimize the tax liability to the most customers possible.

Part III. Your company has decided to add clothing and apparel to your line of products. Several states do not tax clothing or have minimal taxes on clothing as shown in Problem Note 1.

1. Analyze the impact of the warehouse locations from Parts I and II based on the addition of clothing and apparel to your inventory.
2. Discuss any possible changes to the number of warehouses or locations of those warehouses based on increasing your clothing sales.

Part IV. Determine your final recommendation and justification of the number of warehouses and location of the warehouses. Write a one-page letter to your Company’s president summarizing your final recommendation and justification. This letter will be the cover letter to your HiMCM contest report.

Your submission should consist of:

One-page Summary Sheet,

One-page letter to the your Company’s president,

Your solution of no more than 30 pages for a maximum of 32 pages.

Note the appendix and references do not count toward the 32 page limit.

PROBLEM NOTES:

1. Sales Tax
State Sales Tax Rates for 48 Continental US States

问题:购物和运输

随着在线商店开始与传统的实体店竞争,其目标是结合两种类型的业务的好处。实体店提供了查看实际物品,立即购买,无需支付运费的好处。但是,有时商店对您的位置不方便,或者您没有时间去购物。在线商店提供了在家购物的便利,并且在许多情况下,其没有额外的销售或其他税收。而且,通过国际运输,全球各地的购物者可以通过互联网获得更多商品。由于是HIMCM问题,出于此目的,我们将使用来自美国的示例。

您的娱乐设备公司目前不销售服装/服装有一个小实体店,但通过在线销售进行其大部分业务。贵公司的总部和主仓库位于美国新罕布什尔州(NH)。由于对您的产品的需求增加,您正在扩展业务,您的团队的任务是选择新仓库的位置。您最初的扩张目标是为美国48个大陆(阿拉斯加-AK、夏威夷-HI、波多黎各-PR除外)提供服务,并与联合包裹服务公司(UPS)进行为期一天的陆运。

第一部分 分析仓库的最佳位置,以满足一天的地面运输要求。在解决以下问题时,确定并讨论您的标准。

1.为了达到一天的地面运输服务目标,美国大陆所需的最低仓库数量是多少?
2.新仓库应该放在哪里?

例如,图1显示了来自NH的UPS陆运。

第二部分 NH的州没有销售税,这意味着如果您在新罕布什尔州实际购买产品,则无需缴纳销售税。目前的美国联邦法律要求公司必须在有实际位置的地方征收所需的销售税。虽然不同城市,州和国家的税法可能很复杂,但就我们的HiMCM问题而言,我们将假设以下内容:

*任何交付到仓库所在州内某个位置的在线订单都会将该州的税额添加到订单成本中。
*任何交付到仓库所在州以外地点的在线订单都不征税。
*问题说明1提供了州税法信息。例如,DE,MT,NH和OR没有州销售税。
1.描述并讨论您在第I部分中选择的仓库位置将如何影响客户的纳税。
2.分析和讨论仓库数量或仓库位置的任何可能变化,以尽量减少大多数客户的纳税。

第三部分 贵公司决定在您的产品系列中添加服装和服饰。如问题注释1所示,有几个州不对服装征税或对服装征税最低。

1. 根据在您的库存中添加服装和服装,分析第I部分和第II 部分中仓库位置的影响。
2.根据增加服装销售额,讨论仓库数量或仓库位置的任何可能变化。

第四部分 确定仓库数量和仓库位置的最终建议和理由。 给公司总裁写一封长达一页的信,总结您的最终建议和理由。这封信将是您的HiMCM竞赛报告的求职信。

您的提交应包括:

一页摘要表,

给贵公司总裁的一页信,

您的解决方案不超过30页,最多32页。

请注意,附录和参考不计入32页限制。

问题说明:

解题思路1:

你有没有试过永远等待UPS包裹的到来?随着世界各地网店数量的激增,平滑线上线下连接变得越来越重要。在本文中,我们构建了一个数学模型,以确定为分销来自美国48个大陆国家的客户在线购买的商品而建立的仓库的最佳数量和位置。
在第1部分中,我们假设忽略了某些状态中的某些特定琐碎区域。
然后,我们通过构造27-by-270-1矩阵来简化问题。我们根据两个相关状态是否可以在一天的地面运输中相互达到,用1或0填充矩阵。在此基础上,应用贪心算法和计算机分析技术给出了最优解。
在第2部分和第3部分中,我们构建了向量传递模型。在模型中,我们使用点来表示特定的仓库位置,并使用向量来连接每个仓库与仓库通过一天地面运输可以到达的状态。结合图论,我们应用0-1规划求解最优解。
手动调整会产生最佳答案。
建立模型后,我们对每个问题都给出了具体的答案。

后续完整论文:

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