Just here to brainstorm. Problem A looks impossible at first glance—it’s a physics problem; Problem B seems quite simple, though I haven’t looked into it closely; Problem C doesn’t seem too difficult either.

So I’ll mainly write up the approach for Problem C. Since I’m not actually solving it myself, some details might not be fully considered; this is just one possible feasible solution.

Problem C: Raw Material Procurement and Transportation for a Manufacturing Enterprise

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C 题 生产企业原材料的订购与运输
某建筑和装饰板材的生产企业所用原材料主要是木质纤维和其他植物素纤维材料,
总体可分为 A，B，C 三种类型。该企业每年按 48 周安排生产，需要提前制定 24 周的原
材料订购和转运计划，即根据产能要求确定需要订购的原材料供应商（称为“供应商”）
和相应每周的原材料订购数量（称为“订货量”），确定第三方物流公司（称为“转运
商”）并委托其将供应商每周的原材料供货数量（称为“供货量”）转运到企业仓库。
该企业每周的产能为 2.82 万立方米，每立方米产品需消耗 A 类原材料 0.6 立方米，
或 B 类原材料 0.66 立方米，或 C 类原材料 0.72 立方米。由于原材料的特殊性，供应商
不能保证严格按订货量供货，实际供货量可能多于或少于订货量。为了保证正常生产的
需要，该企业要尽可能保持不少于满足两周生产需求的原材料库存量，为此该企业对供
应商实际提供的原材料总是全部收购。
在实际转运过程中，原材料会有一定的损耗（损耗量占供货量的百分比称为“损耗
率”），转运商实际运送到企业仓库的原材料数量称为“接收量”。每家转运商的运输
能力为 6000 立方米/周。通常情况下，一家供应商每周供应的原材料尽量由一家转运商
运输。
原材料的采购成本直接影响到企业的生产效益，实际中 A 类和 B 类原材料的采购单
价分别比 C 类原材料高 20%和 10%。三类原材料运输和储存的单位费用相同。
附件 1 给出了该企业近 5 年 402 家原材料供应商的订货量和供货量数据。附件 2 给
出了 8 家转运商的运输损耗率数据。请你们团队结合实际情况，对相关数据进行深入分
析，研究下列问题：
1．根据附件 1，对 402 家供应商的供货特征进行量化分析，建立反映保障企业生产
重要性的数学模型，在此基础上确定 50 家最重要的供应商，并在论文中列表给出结果。
2．参考问题 1，该企业应至少选择多少家供应商供应原材料才可能满足生产的需求？
针对这些供应商，为该企业制定未来 24 周每周最经济的原材料订购方案，并据此制定
损耗最少的转运方案。试对订购方案和转运方案的实施效果进行分析。
3．该企业为了压缩生产成本，现计划尽量多地采购 A 类和尽量少地采购 C 类原材
料，以减少转运及仓储的成本，同时希望转运商的转运损耗率尽量少。请制定新的订购
方案及转运方案，并分析方案的实施效果。
4．该企业通过技术改造已具备了提高产能的潜力。根据现有原材料的供应商和转运
商的实际情况，确定该企业每周的产能可以提高多少，并给出未来 24 周的订购和转运
方案。
注：请将问题 2、问题 3 和问题 4 订购方案的数值结果填入附件 A，转运方案的数
值结果填入附件 B，并作为支撑材料（勿改变文件名）随论文一起提交。

附件 1 的数据说明
（1）企业的订货量：第一列为供应商的名称；第二列为供应商供应原材料的类别；
第三列及以后共 240 列为企业向各供应商每周的订货量（单位：立方米）；数值“0”表
示相应的周（所在列）没有向供应商（所在行）订货。
（2）供应商的供货量：第一列为供应商的名称；第二列为供应商供应原材料的类别；
第三列及以后共 240 列为各供应商每周的供货量（单位：立方米）；数值“0”表示相应
的周（所在列）供应商（所在行）没有供货。
附件 2 的数据说明
第一列为转运商的名称；第二列及以后共 240 列为每周各转运商的运输损耗率（%），
即 损耗率 = (供货量 - 接收量) / (供货量) X 100%；数值“0”表示没有运送。

Problem 1

  1. Based on Attachment 1, perform a quantitative analysis of the supply characteristics of the 402 suppliers. Establish a mathematical model reflecting the importance of each supplier in ensuring the enterprise’s production. Based on this, identify the 50 most critical suppliers and present the results in a table within the paper.

The first problem is clearly an evaluation model, and the result will likely be used repeatedly later. First, determine evaluation indicators, such as delivery completion rate, total supply volume, and supply trends. You can use gray prediction or fuzzy evaluation models to set weights for each indicator, or search for relevant articles on this type of evaluation. Finally, provide a ranked table.

Problem 2

Referencing Problem 1, how many suppliers should the enterprise select at minimum to potentially meet production demands? For these suppliers, formulate the most economical weekly raw material procurement plan for the next 24 weeks, and based on this, develop a transportation plan with the least loss. Analyze the implementation effectiveness of both the procurement and transportation plans.

There is a very important condition in the problem statement为了保证正常生产的需要，该企业要尽可能保持不少于满足两周生产需求的原材料库存量，为此该企业对供应商实际提供的原材料总是全部收购。. I didn’t notice this condition at first, but when I reconsidered it, there was a significant change.

This question mainly involves two issues: transportation and supply.

First, let’s answer a question from the problem statement; it’s quite simple. However, before solving all subsequent problems, we need to predict the supply volume of the 50 suppliers identified in Problem 1 for the next 24 weeks. There are many methods available; the simplest is linear regression. Once we have this, sort by supply volume, sum from largest to smallest until the supply for 2 weeks is covered. This can be solved via brute force or binary search; given the small data size, a simple iteration will suffice.

The most economical procurement plan and transportation plan are relatively independent problems, but they must be solved in a specific order. First, solve the transportation plan. For each transporter, calculating an average loss rate should be sufficient, or use other metrics to compute and rank them, then select from the top down. For the procurement plan, prioritize suppliers with high completion rates and the lowest cost after deducting loss rates and utilization rates. I’d guess the priority raw material type would be A.

Problem 3

To reduce production costs, the enterprise plans to procure as much of raw material type A as possible and as little of type C as possible, thereby reducing transportation and warehousing costs, while also hoping to minimize the loss rates of transporters. Please formulate new procurement and transportation plans and analyze the implementation effectiveness of these plans.

This is an optimization problem and feels quite open-ended. First, establish a formula for total or comprehensive cost. Then, apply optimization methods such as Newton’s iteration, linear programming, simulated annealing, hill climbing, or ant colony optimization to find a solution. There is no standard answer, of course, but the better the optimization, the better.

Problem 4

Through technical transformation, the enterprise has now acquired the potential to increase production capacity. Based on the current actual conditions of raw material suppliers and transporters, determine how much the weekly production capacity can be increased, and provide the procurement and transportation plans for the next 24 weeks.

The increase in production capacity is constrained by two factors: supply limitations and transportation limitations. For supply constraints, the strategy for the initial weeks should be to transport as much as possible to set the stage for later, but this is limited by transportation capacity. Therefore, the weekly increase should be maximized under other conditions, capped at the upper limit of the constraints.

Thinking back to the last time I participated in the Mathematical Modeling Competition, it feels like just yesterday. Time flies, and things have changed. The senior student who competed with me last year didn’t pursue graduate studies but went straight to work, while another classmate of mine is expected to have successfully secured a recommendation for graduate school and already holds three job offers orz I’ve also transitioned from a contestant to a contestant who can freely ramble (x)