分享興趣、傳播快樂、增長見聞、留下美好，大家好，這裡是LearningYard學苑，今天小編為大家帶來文章：用mathematica複刻論文中的模型（一）（續3）.
今日内容摘要Abstract：
繼續完成論文《大資料服務商參與的三級供應鍊動态合作政策及其比較》中的定理一的證明過程的複刻，同時今天請教我的同門與師姐。Continue to complete the replication of the proof process of Theorem 1 in the paper "Three-level Supply Chain Dynamic Cooperation Strategies Participated by Big Data Service Providers and Their Comparisons", and ask my colleagues and sisters for advice today.
正文 body part：
圖0 上一期的疑惑
Figure 0 Doubts in the previous issue
進入正題Into the title.。
之前寫推文用的代碼都是在上一篇的基礎上求得的，由于一直求解不出來，我考慮重新檢查代碼，争取能找到問題。The code used to write tweets was obtained on the basis of the previous article. Since I couldn’t solve it, I considered rechecking the code to try to find the problem.
圖1 figure 1
圖1展示的是在模組化之前需要設定的表達式和關系式。Figure 1 shows the expressions and relations that need to be set before modeling.
圖2figure 2
圖2中，為了與論文中的式子（6）（10）和（14）相符，進行了改進，其中MaxValue[f,x]指令是求函數f關于x的最大值。In Figure 2, in order to be consistent with the formulas (6), (10) and (14) in the paper, improvements have been made, where the MaxValue[f,x] command is to find the maximum value of the function f with respect to x.
圖3 image 3
到圖3為止，就把所有需要的控制變量的最優值求出來，即FB（大資料服務商的努力水準）、m（零售商的支付水準）、和FM（制造商的努力水準）。在所求出來的個式子中，隻有L1和L2為變量，其他字母符号如a、b、q、w可以是給定的具有特定值的系數，此處看作固定值。接下來，要将這三個式子帶入三個HJB方程，如圖4的三個紅框。Up to Figure 3, the optimal values of all the required control variables are obtained, namely FB (effort level of big data service provider), m (payment level of retailer), and FM (effort level of manufacturer). In the obtained formulas, only L1 and L2 are variables, and other letter symbols such as a, b, q, w can be given coefficients with specific values, which are regarded as fixed values here. Next, bring these three equations into the three HJB equations, as shown in the three red boxes in Figure 4.
圖4 Figure 4
此外，在原論文中，作者也給出了，帶入後的結果（如圖5）。此處需要說明，因為FB、m和FM都是滿足最優條件下的值，是以在書寫代碼時，可以直接忽略原論文中的MAX條件，不需要額外添加相關指令。書寫的代碼如圖7和圖6，我嘗試用各種Solve的指令來求解方程組，然而都無果。In addition, in the original paper, the author also gave the result after bringing in (as shown in Figure 5). It needs to be explained here, because FB, m and FM are all values that satisfy the optimal conditions, so when writing the code, the MAX condition in the original paper can be ignored directly, and there is no need to add additional related commands. The written code is shown in Figure 7 and Figure 6. I tried to use various Solve commands to solve the equation system, but to no avail.
圖5 Figure 5
圖6 Figure 6
圖7 Figure 7
我從軟體自帶的幫助檔案裡，看到關于Solve的相關介紹（如圖8），其中，案例都是非常簡單的，且隻含有幾個簡單的字母，其餘都是數字，是以我在想會不會是Solve無法求解我這個類型的方程組。然後我看了解方程的教程，沒有找到其他指令能夠解決我的問題。（如圖9）From the help file that comes with the software, I saw the relevant introduction about Solve (as shown in Figure 8). Among them, the cases are very simple, and only contain a few simple letters, and the rest are numbers, so I am thinking Could it be that Solve can't solve my type of equation system. Then I looked at the tutorial on understanding equations and found no other commands that would solve my problem. (Figure 9).
圖8 Figure 8
圖9 Figure 9
幾番周折，都沒有解出來，我決定去請教我的同門吳同學和田師姐，看看我的問題到底在哪裡。After several twists and turns, I couldn't solve it. I decided to ask my classmates Wu and Tian to see where my problem was.
然後吳同門給我的意見是圖10，如果隻是求解最後一步，可以參考圖10的代碼，金育的建議是可能我前面的變量設定有問題，然後建議我重新開機電腦，重新計算。Then Wu Tongmen's opinion to me is Figure 10. If you only solve the last step, you can refer to the code in Figure 10. Jin Yu's suggestion is that there may be a problem with the variable settings in front of me, and then suggest me to restart the computer and recalculate.
圖10 Figure 10
确實，重新開機後可以計算出最後一步的解方程組，但是如果從頭開始計算下來，就會得到一個非常複雜的結果。如圖11.It is true that the solution equations for the last step can be calculated after restarting, but if you calculate it from scratch, you will get a very complicated result. Figure 11.
圖11 Figure 11
同門和師姐給我補充的意見入圖12和13.The supplementary comments given to me by my colleagues and senior sisters are shown in Figures 12 and 13.
圖12 Figure 12
圖13 Figure 13
由于着急發推文的關系，隻能晚點解決這個問題了，雖然我真的很想解出來，但是下期繼續。Due to the rush to tweet, I can only solve this problem later. Although I really want to solve it, I will continue in the next issue.
今天的分享就到這裡啦！
感興趣的同學可以留言與小編交流，
咱們下周見！
參考文獻：
【1】吳成霞,趙道緻,潘新宇.大資料服務商參與的三級供應鍊動态合作政策及其比較[J].控制與決策,2016,31(07):1169-1177.
英文翻譯：Google翻譯。
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