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DVD在線租賃
摘要：問題是1個(gè)DVD在線租賃中，網(wǎng)站方如何對于市場進(jìn)行需求預(yù)測，如何對DVD進(jìn)行分配才能同時(shí)最好的實(shí)現(xiàn)其經(jīng)濟(jì)效益和社會(huì)效益。
第1問中，基于需求預(yù)測基礎(chǔ)上的DVD購買方案設(shè)計(jì)中，我們分別考慮了悲觀情況和均值情況。為了保證希望看到某種DVD的會(huì)員中，有50%以上在1個(gè)月內(nèi)能看到該DVD，在悲觀情況下，各種DVD的購買量分別為：9000，4500，2250，1125，450。在均值情況下，各種DVD的購買量分別為：6250，3125，1563，720，313。為了保證在3個(gè)月內(nèi)95%以上的會(huì)員能夠看到，在悲觀情況下，各種DVD的購買量分別為：3959，1980，990，495，198。最后，在不考慮具體的會(huì)員的借還DVD時(shí)間，我們使用概率的方法解決了該問題。結(jié)果與均值情況相近。
對于第2問，對于當(dāng)前問題的分配方案確定。我們建立了0-1規(guī)劃模型，求得此時(shí)的最大滿意度為24746，我們給了此時(shí)的最優(yōu)分配方案。
第3問，是1個(gè)多目標(biāo)規(guī)劃問題，既要考慮使得會(huì)員的滿意度盡量大，還要使得網(wǎng)站購買的中的DVD數(shù)目最少，在具體處理時(shí)，我們讓會(huì)員滿意度在1定的范圍內(nèi)變動(dòng)，給出各種情況下使得總DVD數(shù)最少的方案。其中當(dāng)會(huì)員相對滿意度為0.8時(shí)的最少DVD總數(shù)為2059張。
分析第3問的結(jié)果，我們發(fā)現(xiàn)了有趣的雙峰現(xiàn)象，并對其合理性進(jìn)行了闡述。同時(shí)，我們還可以發(fā)現(xiàn)，會(huì)員相對滿意度與最少DVD之間呈現(xiàn)總數(shù)近似線性的關(guān)系。如下表所示：
相對滿意度 0.5 0.6 0.7 0.8 0.8 1.0
所需DVD數(shù) 1202 1486 1760 2059 2567 3098
對于網(wǎng)站而言，其經(jīng)營的目的是獲得最大的經(jīng)濟(jì)效益，不同的租賃模式設(shè)置下網(wǎng)站會(huì)得到不同的經(jīng)濟(jì)效益，第4問中我們討論網(wǎng)站經(jīng)營管理的最優(yōu)模式。求得了在1種情況下，限定每月最多租賃兩次的情況下，得到使得網(wǎng)站的效益達(dá)到最大時(shí)，應(yīng)該限定每個(gè)會(huì)員每次租賃最多2張DVD。同時(shí)討論了對于限定每次最多租賃3張DVD的情況下，最佳的租賃次數(shù)限制。
本文論證嚴(yán)密，所給出的結(jié)果具有啟發(fā)性和借鑒意義。
關(guān)鍵字 ： 正態(tài)分布；悲觀情況；均值分布；
DVD on-line rents
Information and computation science：zhanghaitao Instructs teacher：tanmin
Abstract：The issue is a DVD rental online, the Web site for how the market demand forecast How to distribute the DVD can also best achieve its economic and social benefits. I asked, based on demand forecasts based on the DVD-buying program design, We consider separately the mean pessimistic and the situation. To ensure that the DVD would like to see some of the members, more than 50% within one month will see the DVD, In a pessimistic case, the various DVD purchases were : 9000,4500,2250,1125,450. In the mean circumstances, the various DVD purchases were : 6250,3125,1563,720,313. To ensure that within three months 95% of the members will be able to see the gloomy situation, all DVD purchases were : 3959,1980,990,495,198. Finally, in consideration of specific members of the DVD also take time, we used probabilistic methods to solve the problem. With the results of similar means. Regarding the second question, the current allocation formulas. We established a 0-1 programming model, then seek the greatest satisfaction to 24,746, At this time we gave the optimal distribution program. Question 3 is a multi-objective planning issue, we should consider making membership of the largest possible degree of satisfaction, Terms of the purchase also makes a number of DVD at least, in terms of handling, We let the membership in a certain satisfaction within the scope of changes in the given circumstances under total DVD makes the least number of programs. When the members of which relative to the satisfaction of at least 0.8 DVD total of 2,059. Analysis third question the results, we found an interesting phenomenon bimodal, and the reasonableness of the paper. Meanwhile, we also can be found, Member relative satisfaction with at least between the DVD has a total approximate linear relationship. As shown in the table below :
Relative satisfaction 0.5 0.6 0.7 0.8 0.8 1.0
DVD for a few 1202 1486 1760 2059 2567 3098
For the site, the purpose of the operation is to maximize the economic benefits, different mode of leasing site will be under different economic benefits, Fourth, we asked for management to discuss the optimal model. Obtained by the case, the maximum monthly leasing limit twice circumstances, be made for maximum efficiency, Each Member should be limited to a maximum of each lease two DVD. Discussed the limit for the maximum number of leasing three DVD cases, the number of the best leasing restrictions. This paper demonstrated tight, given the results enlightening and learn.
Keywords：Normal; Pessimistic; Mean distribution;
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