基于模糊隨機(jī)需求的B2C多品采配協(xié)同模型及其粒子群算法求解

崔利剛，任海利，鄧 潔，張亞軍

基于模糊隨機(jī)需求的B2C多品采配協(xié)同模型及其粒子群算法求解

崔利剛1*，任海利1，鄧 潔2，張亞軍3

（1.重慶交通大學(xué) 經(jīng)濟(jì)與管理學(xué)院 重慶 400074；2.重慶理工大學(xué) 知識(shí)產(chǎn)權(quán)學(xué)院 重慶 400050；3. 貴州財(cái)經(jīng)大學(xué) 工商管理學(xué)院，貴陽(yáng) 550025）

面對(duì)繁多的商品品類和多變的采配流程，B2C (Business to Consumers) 電商物流運(yùn)營(yíng)的主要挑戰(zhàn)之一即是合理刻畫(huà)顧客小批量、不確定性的需求以實(shí)現(xiàn)采配流程的平穩(wěn)高效運(yùn)行。本文針對(duì)B2C電商企業(yè)多品補(bǔ)貨需求的不確定性，將商品需求假設(shè)為三角模糊變量。同時(shí)，考慮基于歷史數(shù)據(jù)的模糊變量確定存在隨機(jī)可能性判斷，本文運(yùn)用模糊期望值理論，構(gòu)建以成本最小化為目標(biāo)的多品采配（Joint replenishment and delivery，JRD）協(xié)同模型。模型采用粒子群算法（Particle Swarm Optimization，PSO）進(jìn)行求解。數(shù)值實(shí)驗(yàn)驗(yàn)證了PSO相比于遺傳算法（Genetic Algorithm，GA）求解JRD的有效性和適用性。

企業(yè)對(duì)消費(fèi)者；聯(lián)合補(bǔ)貨及配送；模糊需求；粒子群算法

0 引言

以京東和亞馬遜為代表的B2C電商以其高水平的物流服務(wù)和高質(zhì)量的商品保證，在眾多電商模式中優(yōu)勢(shì)凸顯。隨著B(niǎo)2C電商由單品向多品和全品類商品的覆蓋，多品需求的不確定性問(wèn)題逐漸成為困擾B2C電商供應(yīng)鏈中采-配平穩(wěn)高效的核心問(wèn)題[1]。然而，顧客需求的差異化加之商品本身需求的不確定性造成B2C電商采購(gòu)、配送流程的脫節(jié)和決策復(fù)雜化。B2C電商困擾于低庫(kù)存成本和高服務(wù)水平的矛盾，導(dǎo)致某些在線商品頻繁缺貨的同時(shí)，另外一些商品庫(kù)存較高。因此，B2C電商如何在面對(duì)不確定性需求條件下，實(shí)現(xiàn)多品補(bǔ)貨和配送的協(xié)同具有很強(qiáng)的現(xiàn)實(shí)意義。

1 文獻(xiàn)回顧

B2C電商多品采配協(xié)同問(wèn)題的難點(diǎn)在于確定共同補(bǔ)貨周期、補(bǔ)貨頻率的同時(shí)確定配送周期。經(jīng)典JRP(Joint replenishment problem，JRP)模型嘗試解決確定性條件下的多品聯(lián)合補(bǔ)貨問(wèn)題[2, 3]。而現(xiàn)實(shí)中，B2C電商多品之間的補(bǔ)貨過(guò)程并不是完全獨(dú)立的，對(duì)同一供應(yīng)商多種商品的采-配的協(xié)同要求很高。同時(shí)，多品類商品的不確定性需求會(huì)對(duì)采-配協(xié)同造成直接影響。經(jīng)典JRP模型假設(shè)建立在理想條件下，不適用于解決需求高度不確定性的B2C電商的多品類交易過(guò)程。

針對(duì)B2C環(huán)境特點(diǎn)，卞文良等[4]以顧客滿意度為出發(fā)點(diǎn)，研究物流服務(wù)感知以及與之相關(guān)的產(chǎn)品價(jià)值感知、商流過(guò)程感知和企業(yè)形象感知等因素及這些因素與顧客滿意度。李聰?shù)萚5]也從顧客出發(fā)，采集多元用戶興趣數(shù)據(jù)，嘗試分析影響用戶交易行為的多個(gè)因素揭示用戶需求。以上這些因素的共同作用下使得顧客表現(xiàn)出需求不確定性和差異性。顧客需求的不確定性最常用的處理方式是作隨機(jī)化處理。例如，王林等通過(guò)假設(shè)正態(tài)分布的隨機(jī)需求，研究了資金和存儲(chǔ)空間雙約束的聯(lián)合采購(gòu)問(wèn)題[6]。肖旦等[7]在假設(shè)隨機(jī)需求的條件下，以較為新穎的視角研究庫(kù)存技術(shù)共享對(duì)零售商聯(lián)合采購(gòu)聯(lián)盟訂貨策略的影響。周繼祥和王勇[8]通過(guò)建立兩級(jí)供應(yīng)鏈體系，嘗試研究部分需求信息下已知條件下有第三方物流企業(yè)參與的企業(yè)采購(gòu)問(wèn)題，作者建立的魯棒模型較為巧妙地刻畫(huà)了第三方物流管理采購(gòu)與零售商管理采購(gòu)的問(wèn)題。面對(duì)電商復(fù)雜的市場(chǎng)環(huán)境，多品類商品需求及狀態(tài)都難以用一般隨機(jī)分布進(jìn)行描述，而將客戶需求模糊化處理是B2C企業(yè)對(duì)借助歷史數(shù)據(jù)以統(tǒng)計(jì)概率刻畫(huà)顧客隨機(jī)需求假設(shè)條件的重要補(bǔ)充。

也有眾多學(xué)者嘗試用模糊化方式處理顧客的不確定性需求。例如，李成嚴(yán)等[2]以不確定資源為約束建立聯(lián)合補(bǔ)貨模糊規(guī)劃模型。曾宇容等[9]建立費(fèi)用、資源雙重模糊條件下的聯(lián)合采購(gòu)模型。張帥等[10]基于多種物件需求的不確定性，建立模糊資源約束下物件的JRP模型。模糊理論中的數(shù)據(jù)及其計(jì)算結(jié)果的模糊表達(dá)通常接近事物本質(zhì)，而隨機(jī)模糊通過(guò)期望值理論確定事物模糊表達(dá)，給決策者提供更大的空間，更有利于決策者柔性決策，為客戶不確定性需求的刻畫(huà)提供了思路。如Dutta等[11]將年需求定義為隨機(jī)變量，對(duì)單品類商品建立連續(xù)盤(pán)點(diǎn)(Q,R)模型，利用模糊數(shù)的期望均值進(jìn)行求解，但多基于單品商品進(jìn)行研究分析。在模糊化處理方面，處理程序較為繁瑣，并且沒(méi)有考慮不同的決策者對(duì)模糊數(shù)據(jù)認(rèn)知的差異性[12]。

當(dāng)前JRP問(wèn)題研究大多假設(shè)需求確定或需求隨機(jī)，而現(xiàn)實(shí)顧客需求性信息難以準(zhǔn)確獲得，為估計(jì)客戶需求，需要借助多個(gè)領(lǐng)域?qū)＜业慕?jīng)驗(yàn)進(jìn)行綜合判斷。JRP模型的求解方法主要有啟發(fā)式方法和進(jìn)化算法[13]。盡管啟發(fā)式算法對(duì)求解特定JRP模型具有一定的優(yōu)勢(shì)[14]，但進(jìn)化算法以其易于理解、方便操作和求解高效的特點(diǎn)得到了很多學(xué)者的重視[3, 15]。李成嚴(yán)等[2]運(yùn)用GA解決多產(chǎn)品聯(lián)合補(bǔ)充問(wèn)題。王林等[16]設(shè)計(jì)改進(jìn)差分進(jìn)化求解模糊規(guī)劃聯(lián)合補(bǔ)貨模型。而粒子群算法(Particle swarm Optimization，PSO)以其較高的求解效率和魯棒性，在諸多優(yōu)化領(lǐng)域得到了驗(yàn)證[17, 18]，但在JRP問(wèn)題求解上還有待探索。

綜合以上，鑒于模糊隨機(jī)化方法兼顧客戶不確定性需求的模糊化處理和模糊決策空間選擇的隨機(jī)化問(wèn)題。本文通過(guò)假設(shè)B2C電商商品模糊需求，構(gòu)建聯(lián)合采購(gòu)配送（Joint replenishment problem and delivery, JRD）協(xié)同模型，以實(shí)現(xiàn)訂購(gòu)成本、持有成本以及運(yùn)輸成本的最小化，并根據(jù)模型結(jié)構(gòu)設(shè)計(jì)PSO算法進(jìn)行求解。

2 基于模糊隨機(jī)需求的JRD協(xié)同模型構(gòu)建

2.1 模型假設(shè)與術(shù)語(yǔ)

2.2 基于模糊隨機(jī)需求的JRD模型

對(duì)于JRD模型，系統(tǒng)運(yùn)行單位時(shí)間內(nèi)總成本如式(1)所示：

運(yùn)用模糊期望值理論可將式(7)、(8)轉(zhuǎn)化為：

同理有：

把(10)，(11)帶入(7)可求得：

3 基于PSO算法的模型求解

PSO算法是模仿集群行為的一種仿生算法，它源于鳥(niǎo)類的捕食行為，依靠群體優(yōu)化來(lái)搜尋全體最優(yōu)[19]。從算法設(shè)計(jì)上來(lái)講，PSO算法簡(jiǎn)單，沒(méi)有選擇、交叉、變異等操作，搜索速度快。同時(shí)PSO 具備全局搜索與局部搜索的能力，有效避免早熟現(xiàn)象。對(duì)于JRD問(wèn)題模型的實(shí)數(shù)編碼，可減少參數(shù)調(diào)整，PSO算法能更快更精確的獲得全局最優(yōu)解?；谀：S機(jī)需求JRD模型的PSO算法設(shè)計(jì)流程如下：

（4）對(duì)出現(xiàn)異常情況的粒子速度進(jìn)行處理。

b.對(duì)出現(xiàn)異常情況的粒子位置進(jìn)行處理。若新粒子位置小于最小值，則令新粒子位置為最小值；若新粒子位置大于最大值，則令新粒子位置為最大值。

4 數(shù)值實(shí)驗(yàn)

4.1 數(shù)據(jù)實(shí)例

表1 JRD模型部分?jǐn)?shù)據(jù)

表2 商品的模糊需求量

表3 商品的模糊需求量

表4 商品的模糊需求量

表5 商品的模糊需求量

4.2 參數(shù)敏感性分析

表6 和為固定值，不同問(wèn)題求解結(jié)果

表7 和為固定值，不同問(wèn)題求解結(jié)果

表8 和為固定值，不同問(wèn)題求解結(jié)果

表9 ，和為固定值，不同種群規(guī)模問(wèn)題求解結(jié)果

圖2 不同種群規(guī)模最優(yōu)值進(jìn)化過(guò)程

圖3 不同迭代次數(shù)下PSO進(jìn)化過(guò)程

Figure 3 The evolutionary processes of PSO under different maximum iteration settings

以上實(shí)驗(yàn)表明，通過(guò)探索 PSO在求解JRD模型的最優(yōu)參數(shù)組合，為下文PSO求解決模糊隨機(jī)需求JRD模型提供最佳參數(shù)組合支持。

4.3 基于最佳參數(shù)設(shè)置的求解結(jié)果

將本模型將GA作為對(duì)照，參數(shù)設(shè)置參考文獻(xiàn)[20]：在輪盤(pán)賭選擇策略下，交叉概率為0.4，變異概率為0.4。GA和PSO算法分別運(yùn)行20次，計(jì)算結(jié)果如表11所示數(shù)據(jù)，其進(jìn)化過(guò)程如圖4所示。

表10 PSO算法計(jì)算結(jié)果

表11與圖4表明，遺傳算法與粒子群算法收斂速度相近，都在50代左右，優(yōu)化結(jié)果相似。但遺傳算法計(jì)算得到的總成本為1599.5，高于運(yùn)用粒子群算法的相應(yīng)總成本。GA和PSO算法分別運(yùn)行20次得到TC平均值分別為2067.33、2065.16，標(biāo)準(zhǔn)誤差分別為211.64、267.61，說(shuō)明處理相同數(shù)據(jù)的情況下，遺傳算法穩(wěn)定性更高，但粒子群算法效率較高，得到的最優(yōu)值也優(yōu)于遺傳算法計(jì)算結(jié)果。

表11 PSO與GA比較結(jié)果

圖4 GA和PSO進(jìn)化過(guò)程

Figure 4 The evolutionary processes comparison between GA and PSO

實(shí)驗(yàn)表明，與GA相比，PSO求解JRD表現(xiàn)出較好的有效性和和較快的求解效率。同時(shí)，算法也揭示了PSO在求解穩(wěn)定性上的不足。本文基于PSO的研究結(jié)果為求解更復(fù)雜的多品采購(gòu)問(wèn)題提供了可行性。

5 結(jié)論

本文以B2C企業(yè)多品采配協(xié)同問(wèn)題為出發(fā)點(diǎn)，分析三角模糊期望值理論在多品采配過(guò)程中的應(yīng)用合理性，利用模糊隨機(jī)期望值方法，構(gòu)建了以總成本最小化為目標(biāo)的JRD模型。并且，本文設(shè)計(jì)了PSO算法的模型求解。通過(guò)對(duì)PSO算法參數(shù)進(jìn)行敏感性分析，完成解決隨機(jī)模糊需求的JRD模型最佳參數(shù)設(shè)置后進(jìn)行了較為嚴(yán)謹(jǐn)?shù)臄?shù)值實(shí)驗(yàn)。數(shù)值實(shí)驗(yàn)結(jié)果表明了PSO求解JRD模型的優(yōu)勢(shì)和適用性，研究結(jié)果可為多品種商品補(bǔ)貨優(yōu)化決策提供方法借鑒。同時(shí)，揭示B2C電商多品采配流程的協(xié)同決策，可增強(qiáng)了企業(yè)的成本控制能力。未來(lái)的研究擬在設(shè)計(jì)改進(jìn)粒子群算法提高算法運(yùn)行效率的基礎(chǔ)上增強(qiáng)算法的穩(wěn)定性。另外，考慮加入更多實(shí)際影響總成本的因素，不斷優(yōu)化采購(gòu)-配送流程。

[1] Cui L, Deng J, Liu F, et al. Investigation of RFID investment in a single retailer two-supplier supply chain with random demand to decrease inventory inaccuracy [J]. Journal of Cleaner Production, 2017,142, Part 4:2028-2044.

[2] 李成嚴(yán), 徐曉飛, 戰(zhàn)德臣. 模糊資源約束的聯(lián)合補(bǔ)充問(wèn)題[J]. 計(jì)算機(jī)集成制造系統(tǒng), 2008,14(1):113-117.

Li C Y, Xu X F, Zhan D C. Joint replenishment problem with fuzzy constraints[J]. Computer Integrated Manufacturing Systems, 2008, 14(1): 113-117.

[3] 王林, 瞿慧, 陳曉溪, 等. 基于差分進(jìn)化算法的運(yùn)輸容量約束下有數(shù)量折扣的模糊聯(lián)合補(bǔ)貨模型研究[J]. 管理學(xué)報(bào), 2014,11(10): 1507-1513.

Wang L, Qu H, Chen X X, et al. Fuzzy joint replenishment model considering transportation capacity constraints and quantity discount based on differential evolution algorithm[J]. Chinese Journal of Management, 2014,11(10):1507-1513.

[4] 卞文良, 鞠頌東, 徐杰, 等. 在線B2C顧客物流服務(wù)感知及相關(guān)因素的實(shí)證研究[J]. 管理工程學(xué)報(bào), 2011,25(2):14-20.

Bian W L, Ju S D, Xu J, et al. An empirical research on online B2C customer perceptions[J]. Journal of Industrial Engineering/ Engineering Management, 2011,25(2):14-20.

[5] 李聰, 馬麗, 梁昌勇. DFM-IA:面向B2C電子商務(wù)的多源用戶興趣數(shù)據(jù)采集機(jī)制[J]. 管理工程學(xué)報(bào), 2017,31(1):58-70.

Li C, Ma L, Liang C Y. DFM-IA: A multi-source user interest data fetching mechanism for business-to-customer E-commerce[J]. Journal of Industrial Engineering/Engineering Management, 2017,31(1): 58-70.

[6] 王林, 陳璨, 曾宇容. 資源約束情況下隨機(jī)性聯(lián)合采購(gòu)模型的差分進(jìn)化算法[J]. 計(jì)算機(jī)集成制造系統(tǒng), 2011,17(7):1541-1546.

Wang L, Chen C, Zeng Y R. Differential evolution algorithm for stochastic joint replenishment model with resource constraint[J]. Computer Integrated Manufacturing Systems, 2011,17(7):1541-1546.

[7] 肖旦, 周永務(wù), 鐘遠(yuǎn)光, 等. 隨機(jī)需求下庫(kù)存技術(shù)共享零售商聯(lián)合采購(gòu)聯(lián)盟的競(jìng)合博弈研究[J]. 管理工程學(xué)報(bào), 2017,31(4):194-199.

Xiao D, Zhou Y W, Zhong Y G, et al. Co-opetition game analysis of retailers' joint purchasing coalitions with inventory technology sharing under stochastic demand. Journal of Industrial Engineering/ Engineering Management, 2017,31(4):194-199.

[8] 周繼祥, 王勇. 部分信息下第三方物流參與管理企業(yè)采購(gòu)模型研究[J]. 管理工程學(xué)報(bào), 2018,32(1):171-177.

Zhou J, Wang Y. Research on the model of corporate's procurement management with the involvement of 3PL with partial information[J]. Journal of Industrial Engineering/Engineering Management, 2018, 32(1):171-177.

[9] 曾宇容, 王林, 馮云濤. 費(fèi)用與資源約束雙重模糊下的聯(lián)合采購(gòu)模型——基于差分進(jìn)化算法的研究[J]. 計(jì)算機(jī)應(yīng)用研究, 2012, 29(3): 880-884.

Zeng Y R, Wang L, Feng Y T. Joint replenishment model under fuzzy costs and resource constraints-differential evolution algorithm approach[J]. Application Research of Computers, 2012,29(3): 880- 884.

[10] 張帥, 糜玉林, 徐吉輝, 等. 模糊資源約束的飛機(jī)消耗件聯(lián)合補(bǔ)充研究[J]. 兵工自動(dòng)化, 2015, 34(11):4-8.

Zhang S, Mi Y L, Xu J H, et al. Research on joint replenishment problem of aircraft consumable items with fuzzy resource constraint[J]. Ordnance Industry Automation, 2015, 34(11):4-8.

[11] Dutta, Chakraborty, Roy. Continuous review inventory model in mixed fuzzy and stochastic environment[J]. Applied Mathematics & Computation, 2007,188(1):970-980.

[12] Dalman H, Güzel N, Sivri M. A fuzzy set-based approach to multi-objective multi-item solid transportation problem under uncertainty [J]. International Journal of Fuzzy Systems, 2016,18(4): 716-729.

[13] Goyal S K, Satir A T. Joint replenishment inventory control: Deterministic and stochastic models [J]. European Journal of Operational Research, 2007,38(1):2-13.

[14] Moon I K, Cha B C, Lee C U. The joint replenishment and freight consolidation of a warehouse in a supply chain [J]. International Journal of Production Economics, 2011,133(1):344-350.

[15] Cui L, Deng J, Wang L, et al. A novel locust swarm algorithm for the joint replenishment problem considering multiple discounts simultaneously [J]. Knowledge-Based Systems, 2016,111:51-62.

[16] 王瑋. 百貨類商品B2C電商配送模式組合選擇研究[D]. 北京交通大學(xué), 2014.

Wang W. A study on the delivery model portfolio selection for general merchandise B2C[D]. Beijing Jiaotong University, 2014.

[17] 楊景明, 侯新培, 崔慧慧, 等. 基于融合多策略改進(jìn)的多目標(biāo)粒子群優(yōu)化算法[J]. 控制與決策, 2018(2):226-234.

Yang J M, Hou X P, Cui H H, et al. Improved multi-objective particle swarm optimization algorithm based on integrating multiply strategies. Control and Decision, 2018(2):226-234.

[18] 王林, 陳璨, 張金隆, 等. 基于改進(jìn)粒子群優(yōu)化方法的供應(yīng)商優(yōu)選與訂貨量分配模型[J]. 中國(guó)管理科學(xué), 2009,17(6):98-103.

Wang L, Chen C, Zhang J L, et al. A study on the supplier selection and order quantity allocation problem based on improved particle swarm optimization algorithm. Chinese Journal of Management Science, 2009,17(6):98-103.

[19] Eberhart R, Kennedy J. A new optimizer using particle swarm theory [C]. Proceedings of the Sixth International Symposium on Micromachine Machine & Human Science, 1995:39-43.

[20] 崔利剛. 基于RFID技術(shù)的聯(lián)合采購(gòu)模型研究[D]. 華中科技大學(xué), 2014.

Cui L. Research on the joint replenishment models with the investment of the RFID technology[D]. Huazhong University of Science and Technology. 2014.

A particle swarm algorithm for a novel B2C multi-item replenishment and delivery coordination model with fuzzy random demands

CUI Ligang1*, REN Haili1, DENG Jie2, ZHANG Yajun3

(1. School of Economics and Management, Chongqing Jiaotong University, Chongqing 400074, China; 2. Intellectual Property Institution of Chongqing, Chongqing University of Technology, Chongqing, 400050, China; 3. School of Business Administration, Guizhou University of Finance and Economics, Guiyang 550025, China)

The rapid development and extraordinary achievements of e-commerce in China in recent years have attracted worldwide attention. As more and more companies embrace e-commerce, the fierce competition between e-commerce companies and traditional companies or even e-commerce companies erupted in an unprecedented situation. In all e-commerce models, business-to-consumer (B2C) is characterized by providing high-quality goods and services, reflecting greater development potential and stronger competitive strength than its rivals. However, in the face of a wide range of commodity categories and various operations of replenishment-delivery processes, B2C e-commerce logistics operations are under tremendous pressure to solve the problem of how to reasonably characterize the needs of customers in small quantities and uncertain demands to achieve stable and efficient operation of replenishment-delivery processes.

By assuming the fuzzy demands of customers, this paper studies the multi-product joint replenishment and delivery (JRD) coordination problem of B2C e-commerce enterprises.

First of all, in order to better assess and predict customer demand for uncertainty, we define commodity demand as a triangular fuzzy variable based on subjective judgments of different experts.

Secondly, considering that the fuzzy interval is obtained based on empirical knowledge data and the fuzzy variables may be judged by different experts when using fuzzy variables, this paper uses fuzzy expected value theory to construct a fuzzy random JRD model to minimize the total cost of the system change.

Thirdly, considering that the JRD model is essentially an NP-hard problem, this paper designs a particle swarm optimization (PSO) algorithm to solve the model. For the PSO algorithm, this paper designs a real and integer mixed encoding scheme to represent the basic processing cycle, the replenishment-delivery frequencies of multi-items.

Fourthly, through the numerical experiment for the parameter sensitivity analysis, the optimal parameter combination for the PSO algorithm for subsequent experiments is found.

Finally, PSO and genetic algorithm (GA) based on the optimal parameter combination were compared and solved. The numerical calculation results show that PSO gives better performance in searching efficiency and effectiveness than GA, but the searching stability is slightly weaker.

Based on the above analysis, our research found that:

(1) Fuzzy random expectation value theory is a suitable and reasonable method to deal with the uncertainty demand and coordinate the cognitive disparities of different experts’ knowledge in judging customer demands;

(2) Compared with GA, PSO algorithm has certain advantages in solving JRD problems, but there is still room for improvement, especially in solving stability.

In future research, we will focus on solving two types of the model under this theme. One is to continue to expand the existing JRD model by considering the waiting costs of customers’ fuzzy random. The other one is to continue to improve the performance of PSO to solve different JRDs.

B2C; Joint replenishment and delivery; Fuzzy demands; Particle swarm optimization

F252.3；F272.3

A

1004-6062(2020)06-0183-008

10.13587/j.cnki.jieem.2020.06.019

2018-06-30

2019-01-01

Supported by the National Social Science Foundation of China (71602015), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (16YJC630014), the Fundamental and Frontier Research Project of Chongqing ( cstc2016jcyjA0530 ), the Project of Guizhou Provincial Education Department (Qian-Jiao-He KY Code [2018]159) and the Innovative scientific research program for postgraduates of Chongqing (CYS17216)

2018-06-30

2019-01-01

國(guó)家自然科學(xué)基金資助項(xiàng)目（71602015）；教育部人文社科青年基金資助項(xiàng)目（16YJC630014）；重慶市基礎(chǔ)與前沿研究計(jì)劃項(xiàng)目（cstc2016jcyjA0530）；貴州省教育廳課題（黔教合KY字[2018]159）；重慶市研究生科研創(chuàng)新項(xiàng)目（CYS17216）

崔利剛（1983—），男，河北唐山人；博士，副教授，碩士生導(dǎo)師；研究方向：物流系統(tǒng)工程。

中文編輯：杜 ?。挥⑽木庉嫞築oping Yan