整車和零擔混合物流配載問題的建模與求解

邢航　張新邦　李貴棟　汪恭書

摘 要：研究了物流作業中同時考慮整車和零擔混合運輸模式的配載問題，決策每個托運物品由哪種運輸模式服務以及物品在整車運輸模式下如何配載，目標為最小化兩種運輸模式下的總配載費用。為該問題建立了新型整數規劃模型，并提出了強化模型的有效不等式，使用商業優化軟件iLog-CPLEX求得了小規模算例的最優解。由于iLog-CPLEX優化軟件不能在有限時間內求得大規模問題的最優解甚至可行解，針對大規模問題提出一種基于分組編碼方式的離散差分進化算法。實驗結果顯示所提出的算法明顯優于傳統啟發式算法，驗證了離散差分進化算法在求解整車和零擔混合物流配載問題的有效性。

關鍵詞：整車運輸；零擔運輸；配載問題；混合整數規劃；差分進化

中圖分類號：U294 文獻標識碼：A

Abstract： This paper studies the logistics loading problem with hybrid of full and less-than truck load modes， which is to decide that each consignment is serviced by which transportation model and how to load consignments under full truck load model such that total loading cost under two transportation models is minimized. A novel integer programming model formulated， and valid inequalities are proposed to strengthen the model. Commercial optimization software iLog-CPLEX is used to solve the model to optimization for small-scale instances. Because no optimal or even feasible solution of the large-scale problem can be obtained by iLog-CPLEX optimization software within limited computational time， a discrete differential evolution algorithm based on group coding method is proposed for the large-scale problems. Experimental results show that the proposed algorithm is obviously superior to the traditional heuristic algorithm， which verifies that the discrete differential evolution algorithm is efficient to solve the logistics loading problem with hybrid of full truck load and less-than truck load.

Key words： full truck load； less-than truck load； loading problem； mixed integer programming； differential evaluation

0 引 言

運輸按照車輛裝載的貨物形態分為整車運輸與零擔運輸兩種模式[1-2]。零擔運輸一般指當一批貨物的重量或容積不滿一輛貨車時，可與其他幾批甚至上百批貨物共用一輛貨車裝運的運輸方式；而整車運輸通常是指因一批貨物的重量、性質、體積或形狀需要以一輛或一輛以上貨車裝運而按整車條件來運輸的運輸方式。對比兩種運輸方式，整車運輸具有一次運載量大、運輸組織相對簡單、單位配載費用較低等特點，而零擔物流則具有一次運載量較小、運輸組織相對復雜、單位配載費用一般較高的特點。對物流公司來說，當貨物數量較多時，其自有車的運輸能力有限不能滿足用戶需求，往往需要外雇其他貨運公司的運輸車輛。……